Paper Title: Early Planet Formation in Embedded Disks (eDisk) XVI: An asymmetric dust disk driving a multi-component molecular outflow in the young Class 0 protostar GSS30 IRS3.



   
   

   European Southern Observatory, 3107, Alonso de Córdova, Santiago de Chile

              alejandrosantamariamiranda@gmail.com
         Academia Sinica Institute of Astronomy & Astrophysics, 11F of Astronomy-Mathematics Building, AS/NTU, No.1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.
        National Radio Astronomy Observatory, 520 Edgemont Rd, Charlottesville, VA, 22903, USA
        Niels Bohr Institute, University of Copenhagen, Øster Voldgade 5-7, 1350 Copenhagen K., Denmark
        Korea Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Republic of Korea
        University of Virginia, 530 McCormick Rd., Charlottesville, Virginia 22904, USA
        Department of Physics and Astronomy, Graduate School of Science and Engineering, Kagoshima University, 1-21-35 Korimoto, Kagoshima,Kagoshima 890-0065, Japan
        Department of Earth Science Education, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea
        SNU Astronomy Research Center, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea
        Division of Astronomy and Space Science, University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea
        Department of Astronomy, University of Illinois, 1002 West Green St, Urbana, IL 61801, USA
        Department of Astronomy, University of Michigan, 1085 S. University Ave., Ann Arbor, MI 48109-1107, USA
        Institute for Astronomy, University of Hawai‘i at Mānoa, 2680 Woodlawn Dr., Honolulu, HI 96822, USA
        



   

 
We present the results of the ALMA Large Program Early Planet Formation in Embedded disks observations of the Class 0 protostar GSS30 IRS3. Our observations included 1.3 mm continuum with a resolution of 005 (7.8 au) and several molecular species including  ^12CO, ^13CO, C^18O, H_2CO and c-C_3H_2. The dust continuum analysis unveiled a disk-shaped structure with a major axis size of ∼200 au. We observed an asymmetry in the minor axis of the continuum emission suggesting that the emission is optically thick and the disk is flared. On the other hand, we identified two prominent bumps along the major axis located at distances of 26 and 50 au from the central protostar. The origin of the bumps remains uncertain and might be due to an embedded substructure within the disk or the result of the temperature distribution instead of surface density due to optically thick continuum emission. The ^12CO emission reveals a molecular outflow consisting of three distinct components: a collimated one, an intermediate velocity component exhibiting an hourglass shape, and a wider angle low-velocity component. We associate these components with the coexistence of a jet and a disk-wind. The C^18O emission traces both a Keplerian rotating circumstellar disk and the infall of the rotating envelope. We measured a stellar dynamical mass of 0.35±0.09 M_⊙. 

 
Early Planet Formation in Embedded Disks (eDisk) XVI: An asymmetric dust disk driving a multi-component molecular outflow in the young Class 0 protostar GSS30 IRS3
    Alejandro Santamaría-Miranda1
          Itziar de Gregorio-Monsalvo1
          Nagayoshi Ohashi2  
          John J. Tobin3
          Jinshi Sai 2
          Jes K. Jørgensen4
          Yusuke Aso5
          Zhe-Yu Daniel Lin6
          Christian Flores2
          Miyu Kido7
          Patrick M. Koch2
          Woojin Kwon8,9
          Chang Won Lee5,10
          Zhi-Yun Li6
          Leslie W. Looney3,11
          Adele L. Plunkett3
          Shigehisa Takakuwa2,7
          Merel L.R  van 't Hoff12
          Jonathan P. Williams13
          Hsi-Wei Yen2
        
    Received 14 March 2024; accepted 29 July 2024
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§ INTRODUCTION


Circumstellar disks arise as a direct consequence of the angular momentum conservation of rotating material from an infalling envelope  <cit.>. In these disks, planets are expected to form at some point during the star formation process. In the last decade, the efforts to understand planet formation have been focused mainly on Class II disks which have dispersed their envelopes. The advent of the Atacama Large Millimeter/submifllimeter Array (ALMA) provided the needed sensitivity and spatial resolution to resolve structures inside disks such as rings, gaps, and dust traps <cit.>. These structures are ubiquitous in the star-forming regions studied in different ALMA programs (e.g., ) and may reflect the presence of planets <cit.>.

If those substructures are the consequence of the presence of planets, we should investigate the origin of planets in earlier evolutionary stages. The lack of sufficient mass to form the observed population of exoplanets in Class II disks <cit.> and the fact that Class 0/I disks are likely more massive and solid-abundant <cit.> support the scenario where planets are formed at earlier stages. 


Dedicated high angular resolution observations millimeter/sub-millimeter wavelengths have revealed the presence of substructures in the dust disks surrounding some young Class 0/I sources <cit.> but it remains a question whether these are ubiquitous and when they arise. To address this question, the ALMA Large Program 'Early Planet Formation in Embedded disks' <cit.> aims to study the origin of substructures systematically in Class 0/I disks with ALMA at 1.3 mm (Band 6) and a spatial resolution of 004. The sample comprises twelve Class 0 and seven Class I protostars in nearby (d < 200 pc) star-forming regions. The program aimed at detecting hints of disk substructures that may indicate the presence of planets or the presence of giant spirals as a byproduct of gravitational instabilities. 

The source GSS30 IRS3 was observed as part of the eDisk Large Program. It is part of the  L1688 molecular cloud, located at a distance of ∼138.4 ± 2.6 pc <cit.> based on the recent Gaia measurements. GSS30 IRS3 is a deeply embedded protostar <cit.>, not detected at optical wavelengths, preventing a direct measurement of its distance from Gaia. Therefore, we assume that the distance to the source is similar to its host cloud. GSS30 IRS3 is classified as a Class 0 protostar, with a bolometric luminosity (L_bol) of  1.7 L_⊙, and the bolometric temperature is 50 K <cit.>. GSS30 IRS 3 was first detected by <cit.>  and later observed at 2.7 mm at higher-angular resolution in a focused paper on the three sources at GSS30 <cit.>. The existence of a molecular outflow has been reported with single-dish observations taken at the James Clerk Maxwell Telescope <cit.> and later with ALMA <cit.> in CO (2-1) at a resolution of ∼15.

In this paper, we present observations of GSS30 IRS3 at a very high angular resolution (0056) in the continuum (at 1.3 mm) and (∼015) in line emission (CO isotopologues, H_2CO and c-C_3H_2) as part of the eDisk ALMA Large Program. The paper is structured as follows: we describe the observations in Section <ref>. Then, we present the continuum, spectral line maps, and dust mass estimation in Section <ref>. Section <ref> presents the molecular outflow analysis and the estimation of the protostar's dynamical mass. We discuss the origin of the continuum asymmetries, twisted feature observed in the C^18O velocity map and the coexistence of a jet and a wide-angle outflow in Section <ref>. Finally, we summarize the main results in Section <ref>. 


 








§ OBSERVATION AND DATA REDUCTION


GSS30 IRS3 was observed with the ALMA 12-m array in Band 6 as part of the eDisk ALMA Large Programme (project code: 2019.1.00261.L: PI N. Ohashi). A separate DDT program (2019.A.00034.S: PI J. Tobin) complements the eDisk data with shorter baselines for the same molecular lines for some sources. Observations toward GSS30 IRS3 from the Large Program were executed four times in October 2021 in configuration C43-8, while two executions were completed for the DDT program in June 2022 with configuration C43-5. Detailed information about the baseline length, number of antennas, precipitable water vapor, and calibrators are provided in <cit.>. 

The correlator was set up in dual-polarization mode using four basebands. The first baseband was divided into four spectral windows to detect C^18O (2-1), ^13CO (2-1), H_2CO (3_2,1-2_2,0), and SO (6_5-5_4) with a spectral resolution of ∼0.17 km s^-1 and a bandwidth of 58.59 MHz. Basebands two and three were set up with a bandwidth of 1875 MHz to detect continuum. A spectral resolution of ∼1.3 km s^-1 was selected for the detection of several molecular lines (CH_3OH, SiO, DCN, H_2CO, and c-C_3H_2) and those lines were identified and masked when measuring the continuum. The fourth baseband has a bandwidth of 937.5 MHz (0.64 km s^-1 spectral resolution) to detect the continuum and the ^12CO (2-1) line. The time on source for data from the Large Program was 2.75 h, and for the DDT program the time on source was 0.5 h. 

Calibration of the ALMA data was performed using the standard ALMA calibration pipeline. Then, we self-calibrated the data using the Common Astronomy Software Applications package <cit.> version 6.2.1 and 6.4.1 for 2019.1.00261.L and 2019.A.00034.S programs, respectively. The pipeline version numbers should be supplied in addition to just the CASA number. Before performing the self-calibration, we first imaged the six executions and aligned the emission peaks using fixvis and fixplanets. After the alignment, we rescaled the flux in the UV plane to the execution on the 27 October. Then we proceeded with the self-calibration but using the rescaled non-aligned data, first with four phase-only cycles and two phase and amplitude cycles of the short-baseline data. Next, we performed joint self-calibration of the long and short baseline data and proceeded with four iterations of self-calibration in phase-only mode. Finally, the self-calibration solutions were applied to both the continuum and the spectral line data, and the task TCLEAN was used to produce continuum and spectral line images after continuum subtraction. The final image is a combination of the short and long configurations. We adopted a Briggs robust parameter equal to 0 for the continuum image and 0.5 for the spectral line data as a compromise between sensitivity and resolution. We also adopted a Briggs robust parameter equal to 2 for the H_2CO and c-C_3H_2 spectral to enhance the sensitivity. The spectral line data were tapered at 2000 kλ to bring out larger-scale structures. Primary beam correction was applied before inferring physical parameters from the images. The angular resolution of the continuum maps is 0056 (7.8 au at a distance of 138 PC), with a maximum recoverable angular scale of 29, which is also the nominal value for Configuration 5 and a field of view of ∼22”. The absolute flux calibration uncertainty in Band 6 is estimated to be 10%. A more detailed explanation of the reduction procedure can be found in <cit.>. 



§ RESULTS













 §.§ Dust emission
 
Figure <ref> shows the dust emission at 1.3 mm of GSS30 IRS3, at an angular resolution of 0068×0045 (Position angle of 76.61^o), obtained using a robust parameter equal to 0. The continuum emission traces a disk-like structure around the central protostar with a high inclination angle. The deconvolved disk size is  055×017 (76×23 au) estimated from a two-dimensional Gaussian fitting (see Table <ref>). The best fit peak intensity is 3.87 ± 0.04 mJy beam^-1 at the Gaussian central position R.A.=16h26m21.715s, Dec= -24^o 22'5109. The flux density obtained from the Gaussian fitting is 123.6 ± 1.2 mJy. The continuum emission measured above a 5σ contour has major and minor axes of 143×062 (∼198 ×∼86 au), while the peak intensity and the flux density obtained by this method are 6.38 mJy beam^-1 and 133.7 mJy, respectively. Since the residuals from the Gaussian fitting show that the fit is far from perfect (see model and residual in Figure <ref>), and also a fitting attempt using two (2-D) Gaussian components did not converge, we will adopt the values of the flux density and size inferred above the 5σ contour in the analysis section. 
Assuming a geometrically flat and axisymmetric disk, we can estimate the disk inclination as cos i = b / a, where a and b  are the major and minor axes. The inclination derived using the deconvolved Gaussian fitting is 71.7 ± 0.3^o while using the 5σ contour, we obtained 64.3 ± 1.5^o, with the same position angle in both cases (109^o). Given the poor quality of the Gaussian fitting, we will adopt a value of 64.3^o as the most reliable inclination estimation. We note that if the disk is geometrically thick this value should be treated as a lower limit.  Additionally, the dust disk exhibits a 'boxy' shape (see Section <ref> for further discussions). 

Moreover, we also detected the dust emission of another source (GSS30 IRS1) in the field of view. See Section <ref> for further information.

  




 §.§ Brightness asymmetries

There are no apparent substructures in the disk surrounding GSS30 IRS3 (Figure <ref>), such as clear spirals, gaps, or sharp rings, similar to those found in many more evolved Class II sources <cit.>. Instead, the image shows a striking asymmetry along the minor axis. To show that asymmetry more clearly, we performed a one-dimensional cut along the minor axis centered on the peak derived from the Gaussian fitting (Figure <ref>). 
Additionally, along the major axis, there are two bumps on both sides of the disk, located at 018  (∼25 au) and 036 (∼50 au) East and West from the disk center, respectively. There is only one bump along the minor axis, which could be due to a flared structure of the disk.  The center of the bump is located at a deprojected distance of ∼20 au from the center of the disk. The radial brightness profile of the continuum emission is discussed in Sections <ref> and <ref>. 





 §.§ Dust disk mass

The dust disk mass surrounding GSS30 IRS3 is estimated under the assumption that the emission at 1.3 mm is optically thin and comes entirely from isothermal dust. We estimated the dust mass using the relationship from <cit.>:


    M =  S_ν D^2/κ_νB_ν(T_d),

where D is the distance to the source (138 pc),  B_ν(T_d) is the Planck function at the observed frequency (225 GHz) at a dust temperature T_d, and κ_ν(2.3 cm^2 g^-1) is the absorption coefficient adopted from <cit.>. S_ν is the flux density. We assumed  two different values of the dust temperature to estimate the dust disk mass. The first temperature value we used was a fixed value of 20 K, commonly assumed for Class II sources <cit.>. For the second temperature, we took into account the typical temperature of the disk based on the source's luminosity. We derived this temperature using the formula T= 43(L_bol/L_sun)^0.25 from <cit.>, which was obtained from a grid of radiative transfer models. For our specific case of GSS30 IRS3, this formula provides a temperature of 49 K.
Using these two temperature values, we calculated the dust disk mass using the flux density derived from the Gaussian fitting and the one calculated above the 5σ contour level. For the Gaussian fitting, we obtained a dust disk mass of 69.5 ± 2.6 M_ and 23.87 ± 0.90 M_, respectively, for a temperature of 20 K and 49 K. The dust mass estimation when using the flux density above the 5σ contour level provides values of  75.1 ± 2.9 M_ and 25.80 ± 0.99 M_ considering a temperature of 20 K and 49 K, respectively. The values that we derived are between 4.9 and 1.5 times more massive than the ones that were derived by <cit.>, however, their κ_ν value is much larger (7.4 cm^2 g^-1)  than the value used in this paper, so we associate the differences to the adopted absorption coefficient. Comparing to other Class 0 sources in the eDISK sample we find relatively similar values to R CrA IRS 5N (protostellar mass of 0.3 M_⊙) with a mass dust disk between 23.3 and 66.6 M_ <cit.> or L1527 (protostellar mass of 0.5 M_⊙) with a mass dust disk between 38.9 and 97.4 M_ <cit.>. Finally, we note that the derived dust mass might be a lower limit than the actual mass because the inclined disk could be optically thick.



 §.§ Gas emission

We report the detection of several molecular species and transitions: ^12CO (2-1), ^13 CO (2-1), C^18O (2-1), c-C_3H_2 (blended lines 6_0,6-5_1,5 and 6_1,6-5_0,5), c-C_3H_2 (5_1,4-4_2,3),   c-C_3H_2 (5_2,4-4_1,3),  H_2CO (3_0,3-2_0,2) and H_2CO (3_2,2-2_2,1). The DCN (3-2), H_2CO  3_2,1-2_2,0, SO (6_5-5_4) and SiO (5-4), lines are not detected. The systemic velocity is 2.84 km s^-1 (which is derived from the C^18O (2-1) diagram fitting discussed in Section <ref>). Moment maps of the detected molecular transitions are presented in Figures <ref>, <ref> and <ref>, where we show integrated intensity (moment 0), mean velocity (moment 1), and peak intensity (moment 8) maps. A summary of the main properties of the detected lines including the angular resolution for each molecule is shown in Table <ref>, and an extensive description is provided in the following subsections.










  §.§.§ ^12CO
 
The ^12CO (2-1) emission line traces primarily a bipolar molecular outflow centered at the position of GSS30 IRS3 and perpendicular to the dust disk, as was also previously reported by <cit.> using lower angular resolution and less sensitive observations. Our ALMA data reveal three different outflow components in morphology and velocity:  a collimated inner high-velocity component,  an intermediate velocity component with an hourglass or conical shape,  and a wider angle lower velocity component that is more prominent in the northern lobe which has a parabolic shape (see Figure <ref>). The velocity channel maps of the  ^12CO (2-1) emission are presented in  Figure <ref> and the intensity-weighted velocity map in Figure <ref>.  In Figure <ref>, we plot the ^12CO contours overlaid on a recent JWST image of the ρ Ophiuchus region (P.I. Klaus Pontoppidan) where the H_2(0-0 S9) emission is tracing the outflow and delimiting very clearly the cavity wall beyond the molecular outflow. 

The collimated high-velocity component shows blueshifted emission to the northeast from the central source (spanning velocities between -19.9 and -18.7 km s^-1 in local standard rest velocity) and redshifted emission to the southwest (23.2 to 23.8 km s^-1; top left panel Figure <ref>). The JWST image reveals the presence of knots located at 49 and 67 from the center of the GSS30 IRS3 disk in the same direction of the blueshifted high-velocity component (right panel in Figure <ref>). Correcting the outflow velocities from the inclination of the system, and considering that the inclination angle is a lower limit of the actual angle, the maximum deprojected velocity in the inner collimated high-velocity component is 52 km s^-1. It is important to note that the deprojected velocity derived is also a lower limit because  the inclination angle is a lower limit of the actual angle. This deprojected velocity falls within the expected velocity range observed in jets associated with Class 0 sources (100 ± 50 km s^-1, ).

The intermediate velocity component of the outflow delineates an hourglass shape, and spanning velocities between  -18.0 and -2.2 km s^-1 for the blueshifted lobe and between 8.6 to 22.6 km s^-1 for the redshifted lobe. Both redshifted and blueshifted emission are present in both sides, as expected in outflows with a non-narrow opening angle and close to the plane of the sky  (see the top right panel in Figure <ref>). 
The wider angle low-velocity component of the molecular outflow shows blueshifted emission between -1.6 and 1.6 km s^-1m and redshifted emission between 5.4 and 7.9 km s^-1. It is formed by an extended but well-defined northeast arc mostly seen at blueshifted velocities and less extended southwestern lobe where both blueshifted and redshifted components overlay in the same area of the sky (see the bottom left panel in Figure <ref>). 


We also report the detection of ^12CO (2-1) in two other sources (GSS30 IRS1 and IRS2) that are in the ALMA field of view. GSS30 IRS1 observations will be presented in a future paper while the IRS2 detection is in Appendix <ref>.



  §.§.§ ^13CO
 
The ^13CO (2-1) emission line, an optically thinner line due to its lower abundance than the ^12CO (2-1) line, is detected at a peak S/N of 10. The velocity channel maps of the ^13CO (2-1) emission line are presented in Figure <ref>.
The blueshifted emission is found at velocities between -0.66 km s^-1 and  2.18 km s^-1, and it is stronger to the west of the central protostar. The redshifted emission is much fainter and found mainly to the east of the protostar. It spans velocities between 4.35  km s^-1 and 6.19  km s^-1. 

Two different faint structures are observed in the channel maps, tracing both the base of the northeast and southwest components of the molecular outflow and a gaseous disk-like structure surrounding the central protostar. The emission associated with the molecular outflow is only detectable between velocities of 0.35 km s^-1 and 2.35 km s^-1. The disk-like structure is detected between -0.66 and 2.18 km s^-1 (blueshifted component) and between 4.35 km s^-1 to 6.19 km s^-1 (redshifted component) velocities. The blueshifted component is more intense than the redshifted one. We plot the position-velocity diagram (PV) in Figure <ref> to discriminate between redshifted emission associated with cloud or disk. Although it is a very faint emission, it is compatible with a rotating disk, which will be further discussed in Section <ref>.




  §.§.§ C^18O
  
The C^18O (2-1) emission line is often considered optically thin and trace envelopes and disks, although it is only sometimes optically thick (e.g. ). Blueshifted emission is detected at velocities ranging from 0.01 km s^-1 to 2.68 km s^-1 (see Figure <ref>). Redshifted emission spans velocities between 3.02 km s^-1 and 5.18 km s^-1. The size of the emission traced by the C^18O (2-1) emission above the 5σ contour is 23×093, with a position angle similar to the 109^o of the dust disk.  

In GSS30 IRS3, C^18O (2-1) clearly traces a disk-like structure with an obvious redshifted and blueshifted pattern compatible with a Keplerian rotating disk (Figure <ref>). When studying the velocity map, we note a weak S-shape close to the systemic velocity (Figure <ref>). Its nature will be discussed in Section <ref>. 
The spectrum of C^18O (2-1) shows a double-peak profile typical of an inclined disk in Keplerian rotation.



  §.§.§ c-C_3H_2
 
 In Class 0 sources, c-C_3H_2 is usually located in the outflow cavity walls due to exposure to UV radiation from the central protostar <cit.>. On the other hand, in Class I sources, hydrocarbons such as c-C_3H_2 are located in the disk <cit.>. We detected the three targeted transitions of c-C_3H_2 at 217.822 GHz, 217.94 GHz, and 218.160 GHz. The first one has two lines blended (6_0,6-5_1,5 and  6_1,6-5_0,5) that are very close (<<m/s) for the kinematic analysis, and it is more intense than the other two detections (see Figure <ref>). c-C_3H_2 at 217.822 GHz and 217.94 GHz shows emission between V_lsr of 0.7 and 4.7 km s^-1 while the c-C_3H_2 at 218.16 GHz is only detected between 0.7 and 3.5 km s^-1. In GSS30 IRS3, the c-C_3H_2 emission is located in the same position as the dust disk Figure <ref>). The association of the c-C_3H_2 detection is consistent with both the disk and the disk wind based on its positional information. Regarding kinematics, its velocities align with a rotation pattern. Therefore we tentatively attribute the association of c-C_3H_2 with the disk-like structure.




  §.§.§ H_2CO
 
Two transitions, H_2CO (3_0,3-2_0,2) and H_2CO (3_2,2-2_2,1), out of three, are detected. The transition H_2CO (3_0,3-2_0,2) at 218.22 GHz seems to be located in the same position as the external part of the dust disk and also exhibits a rotation pattern (Figure <ref>). H_2CO (3_0,3-2_0,2) emission is detected at Vlsr values of 0.7 and 4.7 km s^-1. The transition H_2CO (3_2,2-2_2,1) is tentatively detected at the 3σ level in one channel at a V_lsr of 0.7 km s^-1.



§ ANALYSIS












 §.§ Disk rotation

The C^18O (2-1) emission line traces a disk-like structure exhibiting indications of rotation (Section <ref>). It is important to investigate the nature of the rotation, in particularly whether it is Keplerian. If it is Keplerian rotation, the dynamical mass of the central star can be derived. In order to investigate the rotation curve of the C^18O (2-1) emission, we will use a PV diagram. The C^18O (2-1) line is the most suitable tracer for this analysis because the disk-like structure is clearly detected with good S/N. This is consistent with being optically thinner than the ^13CO (2-1) line, which partially traces the gaseous disk in GSS30 IRS3. In any case, we analyze the rotation curve of both molecular transitions to compare the obtained results. For computing the position-velocity diagram, we use a PV diagram cut of 017 width, that corresponds to the size of the major axis of the synthesized beam, along the major axis of the C^18O (2-1) and  ^13CO (2-1) disk. We adopt a disk position angle value of 109^o estimated in Section <ref>. 

The SLAM code[<https://github.com/jinshisai/SLAM>] <cit.> is used to analyze the rotation curve of GSS30 IRS3. The process is based on two main steps; the first step is to obtain a 1-D intensity profile to derive the edge and ridge data points. Ridge points are defined as the intensity-weighted mean position or the center in the 1-D intensity profile from the Gaussian fitting. The edge points or radius is the outermost position at a certain S/N level. The second step is fitting a power-law (single or double) function, that is defined as a positive value, to the derived representative data as a function of velocity or radius using the Markov-Chain Monte Carlo method. Whether it is a function of radius or velocity depends on along which axis the 1D profile for ridge/edge calculations is obtained see <cit.> criteria to use the v_i-r_i data points as a function of radius or velocity. Note that the edge and ridge data points are independently fitted. Thus, the double power law implies two components having different rotation laws, such as a Keplerian disk and an infalling envelope conserving its specific angular momentum, where the break radius (r_b) is the boundary radius between a Keplerian disk and a rotation/infalling envelope, and where the break velocity (v_b) is the velocity at (r_b). We also derived the reduced chi-squared (χ^2) for each fit in order to compare all the results. A more detailed explanation of the SLAM methodology for the eDisk papers can be found in <cit.>.

The SLAM code can fit the systemic velocity as a free parameter. We ran a first test to derive the systemic velocity as 2.84 km s^-1 for the C^18O (2-1) emission, then we checked this value with the C^18O (2-1) spectra and fixed this value for the following test until we derived the final dynamical mass. 

We tested a single-power law (bottom-left panel in Figure <ref>) and double-power law fit (bottom-right panel in Figure <ref>) to the C^18O (2-1) PV diagram. The single power-law fittings give power-law indices (p_in) of ∼0.71 ± 0.03 for the edge method and ∼0.65±0.02 for the ridge method as shown in Table <ref>. These values are between 0.5 (Keplerian rotation) and 1 (constant specific angular momentum), suggesting that the observed rotation may not be explained by only Keplerian rotation and may also include rotation in an infalling envelope. To investigate such possibility, double power-law fittings were also performed; the fitting results with the edge method give a power-law index (p_in) of ∼0.45±0.08 and dp is the difference of the index between the inner and outer parts that is ∼0.65±0.15 with r_b of 107^+26_-19 au as shown in Table <ref>, meaning that the power-law index for the outside of r_b is ∼1.1. These results suggest that the observed rotation may be explained as a combination of Keplerian rotation and rotation conserving its specific angular momentum. This kind of transition of the rotation between a Keplerian disk and an infalling envelope was observed before in some other protostars as well <cit.>. The ridge method was not converging using p_in as a free parameter, so we fixed it at 0.5 under the assumption that there is a Keplerian disk and we derived a mass of  0.26  ± 0.07 M_⊙. Then, the mass derived from the single power-law fit is 0.27 ± 0.07 M_⊙ and  0.35 ± 0.09 M_⊙ for the double power law fit as the average of the ridge and edge methods because the edge and the ridge methods over- and under-estimate the stellar mass by a factor that depends on the resolution <cit.>.

For the ^13CO (2-1) line, we only considered the blueshifted component of the emission for the fit, since the redshifted component is very faint. The single-power law fit (top-left panel in Figure <ref>) shows a lower value of p_in than the C^18O (2-1) single-power fit. The double-power law fitting is not converging. The single-power fit is returning a mass at the break radius (M_b) of 0.24 ± 0.01 M_⊙. The edge method results were discarded because we are not obtaining stable solutions after several iterations. Additional details about the fitting are described in Appendix <ref>.

The best χ^2, ignoring the value of ridge double-power law because p_in is fixed, is the one obtained from  C^18O (2-1) single power fit ridge method, however the p_in is not close to the expected value of a Keplerian disk, so we should discard this value. Then, the second best  χ^2 value is the one obtained from C^18O (2-1) edge double-power law fit. Therefore, we adopt a mass of GSS30 IRS3 is 0.35±0.09 M_⊙.  




 §.§ Characterization of the molecular outflow

In this subsection, we analyze deeper the three different components of the molecular outflow described in Section <ref>. 

The most collimated inner high-velocity outflow component is extended to a maximum deprojected length of 23 (1.5×10^-3pc). The maximum deprojected extension of the intermediate velocity component with an hourglass shape is 33, while the maximum deprojected length of the wider angle lower velocity component is 83 and 27  for the northeast and southwest arc-like structures, respectively. The size of the different components was measured using a bisecting line from the center of the disk continuum emission to the maximum extension of each component, considering the 5σ contour. 
 

The most collimated inner high-velocity outflow component exhibits an opening angle of ∼34 degrees. On the other hand, the intermediate velocity component with an hourglass shape shows an opening angle of ∼70 degrees. For the wider angle low-velocity outflow component, we estimate values of ∼120 degrees and ∼100 degrees for the northeastern and southwestern lobes, respectively. These values were measured by hand using a protractor over the flux-integrated map (Figure <ref>). Table <ref> summarizes all these values.  

Given that our observations were not designed nor optimized for studying extended molecular outflows and that we are likely filtering structures larger than ∼20, we derived the dynamical parameters of the outflow as a first characterization in Appendix <ref>, however, the results in Table <ref> must be considered cautiously and valid only for the most compact emission of the outflow. 


















§ DISCUSSION
 


 §.§ Asymmetric Intensity Distribution along the minor axis of the Dust Disk


The eDisk results has shown the presence of asymmetric intensity distribution along the disk minor axis in several sources <cit.>. The asymmetries found in the minor axis in these eDisk subsample are generally explained due to a combination of optically-thick emission and disk flaring, as proved in the radiative transfer studies of <cit.> and <cit.>. As a result, dust is not settled onto the midplane but is distributed vertically, which, in some cases, can create a dark lane. This dark lane observed in edge-on disks has been described as a “hamburger" shape <cit.> .

In the case of the orientation of the GSS30 IRS3 disk, the northeastern region corresponds to the far side of the disk. This conclusion is based on the peak intensity position, which exhibits a slight skew from the geometric center and towards the northeast, as determined by fitting an ellipse to a 5σ contour level. Moreover, this is supported by the orientation of the collimated high-velocity molecular outflow, where the blueshifted emission points towards the northeast. This alignment provides a rationale for the observed brightness asymmetry in the minor axis between the two sides of the disk. Additionally,  the dust disk 'boxy' shape (Figure <ref>) can be potentially explained by the truncated edge of a flared disk. 

Consequently, the asymmetry in the minor axis can be attributed to a combination of disk flaring and optically thick emission.




 §.§ The origin of the bumps along the major axis

A subset of eDisk sources reported the presence of brightness asymmetry or bumps along the major axis of the protostellar disks <cit.>. In the case of GSS30 IRS3, two bumps are detected along the disk major axis. 
To confirm the authenticity of the bumps and eliminate the possibility of them being spurious artifacts from the cleaning process, we fit the radial intensity profile in the uv plane using Frank (see Appendix <ref>). Frank <cit.> first deproject the visibilities to correct the disk inclination and uses the Fourier-Bessel series to reconstruct the radial brightness profile. The bumps are located at a radius of ∼019 (∼26 au) and the other located at ∼036 (∼50 au) from the center of the disk. The positions of the identified bumps, closely coincide with those obtained from the radial intensity profile in the image plane. This alignment strongly rules out the possibility of being artifacts. However, we emphasize that our interpretation is only limited to discarding spurious signals in the cleaning process given the Frank limitations when dealing with a flared disk. 

We discuss two main possible explanations for the origin of the bumps. First, there could be a real substructure within the dusty disk that will likely evolve into a more well-defined structure over time. Alternatively, the bumps might be the result of the temperature distribution due to optically thick continuum emission. To test the second possibility, we compare the dust brightness temperatures at the bumps' locations with the expected midplane temperature at the same location in a passively heated and flared disk.

To obtain the midplane temperature, we employ the equation T_mid(r) = (ϕ L_*/8πr^2σ_SB)^0.25  <cit.>, where r is the radius (019 and 036), σ_SB denotes the Stefan-Boltzmann constant, L_* is the bolometric luminosity of the central protostar (1.7 L_⊙) and ϕ corresponds to the assumed flaring angle of 0.02 radian <cit.>. The predicted midplane temperature is 27.8 K at a radius of 019 and 20.2 K at a radius of 036. However, the observed brightness temperature at  019  and 036 are 18.9 K and 9.6 K, respectively. The observed brightness distribution along the major axis of the disk is compared with the estimated midplane temperature distribution in Figure <ref>, which shows that the observed brightness temperature is lower than the estimated midplane temperature. This suggests that the 1.3 mm continuum emission is not completely optically thick, as we would expect the observed brightness temperature to be similar to the actual physical temperature. It is, however, advisable to exercise caution in interpreting the observed brightness temperature distribution as an accurate representation of the actual radial brightness temperature distribution of the disk. This is due to the fact that the disk is inclined at a significant angle, which introduces a number of complications. In an edge-on disk, the brightness temperature is measured at a point where the optical depth along the line of sight becomes unity. Consequently, the distance of the measurement point from the center is not necessarily equivalent to the corresponding project distance from the center.



Future continuum observations at lower frequencies with ALMA that trace optically thinner dust emission could help to validate our findings. Also, a more detailed radiative transfer modeling, which is beyond the scope of this paper, might further elucidate the true nature of these bumps and their relationship with the substructures observed in more evolved sources.











 §.§ Kinematics and the origin of the S-shape in the C^18O line emission


In this subsection, we discuss the origin of the twisted feature observed in the C^18O (2-1) velocity map (Section <ref>). Similar S-shape or twisted velocity map close to the systemic velocity are usually associated with warped disks in young stellar objects <cit.>. There are several possible explanations for the origin of these features: the existence of a misaligned binary <cit.>, a fast radial infall attributed to the presence of a giant planet, brown dwarf, or low-mass companion <cit.>, the effect of a stellar fly-by <cit.>, or the transition from a Keplerian disk to an infalling envelope <cit.>. The first two theories are usually applied to more evolved young stellar objects. 

In the eDisk sample there is another source with a twisted kinematic map<cit.>. The C^18O (2-1) and SO (6-5) moment 1 maps showed an S-shaped feature which is explained by infalling motion. In the case of GSS30 IRS3 observations we are also detecting an infalling envelope according to the double-power law fit from SLAM (see Section <ref>)
Although the most likely explanation is an infalling envelope onto the disk, the twisted kinematic feature alone does not provide sufficient evidence for further analysis. On the other hand,  we are unable to confirm that the origin of the S-shape is due to the presence of an undetected close binary (within ∼8 au) or an embedded companion. Also, we do not observe indications of a recent star flyby. Future modeling, incorporating hydrodynamic simulations may be able to explain the origin of the S-shape; however, such modeling is beyond the scope of this initial analysis.





 §.§ Coexistence of a jet and a wide-angle outflow

Accretion and ejection are fundamental processes in star formation, shaping the evolution of young stars and their environment. The relation between ejection and accretion processes is not completely understood, but the accretion of gas and dust that fall from the protoplanetary disk´s inner edge onto the young stellar object drives the ejection of material. Ejection of material removes the excess of angular momentum through two different types of structures: a collimated component at high velocity and a wider-angle component at lower velocities.  The collimated component or jet propagates into the surrounding molecular cloud, forming bow shocks that push the gas and produce outflow shells in the jet´s vicinity <cit.>. Different knots are usually detected along the jet direction as a signal of episodic material ejection. On the other side, the wide-angle component is a radial disk wind that blows the ambient cloud, forming expanding shells <cit.>. Therefore, the jet and wind angle disk-driven structures are able to explain the mass loss process in star formation with different theories. Interestingly, <cit.> presented simulations demonstrating that jet and wide-angle disk-wind driven ejections could coexist, expecting the simultaneous detection of collimated and wide-angle outflow components during the early stages of star formation

The ^12CO observations of GSS30 IRS3 reveal three distinct components: a collimated outflow which axis is aligned with several knots seen in molecular hydrogen  (Figure <ref>), a conical hourglass shape and a wide-angle, low-velocity component with a parabolic morphology (Figure <ref>). The analysis of the conical outflow, described in Section <ref>, suggests that it is produced by a jet. While the blueshifted lobe of the wider angle outflow clearly exhibits emission shifting away from the central object as velocity increases, this is consistent with the predictions of the wind-driven shell model <cit.>. 

The coexistence of collimated jets/outflows and slow wider-angle molecular outflows has been previously detected in young protostars at early stages, specifically in two Class I sources in HH 46/47 <cit.> and DG Tauri B <cit.> or more recently in several sources <cit.>. Compared with those sources, GSS30 IRS3 exhibits very distinguishable components, even with observations that were not initially designed to study molecular outflows. Moreover, this is one of the few sources that the coexistence of a jet and a wide-angle outflow has been clearly detected in a young Class 0 protostar in the submm regime, making this source one of the best objects for future detailed studies of the accretion-ejection processes at the early stages of star formation.



§ CONCLUSIONS


We present high-resolution ALMA observations at 1.3 mm of the Class 0 protostar GSS30 IRS3, conducted as part of the eDisk ALMA program at a spatial resolution of ∼8 au. Our observations targeted the continuum emission as well as several molecular species, including ^12CO (2-1), ^13CO (2-1), C^18O (2-1), and c-C_3H_2 (blended lines 6_0,6-5_1,5 and 6_1,6-5_0,5 217.822 GHz), c-C_3H_2 (5_1,4-4_2,3 217.940 GHz), c-C_3H_2 (5_2,4-4_1,3 218.16 GHz), H_2CO (3_0,3-2_0,2 218.22 GHz), and H_2CO (3_2,2-2_2,1 218.47 GHz). We summarize our findings as follows: 


1. We detect dust continuum emission tracing a disk-like structure. The dust disk size is 143×062 (∼198 ×∼86 au) with an inclination of 64.3 ± 1.5^o and a  position angle of 109^o. The mass of the dust disk in GSS30 IRS3 is estimated to range between 23.87 ± 0.90 M_ and 75.1 ± 2.9 M_ depending on the adopted T_dust. 

 
2. The dust disk of GSS30 IRS3 does not exhibit clear substructures such as spirals. We report the presence of an asymmetry in the minor axis, which can be attributed to an optically thick emission and disk flaring. Additionally, we note the detection of two bumps located at 26 au and 50 au from the disk center along the major axis. The origin of these bumps remains unclear, and we propose two main hypotheses: they could indicate embedded real substructures within the disk, or that we are tracing the temperature distribution. 
 

3. The C^18O (2-1) emission traces a Keplerian disk and the infalling rotating envelope, allowing us to derive a dynamic mass of 0.35±0.09 M_⊙ of the central protostar with a disk gas size radius between 47 and 107 au. 

4. Our ^12CO (2-1) high-resolution and sensitive observations reveal the coexistence of a jet and a wide-angle outflow. 



    We thank the referee, Tien-Hao Hsieh, for the helpful comments and suggestions on this manuscript. We would like to thank all the ALMA staff supporting this work. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2019.1.00261.L, 2019.A.00034.S ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. J.J.T. acknowledges support from NASA XRP 80NSSC22K1159.  The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
    N.O. acknowledges support from National Science and Technology Council (NSTC) in Taiwan through the grants NSTC 109-2112-M-001-051, 110-2112-M-001-031, 110-2124-M-001-007, and 111-2124-M-001-005.
    J.K.J. acknowledges support from the Independent Research Fund Denmark (grant No. 0135-00123B). C.W.L. is supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2019R1A2C1010851), and by the Korea Astronomy and Space Science Institute grant funded by the Korea government (MSIT; Project No. 2022-1-840-05).
    Z.-Y.L. is supported in part by NASA NSSC20K0533 and NSF AST-2307199 and AST-1910106.
    L.W.L. acknowledges support from NSF AST-2108794.
    J.P.W. acknowledges support from NSF AST-2107841.
    W.K. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2021R1F1A1061794).
ZYDL acknowledges support from NASA 80NSSCK1095, the Jefferson Scholars Foundation, the NRAO ALMA Student Observing Support (SOS) SOSPA8-003, the Achievements Rewards for College Scientists (ARCS) Foundation Washington Chapter, the Virginia Space Grant Consortium (VSGC), and UVA research computing (RIVANNA). S.T.  is supported by JSPS KAKENHI grant Nos. 21H00048  and 21H04495, and by NAOJ ALMA Scientific Research grant No. 2022-20A.
    H.-W.Y. acknowledges support from the National Science and Technology Council (NSTC) in Taiwan through the grant NSTC 110-2628-M-001-003-MY3 and from the Academia Sinica Career Development Award (AS-CDA-111- M03).
    IdG acknowledges support from grant PID2020-114461GB-I00, funded by MCIN/AEI/10.13039/501100011033.
    ASM thanks Laura Pérez and Anibal Sierra for their valuable help and insights on using the Frank. 

aa.bst 






§ CHANNEL MAPS
 
This section shows the channel maps for ^12CO (Section <ref>), ^13CO (Section <ref>) and C^18O (Section <ref>)









§ JWST IMAGES

We compare the image of the ^12CO molecular outflow with recent JWST images obtained with NIRCAM (PI K. Pontoppidan) centered over GSS30 IRS3.




§ OTHER SOURCES DETECTED IN THE FIELD OF VIEW



 §.§ GSS30 IRS 1

We report the continuum detection of GSS30 IRS1, a Class I young stellar object <cit.>, located at a distance of approximately 14.7 arcseconds from GSS30 IRS3. Figure <ref> shows the 1.3 mm dust emission from GSS30 IRS1 with an angular resolution of 0052×0042 (position angle of 2.5^o), obtained using a robust parameter equal to 0.5. The continuum emission traces an inclined disk-like structure around the central protostar, with a small appendix similar to a spiral-like structure located at the west-south of the disk. The continuum emission measured above a 5σ contour for the disk-like structure (excluding the spiral-like structure) has major and minor axes of 034×022 (∼67 ×∼44 au), with a peak intensity and flux density of 2.72 mJy beam ^-1 and 3.92 mJy, respectively. Coordinate of the peak intensity is R.A.=16h26m21.354s, Dec= -24^o 23'0503. The rms is 17.1 µJy beam s^-1. The inclination derived from the disk-like structure is approximately 50^o.

Several emission lines, including ^12CO (2-1), ^13CO (2-1), C^18O (2-1), SO (6_5-5_4), and SiO (5-4), were detected surrounding GSS30 IRS1. A detailed analysis of the gas source and the spiral-like structure will be presented in a follow-up paper (Santamaría-Miranda et al. in prep).








 §.§ GSS30 IRS2

We report the detection of gas material surrounding the Weak-line T-Tauri star <cit.> GSS 30 IRS2 that is classified as M2 spectral type <cit.>. The ^12CO emission is detected between -2.2 km/s and 1.6 km/s with respect to the local standard of velocity rest, and it integrated map is shown in Figure <ref>. Redshifted emission is very contaminated by cloud emission, and it is impossible to distinguish between emission from the source and from the cloud. The emission size is 13×08 based on the 5σ contour. There is not also very clear molecular outflow emission. Furthermore, there is no clear rotation in the intensity-weighted velocity map (Right panel in Figure <ref>). There is no detection of the continuum at 3σ level (5.2 μJy/beam) or any other of the emission lines. A summary of the main properties is shown in Table <ref>.







§ SLAM FITTING
 
This section shows the result of corner plot (Figures <ref> and <ref>) of the SLAM fitting in Section <ref> for the C^18O and  ^13CO lines.










§ DYNAMICAL PARAMETERS OF THE MOLECULAR OUTFLOW COMPONENTS
 

In this subsection of the Appendix, we will analyze the dynamic properties of the three different components of the molecular outflow, separated in blueshited and redshifted emission with respect to the systemic velocity (2.84 km s^-1, as inferred in Section <ref>). We will consider the emission inside the 3σ contour level in Figure <ref> to perform the calculation in this subsection.  For inferring the dynamical properties of the molecular outflow, we will consider the ^12CO (2-1) molecular line  since this transition clearly traces the different components of the outflow with good S/N, and the ^13CO (2-1) line traces only the outflowing material closer to the central protostar together with a rotating disk.  
We calculate the dynamical time, the outflow mass, the mass-loss rate,  the outflow momentum, the kinetic energy, the mechanical luminosity,  and the outflow force.  

The dynamical time of the various outflow components was determined by considering the deprojected maximum velocity, the  deprojected length, and an outflow axis perpendicular to the dust disk, whose inclination is derived in Section <ref>.

The maximum inferred dynamical time is approximately 535 years for the wider angle lower velocity blueshifted component. When considering both the blueshifted and redshifted emission, the average dynamical time for this component is around 340 years. We used the maximum velocity to calculate the dynamical time of each of the components. Then we averaged the dynamical time between the blue and red component. The intermediate velocity hourglass shape component exhibits an average dynamical time of approximately 43 years when considering both blueshifted and redshifted emission. Similarly, the most collimated inner high-velocity component shows an average dynamical time of approximately 31 years. 

The ^12CO (2-1) emission line is optically thick at systemic velocities, since the brightness temperature of the line peak 57.9 K is similar to the kinetic temperature that we measured (58.7 K) from the linewidth. Therefore we determine the excitation temperature for the ^12CO (2-1) line using the peak intensity obtained close to the position of the star as 
    T_ex = hν_12/k/ln[1+ hν_12/k/T_o12+J_12(2.7 K)],
 where T_0 is the peak brightness temperature obtained close to the central continuum peak position. We derived a T_ex for the ^12CO (2-1) of 25.7 K, and we assumed this value for all the molecular outflow components. 
 
Then, we followed the prescription in <cit.> and <cit.> to calculate the column density and the mass of the outflow. We derived the mean optical depth in the wings of the ^12CO (2-1) emission line. We define the line wings as [-19.9 km/s, -18,7 km/s] and [23.2 km/s, 23.8 km/s] for the inner molecular outflow, [-18.0 km/s, -17.4 km/s] and [21.9 km/s, 22.6 km/s] for the intermediate hourglass shape and only two channels (-1.6 km/s and 7.9 km/s)  for the wider angle low velocity molecular outflow. The optical depth is obtained for each of the three molecular outflow components, obtaining  values between 0.04 and 0.51, in the optically thin regime. Then we assume that the emission is optically thin in the line wings. We infer a column density ∼2×10^16cm^2 for the wider angle and the inner molecular outflow components and a value one order of magnitude smaller for the highly collimated high-velocity molecular outflow component. Finally, we calculated the outflow mass using the inferred column density, the emission area, and a CO abundance of 10^-4. 


We derived the rest of the parameters following the formulas in <cit.> correcting for inclination. The total outflow mass of the molecular outflow is 6.1×10^-5 M_⊙, the momentum varies between 9.8×10^-6  M_⊙ km s^-1 and 4.5×10^-3 M_⊙ km s^-1, the kinetic energy varies between 4.7 ×10^39 erg and  4.7 ×10^41 erg, and the mechanical force varies between 4.8×10^-7 M_⊙ km s^-1 yr^-1 and 1.0×10^-5 M_⊙ km s^-1 yr^-1. All these parameters are summarized in Table  <ref>.


These results are affected by several assumptions that may affect the estimated mass. Previous studies point out that the optical depth of molecular outflows is underestimated, and masses should be at least a factor two higher <cit.> or five <cit.>. The first source of uncertainty is T_ex; our value is in the expected range for molecular outflows (T_ex = 10-50 K ); if we use a T_ex=50 K, the mass will increase by a factor of 1.4 with respect to that with T_ex=25.7 K. Another source of uncertainties is related to the parental cloud material that contaminates the emission of the molecular outflow close to the systemic velocity, needing the exclusion of those channels for the dynamical parameters calculations.  <cit.>, using synthetic observations, found that the missed outflow mass might increase by a factor 5 to 10 within 2 km s^-1 from the rest velocity. However, the most significant uncertainty factor in our calculations is the interferometric filtering. It is noticeable when comparing our dynamical properties with the ones obtained in low-mass Class 0 molecular outflows observed with single-dish telescopes. For example, the outflow mass in Class 0 and I sources is in the range between ×10^-3 M_⊙ and ×10^-1 M_⊙  <cit.>, and our total outflow mass is below these values. Another example is the mechanical force  expected to be between  1.0×10^-5 M_⊙ year^-1 km  s^-1 and ×10^-2 M_⊙ yr^-1 km s^-1 for Class 0 sources <cit.> and the mechanical force of GSS30 IRS3 outflow is in the lower limit.
Therefore, we conclude that all derived parameters may be treated as lower limits. 




§ RADIAL BRIGHTNESS PROFILE FITTING


To further investigate if the bumps detected in the major axis of the radial intensity profile of the dust disk surrounding GSS30 IRS3 are real features and not a byproduct of the cleaning process, we fit a 1D profile to the ALMA visibilities with a nonparametric model using the Frank library <cit.>, which provides a super-resolution brightness profile reconstruction. A major advantage of fitting visibilities is avoiding false structures created during the CLEAN process. Data were averaged in frequency to get spectral windows of 8 channels to reduce data volume and speed up calculations, excluding baseband 1 and 4, which are dedicated to detecting molecular emission lines or has a strong detected line where the contribution to the continuum was negligible. Frank can estimate the inclination and position angle of the protoplanetary disk; however, <cit.> noted that Frank does not fit these two parameters accurately, so we fixed them to an inclination of 64.30 deg and a position angle of 109 deg, as inferred in Section <ref> considering the emission above the 5σ contour.

Before fitting a Bessel functions to the brightness profile, Frank applies a power spectrum estimate as a prior. There are several hyperparameters that affect this power spectrum, but the two most relevant ones are α and w_smooth.  α  works as an S/N threshold for the maximum baseline where visibilities are fitted (a higher value implies a stricter S/N threshold), while w_smooth affects the smoothness of the power spectrum, where a higher value implies a smoother power spectrum. We explore the fitting quality using different hyperparameters values (α between 1.05 and 1.30 and w_smooth between 10^-4 and 10^-1), not finding any substantial difference between the different fittings. We fixed the hyperparameters to α= 1.30 and w_smooth=10^-4 because they present the least noisy results. The best-fit model (Figure <ref>) showed the presence of two bumps. 
To obtain the bumps size and location, we fit an exponential to the brightness profile obtained from Frank to isolate the bumps. Then, we fitted Gaussians around the areas where the bumps are located. Their positions are ∼019 (∼26 au) and  ∼036 (∼50 au) from the center of the disk, 009  (∼13.6 au) and 014 (∼19 au) wide, respectively.



  





 Paper Title: Quasilocal Newtonian limit of general relativity and galactic dynamics.


apsrev4-1



marco.galoppo@pg.canterbury.ac.nz
School of Physical & Chemical Sciences, University of Canterbury, 
 Private Bag 4800, Christchurch 8140, New Zealand


federico.re@unimib.it
Dipartimento di Fisica Giuseppe Occhialini, Università di Milano Bicocca,
 Piazza dell'Ateneo Nuovo 1, 20126, Milano, Italy
 &
INFN, sezione di Milano, Via Celoria 16, 20133, Milano, Italy


david.wiltshire@canterbury.ac.nz
School of Physical & Chemical Sciences, University of Canterbury, 
 Private Bag 4800, Christchurch 8140, New Zealand

§ ABSTRACT 
A new Newtonian limit of general relativity is established for stationary axisymmetric gravitationally bound differentially rotating matter distributions with internal pressure. The self-consistent coupling of quasilocal gravitational energy and angular momentum leads to a modified Poisson equation. The coupled equations of motion of the effective fluid elements are also modified, with quasilocal angular momentum and frame–dragging leading to novel dynamics. The solutions of the full system reproduce the phenonomenology of collisionless dark matter for disc galaxies, offering an explanation for their observed rotation curves. Halos of abundant cold dark matter particles are not required. 


Quasilocal Newtonian limit of general relativity and galactic dynamics
    David L. Wiltshire
    August 5, 2024
======================================================================



The Newtonian limit of general relativity is crucially important to both fundamental physics and astrophysical phenomenology. In cosmology two key features consistent with observation are: (i) far from any localised sources the Universe is not empty; (ii) the Universe is not globally rotating on the largest scales. 

Conventionally, one invokes an asymptotic Minkowski space, with respect to which additive Newtonian potentials are defined, despite observation (i). Moreover, even though known rotating asymptotically flat solutions of Einstein's equations—the Kerr and Kerr-Newman geometries—possess global non-zero angular momenta at spatial infinity, it is implicitly assumed that superposition of the effectively quasilocal angular momenta of such pointlike sources can be reconciled with observation (ii).

In this Letter we show that such implicit assumptions are misguided, even at nonrelativistic orbital speeds. The conventional limit neglects an important coupling of the quasilocal energy and angular momentum defined by the regional time–averaged motion of matter sources. We set out a new, self-consistent quasilocal Newtonian limit of general relativity, which does not assume a Minkwoskian spacetime background a priori. It introduces novel, first-order features that fundamentally modify the dynamics considered. A direct consequence is the elimination of the need for abundant cold dark matter particles in the modelling of galactic dynamics.

The prescription of a fixed, global spacetime background is not a requirement of general relativity. Indeed, the nonlinearity of Einstein's field equations (EFE), which arises from the self–interaction of matter and geometry, results in dynamical, regional backgrounds in which spacetime itself carries its own energy and angular momentum <cit.>. Moreover, the highly nonlinear nature of general relativity gives rise to a noncommutativity of averaging and limiting procedures in spacetime <cit.>. This has fundamental consequences for the dynamics of non-pointlike sources of large spatial extent, such as disc galaxies <cit.>.

The crucial ingredient of the differentially rotating models <cit.>, and in particular of the exact solutions of Ref. <cit.>, is that essential nonlinearity is retained before any low energy limit is considered. No global background is assumed. This contrasts with: (a) approaches that investigate frame–dragging on asymptotically flat <cit.> or asymptotically Friedmann <cit.> backgrounds, necessitating dark matter halos; (b) dark matter alternatives which modify the laws of gravitation, e.g., modified Newtonian dynamics (MOND) <cit.>.

In this Letter we demonstrate how insights from the conventional Newtonian framework may nonetheless be embedded in a quasilocal framework with an effective fluid. Furthermore, Einstein was never fully satisfied by the extent to which the EFE embody Mach's principle, viz., “Local inertial frames are determined through the distributions of energy and momentum in the universe by some weighted average of the apparent motions” <cit.>. The quasilocal Newtonian limit exhibits such a suitable weighted average, which we apply to disc galaxies showing that the EFE may actually contain an understanding of inertia consistent with MOND phenomenology.

The spacetime metrics can be written in the generalized Lewis–Papapetrou–Weyl form <cit.>,

    
    s^2     =-c^2 e^2Φ(r, z)/c^2( t+A(r, z)  ϕ)^2 +e^-2Φ(r, z)/c^2[W(r,z)^2 ϕ^2 +e^2k(r, z)/c^2( r^2+ z^2)]  ,



The energy-momentum tensor takes the form

    T^μν=((r, z)+p(r,z)/c^2)   U^μU^ν  + p(r,z) g^μν,

where (r,z) is the local matter density, p(r,z) is the effective pressure, and each element of the fluid possesses a 4–velocity U^μ, given by

    U^μ∂_μ=(-H(r,z))^-1/2(∂_t +Ω(r,z)  ∂_ϕ)  .

Here dϕ/dt=Ω(r, z) uniquely defines the angular speed of rotation at any point, and H(r, z) is a normalization factor. Since U^μU_μ=-c^2, it follows that

    H=-e^2Φ/c^2(1+A  Ω)^2+e^-2Φ/c^2W^2   Ω^2/c^2  .

Relevant physical velocities have to be identified to correctly implement any low-velocity limit. In the present case, we define the kinetic and dragging velocities

    := r Ω  , 
        := r χ  ,

where χ := -g_tϕ/g_ϕϕ is the frame–dragging term. For systems in the low-energy regime—i.e., nonrelativistic relative local velocities v ≪ c, weak pseudo-Newtonian potential Φ v^2, nonrelativistic frame–dragging, and small pressure p  v^2—then to leading order  coincides with the special relativistic interpretation of the redshift, whilst  follows by analogy <cit.>.

Let us then write the EFE as

    R_μν = 8 π G/c^4(T_μν-1/2T g_μν)  ,

where T=T^μ_μ = 3p- c^2. With (<ref>)–(<ref>) this yields the partial differential equations (PDEs) <cit.>

   
    Φ^,a_,a + W^,aΦ_,a/W + c^4A^,aA_,a/2W^2e^4Φ/c^2 = 4 π G e^2(k-2Φ)/c^2[(+p/c^2)(1+AΩ)^2e^2Φ/c^2+c^-2W^2Ω^2e^-2Φ/c^2/-H+2p/c^2]   , 
       A^,a_,a - W^,aA_,a/W + 4/c^2Φ^,aA_,a = 16 π G/c^4 W^2Ω1+AΩ/H(+p/c^2)e^2(k-2Φ)/c^2  , 
       W^,a_,a = 16 π G/c^4p   , 
        W_,rr-W_,zz+2/c^2(k_,zW_,z-k_,rW_,r)+2W/c^4(Φ_,r^2 - Φ_,z^2) + c^2/2We^4Φ/c^2(A_,z^2 - A_,r^2) = 0   , 
       c^2/2We^4Φ/c^2A_,z A_,r-W_,rz-2W/c^4Φ_,rΦ_,z+1/c^2(k_,zW_,r-k_,rW_,z) = 0   , 
       1/c^2(Φ^,a_,a-k^,a_,a)-1/2WW^,a_,a + 1/c^2W^,aΦ_,a/W - 1/c^4Φ^,aΦ_,a+ c^2/4W^2e^4Φ/c^2(A_,z^2 + A_,r^2) = 4 π G/c^2e^2(k-2Φ)/c^2(-p/c^2)  ,
 

where a∈{r,z}. Eq. (<ref>) and (<ref>) are the tt and rzcomponents of (<ref>) respectively, (<ref>) and (<ref>) are obtained from the R_zz± R_rr equations, (<ref>) is found by taking the combination W^-1c^-2(g_ϕϕR_tt-2 g_tϕR_tϕ+g_ttR_ϕϕ), and finally (<ref>) follows from the combination 2c^-2(R_tϕ-A R_tt). 

The system of PDEs is completed by the perfect fluid elements' equations of motion, which give 

    
    Hp_,a/e^2(k-Φ)/c^2=[Φ_,a+(c^2 A_,a+2AΦ_,a)Ω+(c^2AA_,a+A^2Φ_,a)Ω^2]e^2Φ/c^2+Ω^2(W^2Φ_,a/c^2-WW_,a)e^-2Φ/c^2  ,


We now take an expansion in powers of v/c to implement the nonrelativistic limit, where v is any relevant local velocity. We apply the self-consistent ansatz 

    W(r,z) = r + 𝒪(v^4/c^4)   ,

to solve (<ref>) up to fourth order. From (<ref>), and the definition of χ, we find A = r  /c^2+𝒪(v^3/c^3). Thus, by (<ref>) it follows that 

    H = -1 + ^2/c^2 - 2/c/c + 2 Φ/c^2 + 𝒪(v^4/c^4) .

Hence, by direct substitution of (<ref>) into (<ref>)–(<ref>) we find

    ΔΦ + 1/2r^2||∇⃗Ł_D||^2 = 4 π G  + 𝒪(v^2/c^2)  , 
       Δ̂Ł_D = 0 + 𝒪(v^2/c^2)   , 
        k_,r = 1/4r(Ł_D,z^2-Ł_D,r^2)+ 𝒪(v^2/c^2)    , 
        k_,z = -1/2r(Ł_D,z Ł_D,r) + 𝒪(v^2/c^2)   ,

where Ł_D := r is the quasilocal angular momentum per unit of mass associated with spacetime rotation, Δ is the standard laplacian and Δ̂ := ∂^2_r -(1/r)∂_r + ∂^2_z, is the Grad–Shafranov laplacian <cit.>. The number of equations reduces by one, as (<ref>) is equivalent to (<ref>) to the order considered. Furthermore, we see that the fluid effective pressure does not enter the EFE as a source term at this order of approximation. 

Eq. (<ref>) is a general relativistic generalization of the Poisson equation, and coincides with it in the absence of spacetime rotation. The extra term in (<ref>) can be interpreted as the rotational energy associated with the quasilocal angular momentum of the averaged background spacetime. This term is absent in the conventional Newtonian approximation in which the background is taken to be Minkowski space a priori. Furthermore, when moved to the r.h.s. of (<ref>), it can be identified as an effective density, ρ𝒬=-||∇⃗Ł_D||^2/(8π G  r^2).  This represents a negative gravitational binding energy relative to the background <cit.>.

Even for nonrelativistic dragging velocities spacetime rotation gives first-order corrections to the field equations. For fixed , Eq. (<ref>) shows that the strength of the pseudo-Newtonian potential needed to sustain equilibrium decreases as the local rotational energy of the background geometry increases. Furthermore, the pseudo-Newtonian potential in (<ref>) is essential to accommodate nonrigid rotation of the perfect fluid source. Indeed, if we set Φ=0 then (<ref>)–(<ref>) are the same equations that characterize a system of rigidly rotating dust <cit.>. As such this choice is unphysical, requiring an identification of  purely with rotational energy.

At the same order, equations (<ref>) reduce to 

    -p_,r/=Φ_,r+Ω Ł_D,r - ^2/r + 𝒪(v^2/c^2)   , 
       -p_,z/=Φ_,z+ΩŁ_D,z+𝒪(v^2/c^2)  .

Hence, the effective pressure of the fluid still plays a crucial role in determining the physics of the system, as expected. In Eq. (<ref>) and (<ref>), we recognize the gradient of the pseudo-Newtonian potential and the centrifugal acceleration in the term ^2/r. The conventional Newtonian equations follow in the case of negligible dragging (≪). However, more generally Eqs. (<ref>), (<ref>) once again show the crucial role that the quasilocal angular momentum of the regional background plays in determining the dynamics. For fixed  and p, the magnitude of the pseudo-Newtonian potential needed to match the l.h.s. of (<ref>) and (<ref>) decreases linearly with the quasilocal angular momentum of the underlying averaged geometry.

The quasilocal Newtonian limit defined here is thus realized by Eqs. (<ref>)-(<ref>). As a first application of the quasilocal Newtonian limit, we derive the dragging velocity profile for a disc galaxy rotation curve supported exclusively by baryonic matter. The baryonic mass distribution in a disc galaxy can be written as =  +, where  and  are the densities of the bulge and the disc, respectively. 

We assume a spherical bulge component given by the Plummer density profile <cit.>

    (R) = 3^2/4π(R^2+^2)^5/2 ,

where R = √(r^2+z^2),  is the scale parameter of the bulge and  is the total bulge mass. The resulting circular velocity in the conventional Newtonian limit is

    (R) = √(G R^2(R^2+^2)^-3/2)  .


The baryonic disc matter distribution is usually taken as (r, z)=Σ(r)Z(z). The surface density of the disc is well approximated by the exponential profile

    Σ(r)=/2π^2e^-r/  ,

where  is the total disc mass and  is the scale length in the radial direction for the galactic disc. The distribution along z, with ∫ Z(z)dz=1, is assumed to be

    Z(z)=1/2e^-|z|/  ,

where  is the thickness scale length and ≪. When the thickness  tends to zero, we apply the conventional infinitely thin disc approximation, i.e., Z(z)=δ(z)<cit.>. The Newtonian circular velocity field in the thin disc approximation, , is given by <cit.>

    
    (r) = √(G/2^3r^2[I_0(r/2)K_0(r/2) -I_1(r/2)K_1(r/2)])  ,


where I_{0,1} and K_{0,1} are modified Bessel functions of the first and second kind.

To explain the observed rotation curves in the conventional Newtonian framework, a spherical cold dark matter (DM) halo must be included, so that the matter density is =  +, where  is typically given by the isothermal profile <cit.>

    (R)=ρDM0/1+(R/)^2  .

Here  is the halo scale parameter, and ρDM0 is the maximum DM density. The DM halo contribution to the rotation curve, , is then <cit.>

    (R)^2=4π G ^2 ρDM0(1- arctan(R/)/R/)   .

Thus the circular velocity of the matter in Newtonian modelling of the disc galaxy, , on the equatorial plane, is given by

    (r,0)=√((r,0)^2+(r)^2+(r,0)^2)  .

In Fig. <ref>, we consider a Milky Way-like galaxy with = 0.8 · 10^10M_⊙, = 0.8 kpc, = 8.1 · 10^10M_⊙, = 2.1 kpc, = 5.69 kpc and ρDM0= 1.88·10^-21 kg/m^3. We plot the predicted rotation curve (r,0), and the respective (r,0), (r) and (r,0). 


To apply the general relativistic solution, let us now assume that =, i.e., that the inferred Newtonian rotation curve corresponds to that of a disc galaxy, and that =. We will demonstrate that the quasilocal energy and angular momentum of the galaxy produce observations equivalent to those of a conventional cold dark matter halo.

We begin by writing the pseudo-Newtonian potential as Φ=-, so that  is given by the Newtonian solution for the chosen , while  is defined as the solution of the Poisson equation sourced purely by the quasilocal rotational energy of the spacetime 

    Δ=||∇⃗Ł_D||^2/2r^2  .


We now solve (<ref>), (<ref>), and (<ref>) for Ł_D by noting that in the thin disc approximation the pressure term is exactly the same for both the Newtonian and the general relativistic cases. Moreover, a similar ansatz can be applied to the spherical bulge, where dark matter is not required to explain the observed dynamics, i.e., it is well captured by purely Newtonian models with purely baryonic matter. Thus we can take p(r,z):=p N (r,z) for the whole system, where p N (r,z) is the expected effective Newtonian pressure. We then use Eqs. (<ref>),(<ref>) to deduce

    = ΩŁ_D,r -(^2-^2)/r   , 
        = ΩŁ_D,z ,

where := √(^2+^2) is the Newtonian contribution to the observed rotation curve from the baryonic mass.

Substituting (<ref>), (<ref>) in (<ref>) it follows that

    Δ =Ω_,rŁ_D,r +2ΩŁ_D,r/r +Ω_,zŁ_D,z -(^2-^2)_,r/r  ,

where we have also used the quasilocal Newtonian limit of the (tϕ) Einstein Eq. (<ref>). Eqs. (<ref>), (<ref>) then give a first-order nonlinear PDE for Ł_D

    ∇⃗Ł_D·[∇⃗Ł_D - 2∇⃗(r)] + 2r(^2-^2)_,r = 0  .

We evaluate Eq. (<ref>) on the galactic plane, z=0, where thanks to the plane symmetry we have Ł_D,z(r,0)=vK,z(r,0) = 0. Thus, the nonlinear PDE (<ref>) is reduced to an algebraic equation for Ł_D,r on the galactic plane, whose solutions are given by 

    Ł_D,r=(r)_,r±√([(r)_,r]^2 - 2r(^2-^2)_,r)  .


We choose the minus sign in (<ref>) so that it reduces to the expected Newtonian case for =. Furthermore, given the baryonic density distribution and the conventional Newtonian profile for (r,0), we can numerically solve (<ref>) for (r,0). In Fig. <ref> we show the resulting frame–dragging velocity profile generating the simulated galaxy rotation curve, . The frame–dragging speed reaches a maximum 42.2km/s at r=24.4kpc, well within our nonrelativistic approximation. Furthermore, as we would expect: (i)  decreases with increasing radius, tending to zero at infinity; and (ii)  is negligible in the bulge, showing the self-consistency of the pressure ansatz used in the calculations. 


The new quasilocal Newtonian limit applies to stationary axisymmetric matter distributions with geometry (<ref>). These symmetry assumptions mean that for a Milky Way-like disc galaxy the approximations here, along with the exact solutions <cit.> hold on time scales, 10^7 t10^9yr. Eqs. (<ref>)–(<ref>) will not apply during galaxy formation, and therefore do not explain how disc galaxies form in a cold dark matter free environment. While such complex problems must be left to future work, the precise definition of finite infinity <cit.> provides a mathematical framework for further exploring the quasilocal Newtonian limit, in settings from the early Universe through to highly dynamical astrophysical systems. The interplay of quasilocal gravitational energy and angular momentum must play a key crucial role.

In summary, we have shown that via a novel self-consistent quasilocal Newtonian limit, general relativity can explain the observed rotation curves of disc galaxies without the need for halos of cold dark matter particles. The phenonomenology of collisionless dark matter is reproduced by the regional gravitational energy and angular momentum of the average spacetime geometry.

This discovery has far-reaching consequences for cosmology, astrophysics and particle physics. Indeed, many interesting questions are now opened up. Within the given realization of the quasilocal Newtonian limit, disc galaxy stability, gravitational lensing and fits to observational datasets must be addressed to definitively test the new paradigm. Comparisons with MOND phenomenology potentially opens the prospect not only of placing MOND within the theoretical framework of general relativity, but also of providing insights into the development of this important new physical limit of Einstein's theory. Finally, in light of our results, the phenomenology of dark matter in the early universe, in the dynamics of galaxy clusters, and in other astrophysical environments should now be reconsidered and further investigated.

Acknowledgments  DLW is supported by Marsden Fund grant M1271 administered by the Royal Society of New Zealand, Te Apārangi. We thank Davide Astesiano, Luca Ciotti, Sergio Cacciatori, John Forbes, Vittorio Gorini, Christopher Harvey-Hawes, Frederic Hessman, Morag Hills, Emma Johnson, Zachary Lane, Ryan Ridden-Harper, Antonia Seifert, Chris Stevens, Shreyas Tiruvaskar and Michael Williams for useful discussions. 






 Paper Title: Modelling the multi-wavelength detection of protoclusters. I: An excess of submillimetre galaxies in protocluster cores.





0000-0003-2860-5717]Pablo Araya-Araya
Departamento de Astronomia, Instituto de Astronomia, Geofísica e Ciências Atmosféricas,
Universidade de São Paulo, 

Rua do Matão 1226, Cidade Universitária, 05508-900, São Paulo, SP, Brazil
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
paraya-araya@usp.br

0000-0001-8855-6107]Rachel K. Cochrane
SUPA, Institute for Astronomy, Royal Observatory Edinburgh, EH9 3HJ, UK
Columbia Astrophysics Laboratory, Columbia University, 550 West 120th Street, New York, NY 10027, USA
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

0000-0003-4073-3236]Christopher C. Hayward
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

0000-0001-9320-4958]Robert M. Yates
Centre for Astrophysics Research, University of Hertfordshire, Hatfield, AL10 9AB, UK

0000-0002-3876-268X]Laerte Sodré Jr.
Departamento de Astronomia, Instituto de Astronomia, Geofísica e Ciências Atmosféricas,
Universidade de São Paulo, 

Rua do Matão 1226, Cidade Universitária, 05508-900, São Paulo, SP, Brazil

0000-0002-9191-5972]Marcelo C. Vicentin
Departamento de Astronomia, Instituto de Astronomia, Geofísica e Ciências Atmosféricas,
Universidade de São Paulo, 

Rua do Matão 1226, Cidade Universitária, 05508-900, São Paulo, SP, Brazil

0000-0002-1619-8555]Douglas Rennehan
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

0000-0002-8214-7617]Roderik Overzier
Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, The Netherlands
Observatório Nacional/MCTI, Rua General José Cristino, 77, São Cristóvão, 20921-400, Rio de Janeiro, RJ, Brazil

0000-0002-8801-4911]Marcel van Daalen
Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, The Netherlands

 
§ ABSTRACT 

Studies of galaxy protoclusters yield insights into galaxy cluster formation complementary to those obtained via `archaeological' studies of present-day galaxy clusters.
Submillimetre-selected galaxies (SMGs) are one class of sources used to find high-redshift protoclusters.
However, due to the rarity of protoclusters (and thus the
large simulation volume required) and the complexity of modeling dust emission from galaxies, the relationship between SMGs and protoclusters has not been adequately addressed in the theoretical literature.
In this work, we apply the  semi-analytic model (SAM) to the  N-body simulation.
We assign submillimetre (submm) flux densities to the model galaxies using a scaling relation from previous work,
in which dust radiative transfer was performed on high-resolution galaxy zoom simulations.
We find that the fraction of model galaxies that are submm-bright is higher in protocluster cores than in both protocluster `outskirts' and the field; the fractions for the latter two are similar.
This excess is not driven by an enhanced starburst frequency. Instead, the primary reason is that
overdense environments have a relative overdensity of high-mass halos and thus `oversample' the high-mass end of the star formation main sequence relative to less-dense environments.
The fraction of SMGs that are optically bright is dependent on stellar mass and redshift but independent of environment. The fraction of galaxies for which the majority
of star formation is dust-obscured is higher in protocluster cores, primarily due to the dust-obscured fraction being correlated with stellar mass.
Our results can be used to guide and interpret multi-wavelength studies of galaxy populations in protoclusters.






§ INTRODUCTION
 

Protoclusters, defined as the progenitors of present-day galaxy clusters, are powerful laboratories for studies of the assembly
of both baryonic and dark matter <cit.>. Studying protoclusters can yield insight into galaxy cluster formation
complementary to that obtained by studying mature clusters. For example, one can directly investigate the origin of the
intracluster medium (ICM).
Protoclusters are ensembles of dark matter halos occupying large comoving volumes at early
epochs that will eventually collapse into a galaxy cluster <cit.>.
In simulations, in which the full history of any given dark matter halo is known, identifying the halos that will end up in a cluster by z = 0 – i.e. the protocluster members – is straightforward. In contrast, observationally identifying protoclusters is very challenging: due to the great diversity of dark matter halos' growth histories, a dark matter overdensity at high redshift may continue to grow rapidly and end up as a
massive galaxy cluster at z = 0, but it could also stall and wind up as an isolated massive elliptical <cit.>. 

A wide variety of galaxy populations reside in protoclusters, including Hα emitters <cit.>, Lyman α emitters <cit.>, [OII] emitters <cit.>, Lyman Break Galaxies <cit.>, Balmer Break Galaxies  <cit.>, radio-loud <cit.> and radio-quiet active galactic nuclei <cit.>, and submillimetre-selected galaxies <cit.>.
Protoclusters can thus be used to study diverse galaxy populations in order to understand the impact of the environment on galaxy evolution – in particular, how environment can affect gas fueling, star formation and quenching, eventually producing populations characteristic of local clusters (see  for a review). 

Protoclusters are typically found by searching for overdensities in galaxy surveys. Various classes of galaxies
can be used as tracers, with some being more effective than others.
However, a given structure may be overdense in terms of one galaxy population but not others.
<cit.> found just 4 LBGs in the SPT2349-56 protocluster core at z ∼ 4.3, which harbors more than 14 SMGs; this region would not be identified as a massive protocluster with the LBG dropout technique alone. <cit.> noted that SMGs tend to reside at the outskirts of HAE density peaks in two z ∼ 2.2 protoclusters, and this is also the case for the Spiderweb protocluster <cit.>. This phenomenon is usually attributed to assembly bias, i.e. the properties of galaxies in dark matter halos of similar mass also depend on their formation history. 
In searching for protoclusters, it is often assumed that most of the constituent galaxies will be star-forming, as is predicted by theoretical models <cit.>. However, recent work has revealed
concentrations of quiescent galaxies already in place by z ∼ 2.7 <cit.>.

How the selection of overdense regions depends on the tracer used remains unclear. For example, there is still debate about whether AGN <cit.> or SMGs <cit.> are good protocluster tracers.
Since bright SMGs inhabit some of the most massive dark matter halos at a given epoch <cit.>,
one might expect that searching for overdensities of SMGs should be an effective means for finding galaxy protoclusters.
However, the rarity of SMGs (N ∼ 10^-5 to 10^-6 cMpc^-3 at z ∼ 2-3; ) may cause them to be incomplete tracers of protoclusters,
and `downsizing' (more massive galaxies form their stellar mass quickly and quench earlier) may result in lower-redshift protoclusters not being traced by SMGs <cit.>.

To better understand how different galaxy populations trace protoclusters, one can employ mock catalogs
generated using theoretical models (i.e. hydrodynamical simulations or semi-analytic models, hereafter SAMs).
To do this, it is necessary to select tracer populations analogous to those used to search for protoclusters observationally. This is done by predicting the spectral energy distributions (SEDs) of the model galaxies, which is challenging.
Ideally, one would simulate protoclusters
at high resolution in order to accurately capture the structure of the interstellar medium (ISM) and then perform
dust radiative transfer to compute the SEDs of the simulated galaxies.
However, because protoclusters are rare, large simulation volumes
are required, making high-resolution hydrodynamical simulations an infeasible approach. Zoom simulations of
protoclusters selected from a large N-body simulation are an alternative approach <cit.>, but due to the computational expense of simulating extremely high-mass halos, one must either use
relatively coarse resolution  or simulate a small number of protoclusters (see  for discussion). 

SAMs provide an alternative, inexpensive means to `populate' large N-body simulations with galaxies. However, for studies of observability, it is still necessary to compute SEDs for the model galaxies. In SAMs, the 3D geometry of
the model galaxies is either ignored entirely or treated in a highly idealised fashion, making directly performing radiative
transfer infeasible. However, alternative approaches can be applied. One approach is to use empirically derived SED
templates <cit.>.
Alternatively, given the star formation histories (SFHs) and metallicities of model galaxies, one can perform stellar population
synthesis to compute the intrinsic SED and then attenuate the SED using a
simple model for dust attenuation.
To compute thermal dust emission, one can apply scaling relations derived by performing dust radiative transfer
on high-resolution galaxy simulations that enable accurate and efficient submm flux density predictions given a small
number of integrated galaxy properties, most importantly star formation rate (SFR) and dust mass
<cit.>. This approach can be applied to both SAMs <cit.>
and coarse-resolution large-volume cosmological simulations <cit.>.
By applying these well-calibrated scaling relations to model galaxy catalogs yielded by running a SAM on a large
N-body simulation, we can generate a sufficiently large mock catalog that can be used to
study and refine multiwavelength strategies to find protoclusters and understand where (environment)
and when (redshift) different galaxy populations occur. 

In this work, the first of a series, we construct a 36 deg^2 mock galaxy catalog by applying the <cit.>
version of the  SAM to the  <cit.> simulation. 
We apply scaling relations from previous work to predict the submm flux density and use the resulting mock catalog to investigate the relationship between SMGs and protoclusters in the model.

The remainder of this work is
organised as follows: in Section <ref>, we briefly describe the N-body simulation and SAM used and
how we generate the mock catalog, including optical magnitudes and submm flux densities for the model galaxies.
In Section <ref>, we identify the structures in the mock and define the selection of (proto)cluster members
and environments. We then investigate how SMGs trace protoclusters in the model across cosmic time in
Section <ref>. We investigate the physical drivers of the identified trends in Section <ref>.
In Section <ref>, we explore the optical properties of the model SMGs, and
in Section <ref>, we quantify the obscured fraction
in protocluster regions and as a function of stellar mass and redshift.
We discuss our results in Section <ref> and summarize our findings in Section <ref>. 

Throughout this work, for consistency with the cosmologically re-scaled version of the  simulation <cit.>, we assume a Planck-1 cosmology: h = 0.673, Ω_m=0.315 and Ω_Λ= 0.685 <cit.>.



§ METHODOLOGY TO CREATE THE MOCK CATALOG
 

We use a mock catalog constructed generally following the methodology presented in <cit.>, but
with some differences, mainly in terms of the approach for predicting the SEDs of the model galaxies.
In this section, we briefly describe the main aspects of the SAM and detail the
improvements compared to the original version.



 §.§ Semi-analytic galaxy formation model


We use the <cit.> version of the  SAM run on the  simulation <cit.> scaled to the Planck-1 cosmology with the <cit.> algorithm. This version of  includes a wide range of important galaxy evolution processes, such as gas infall and cooling, star formation, galaxy mergers, metal enrichment,
satellite quenching,
supermassive black hole growth, and supernova and AGN feedback (see the Supplementary Material in ).
Our set-up produces ∼ 4 million galaxies with M_⋆ > 10^9 at z=0 in a (480 cMpc/h)^3 box, from which mock galaxy samples can be extracted within pre-defined lightcones. 

In <cit.>, several πdeg^2 lightcones were created by configuring the line-of-sight to pass through
pre-selected structures at desired redshifts. This is helpful for studies of individual detections, as implemented
in <cit.>. Here, we analyze a single larger lightcone of area 36 deg^2 extending from z = 0-5. The large
field of view studied here is
crucial to minimize the effects of cosmic variance and increase the number of structures within the lightcone.
However, the larger the field of view, the higher the possibility of encountering the same galaxy in the mock (replication).
In principle, this is not a problem as long as the galaxies are at different redshifts. Here, the volume corresponding to
an area of 36 deg^2 located between redshifts z ∼ 4.28 and z ∼ 5.03 (the redshifts of the last
two snapshots used in this work) is comparable to the  volume. Extending the mock to higher
redshift would thus lead to many galaxy replications and is hence not advisable. Consequently, we do not study
higher redshifts in this work. As we will discuss in Section <ref>, the mock contains a sufficient number
of (proto)clusters in our redshift range of interest.



 §.§ Updated approach to predict SEDs of the model galaxies


The previous mock version used the single-age stellar population (SSP) SED templates from <cit.>,
assuming a <cit.> initial mass function. 
We have changed our base SSP templates to the upgraded version (2016) of <cit.>[<http://www.bruzual.org/g̃bruzual/bc03/Updated_version_2016/>]. The main difference between these two is the treatment of TP-AGB stars; predicted synthetic observables considered here are similar for the two sets of SSP templates. These templates comprise 7×220 SEDs, with seven metallicities from log(Z/Z_⊙)=-2.30 to 0.70 and 220 ages (from 0.1 Myr to 20 Gyr). The median SED wavelength resolution is Δλ = 0.89 Å, which is ∼ 20 times better than that of <cit.>. 


An important  output is the SFH arrays <cit.>. These
have 20 age bins, with a median bin width
equivalent to a single internal time-step for the SAM (20 times smaller than the
time interval between snapshots; see Figure 2 of , which shows the binning as a function of the
snapshot).
Each SFH bin contains a composite of stellar populations, which for simplicity are assumed to share the average
metallicity and formation time.
At short lookback times, the SFH bin resolution is fairly high (∼ 20 Myr), but at large lookback times, this increases
to up to ∼ 2 - 3 Gyr <cit.>. 
At low redshifts, the youngest median age is ∼ 10 Myr.
If we were to use a minimum stellar age of 10 Myr, we would underestimate the luminosity at short wavelengths
(in particular, λ < 3000 Å). Since the bluest wavelengths are most efficiently absorbed by dust, it is crucial to address this for robust submm predictions.

The easiest way to address this issue is to generate younger SFH bins for both the disk and bulge galaxy components in post-processing.
We call this process `SFH refinement'. In principle, from the  SFHs, we know the difference in stellar mass between two age bins. In particular, from the youngest SFH bin, we can derive the instantaneous star formation rate, SFR(t=0). Then, assuming this is constant within the time interval of the youngest bin, we can construct five younger SFH bins. 



In practice, we assume that we can describe SFR(t) as a constant equal to SFR(t=0) between t=0 and t = t_y,l, where t_y,l is the age limit of the initial youngest SFH bin, and SFR(t = 0) is approximated by  M_⋆,y/(Δ t_y  s_⋆,y), where M_⋆,y is the stellar mass in the original youngest SFH bin and s_⋆,y is the fraction of survivor mass given the initial SFH bin metallicity and age. We obtain s_⋆,y from the simple stellar population model used in this work.  
Then, we create five new logarithmically spaced SFH bins from 0.1 Myr to t_y,l, and ascribe to each new bin a stellar mass obtained by simply multiplying SFR(t=0) to the time width of each new steps. Notice that the new SFH bins represent the total stellar mass. Then, we re-correct them to obtain the survivor mass at the new SFH ages. Figure <ref> shows the new SFH bins produced with our method for the disk and bulge components of an example galaxy (blue and red dashed lines, respectively), alongside the original bins (solid lines).  
We assume that all of these new bins have the same metallicity, equal to the cold gas metallicity. 

Another upgrade to the method to derive galaxy SEDs is the implementation of intergalactic medium absorption. Instead of using pre-computed tables, i.e. magnitude corrections as a function of redshift, we have applied a transmission curve to each modeled galaxy SED. To do this, we constructed a grid with the IGM transmission curves for sources at redshifts from z=0.1 to z=7.0 (although our mock goes up to z ∼ 5) spaced by Δ z = 0.1. We used the  code <cit.> to obtain standardized curve sets. This algorithm performs Monte Carlo simulations to distribute absorbers along a line-of-sight, where we sample their redshift and optical depth following the <cit.> model. This component is crucial for obtaining reliable magnitudes at optical wavelengths for high-z galaxies, since features such as the Lyman break and Lyman-α forest are detected in the u and g bands, respectively, for z ∼ 3.0 sources.




 §.§ Dust attenuation model
 

Because it is particularly relevant for this work, we describe the dust attenuation model employed,
based on that of <cit.>, in detail here.
The same model has been employed in numerous previous works <cit.>.
The dust model assumes two components: the ISM and molecular clouds (MCs; also called birth clouds)
around recently formed stars. The ISM attenuation affects the entire stellar population of the disk, whereas
the MC attenuation acts only on the light from young stars (age ≤ 10 Myr). 

The optical depth as a function of the wavelength for the ISM component is


    τ_λ^ ISM =  ( A_λ/A_V )_Z_⊙ ( Z_ gas/Z_⊙ )^s (1 + z)^-1 ( ⟨ N_H⟩/2.1 × 10^21 cm^-2 ).

The mean hydrogen column density, ⟨ N_H ⟩, can be obtained directly from
the SAM output parameters as follows:

    ⟨ N_H⟩ = M_ cold/1.4 m_p π (a R_ gas, d)^2cm^-2 ,

where M_ cold is the mass of the cold gas, R_ gas, d is the radius of the gaseous disk, m_p is the proton mass,
and a = 1.68.
This value for a is selected so that ⟨ N_H ⟩ represents the mass-weighted average column density
of an exponential disk. The factor 1.4 takes into account the helium abundance <cit.>. The (Z_ gas/Z_⊙) factor in Equation <ref> is the mass fraction of metals in the cold gas in solar metallicity units (we use Z_⊙ = 0.02 for consistency with <cit.>). In this model, the index for the power-law dependence on metallicity, s,
depends on the wavelength: s=1.35 for λ < 2000 Å, and s=1.60 for λ≥ 2000 Å  <cit.>.
(A_λ/A_V)_Z_⊙ represents the solar-metallicity extinction curve from <cit.>.

The optical depth of the MC component is

    τ_λ^ MC = τ_V^ ISM ( 1/μ - 1  )  ( λ/5500 Å )^-0.7 ,

where τ_V^ ISM is the optical depth of the ISM in the V band (λ_ eq∼ 5500  Å), and μ is a random Gaussian variable with values between 0.1 and 1, with mean 0.3 and standard deviation 0.2 <cit.>.

Therefore, the attenuation as a function of wavelength is given by

    A_λ^ISM =  ( 1 - e^(-τ_λ^ISMθ)/τ_λ^ISMθ );  
    A_λ^MC = (1 - e^-τ_λ^MC) ,

where θ represents the inclination of the galaxy. The inclination cosine is first randomly sampled between 0 and 1.
Then, all values less than 0.2 are set to 0.2 <cit.>. 



 §.§ Dust emission modeling
 

The thermal dust emission SED of a galaxy is determined by the radiation field heating the dust, dust density field, and grain properties. If the
3D stellar and AGN radiation field, 3D dust density field, and grain properties are known, one can perform radiative transfer to compute the dust
temperature distribution and thus dust emission SED. In a SAM, one can assume an idealised geometry and perform radiative transfer
<cit.>. However, to avoid introducing additional free parameters, we adopt an alternative approach: we use scaling relations derived from performing radiative transfer on hydrodynamical simulations.
We present a brief comparison with an empirical SED template-based approach to demonstrate that our method yields reasonable results.



  §.§.§ Scaling relations
 

The dust temperature distribution, and thus dust emission SED, is affected by the total luminosity absorbed by dust and the dust mass.
Multiple authors have performed radiative transfer in post-processing on galaxies from simulations that differ considerably in terms of
spatial resolution, the galaxy formation model employed, and the code used and found that the submm flux density can be predicted
reasonably well if only the total infrared (IR) luminosity and dust mass are known <cit.>.
Parameterising submm flux density as a double power law in SFR (i.e. assuming AGN heating of dust is subdominant) and dust mass, 
they found similar values for the free parameters, suggesting that although simple, this approach is a robust method for predicting submm
flux density in models.

Here, we will use the fit derived by <cit.>, whose free parameters were obtained by applying the Stellar Kinematics Including Radiative Transfer () Monte Carlo radiative transfer code <cit.> to massive, high-redshift galaxies drawn from the Feedback in Realistic Environments
(FIRE) project (; see also ). In addition to SFR and dust mass, the relation from <cit.> uses stellar mass and redshift as input
quantities to predict the observed-frame 870-μm flux density. Their relation is the following:

    S_870/ mJy = α (   SFR/100  yr^-1 )^β (  M_⋆/10^10 )^γ (  M_ dust/10^8 )^δ (1 + z)^η,

where logα = -0.77, β = 0.32, γ=0.13, δ=0.65, and η=0.65. 
The version of  used here does not provide dust mass as an output.
Thus, we simply assume that 40 per cent of the metals in the cold gas are in the form of dust grains, M_ dust = 0.4 M_ Z,ColdGas <cit.>,
which is a reasonable approximation for the relatively metal-enriched, massive galaxies studied in this work, as seen in observations <cit.>, and in later versions of  which incorporate dust physics <cit.>.

<cit.> show that their scaling relation can recover the true values of submm flux density from the radiative transfer calculations with an error of
∼ 0.1 dex, independent of flux density. To incorporate this error, when assigning S_870 values to the model galaxies using Equation <ref>,
we add values drawn from a normal distribution with zero mean and standard deviation of 0.1 dex.





  §.§.§ Template approach
 

An alternative method for modelling the thermal dust emission SED is using templates.
Although we use the scaling relation approach as our fiducial method, we also derive submm flux densities using empirical templates to determine
the sensitivity of our results to how submm flux density is computed. We use the <cit.> templates, which are parameterised by the
specific SFR (sSFR ≡ SFR/M_∗) and the total IR luminosity of the galaxy. We obtain the latter by integrating the total luminosity absorbed by dust (see Section <ref>).

For illustration, we present in Figure <ref> the full SED of a galaxy at z=3.23 computed using the template approach and overplot flux densities at a number of rest-frame far-IR wavelengths using the <cit.> scaling relations. We show flux densities in ALMA bands 10, 9, 8, and 7
(observed-frame effective wavelengths of 345 μm, 426 μm, 652 μm, and 870 μm, respectively) because
<cit.> derived scaling relations for each of these bands. The two approaches yield very similar results.





  §.§.§ Comparison with observations
 

In Figure <ref>, we plot the differential submm number counts (i.e. integrated over redshift) predicted using the two approaches for computing S_870 and
compare the predictions with observations from <cit.> and <cit.>.

The two methods for computing S_870 yield similar predictions for the submm number counts (the lines in Figure <ref>).
As is the case for most models that assume a standard IMF <cit.>,
we underpredict the observed counts. To explore the severity of this discrepancy, we show how much the differential counts change when
we artificially increase or decrease the SFR (top panel) or dust mass (bottom panel) by a factor of 2.5.
In the case of the SFR, our motivation for this factor comes from the fact that the cosmic star formation density in
the <cit.> version of the  model is less than the empirically derived values from <cit.> and <cit.>
by a similar factor.
For the dust mass, since we have implemented a constant cold gas dust-to-metals ratio equal to 0.4,
the factor of 2.5 would represent the extreme case in which all metals in the cold gas phase are locked up in dust.
We can see that boosting the SFR and dust mass simultaneously could lead to number counts in agreement with those observed. In follow-up work,
we will examine what modifications to the model are necessary to match the observed submm number counts while maintaining agreement
with the other observational constraints employed. In the present work, we simply use the version of  from
 <cit.> and focus on differential quantities, such as the enhancement in the submm-bright fraction in protocluster cores
 compared with the field, which are unlikely to be affected by the overall underprediction of the submm counts.



§ IDENTIFYING (PROTO)CLUSTERS IN THE MOCK
 





In order to identify the predicted (proto)clusters within the lightcone, we have to link them to the dark matter halo information of the base simulation. We first define clusters following <cit.>: principal dark matter halos with  > 1 × 10^14. There are 3,279 such clusters at z=0. 

In the second step, we select all galaxies hosted by z = 0 cluster progenitors halos using the  key identifier. Note that we could adopt an intermediate step where we identify the other bound subhalos of those progenitor clusters (e.g. by matching their ), but we verified that this does not make any significant difference for the structures at z > 1.

As mentioned in Section <ref>, galaxy replication can occur, and we can find up to six progenitors (with a median value of four) of the same galaxy in the mock but at different redshifts and celestial coordinates. Consequently, the procedure described above to identify structures in the mock by searching for cluster progenitors reflects the effect of replications. The redshift distribution of galaxies hosted in progenitor halos of a given z = 0 cluster exhibits peaks where replication occurs. Although replicated galaxies are progenitors of the same cluster, they are effectively different structures since they are at distinct evolutionary stages. We thus identify these peaks to separate them into single structures. To do this, we first construct redshift histograms with a bin size equal to Δ z= 0.01. If the number of galaxies in a redshift bin is greater than the numbers for the two adjacent ones, we consider this redshift to be the initial structure redshift, z_i. To obtain accurate (proto)cluster redshifts and celestial coordinates, we select all galaxies (in progenitor halos) with redshift z_i ± 5 Δ z and then compute the median right ascension, declination, and redshift. With this approach, we identify 16,320 structures within the 36 deg^2 mock at z ≲ 5.0.

Here, we adopt the same classification of (proto)clusters as in <cit.>, based on their descendant cluster's z = 0 mass (M_z = 0). We refer to protoclusters as Fornax-, Virgo-, or Coma-type if their z=0 descendant cluster masses are M_z = 0 = (1.37 - 3)× 10^14, (3 - 10)× 10^14,
or ≥ 10^15 , respectively.[This terminology is simply a convenient way to put descendant masses in context. We do not intend to imply that Coma-type protoclusters will resemble the Coma cluster at z = 0 in terms of any property except for mass or that the detailed formation histories of a given protocluster type are similar.]
Additionally, following  <cit.>, a protocluster becomes a cluster once its main dark matter halo has virial mass  > 10^14 . We show the redshift distributions of the structures in the mock in Figure <ref>.

In total, our sample comprises the following: 

    
  * Fornax-type: 452 clusters; 12,080 protoclusters.
    
  * Virgo-type: 542 clusters; 4,199 protoclusters.
    
  * Coma-type: 65 clusters; 247 protoclusters.


Although we have divided the sample of z=0 cluster progenitors into already-formed clusters and protoclusters to construct Figure <ref>, we do not employ this separation in the remainder of our analysis, and for convenience, we will use the term `protocluster'
even though some of the structures already have mass > 10^14  at high redshift.
This is because the definition of a cluster purely based on mass ignores other important characteristics of clusters, such as whether a hot intracluster
medium has formed.
In practice, this is important only at z  1.5, as above that redshift, protoclusters with  > 10^14  constitute a negligible
fraction of the population.

Since we know the full dark matter halo merger history in the simulation, we can unambiguously define which galaxies are protocluster
members using the . Since this is not possible for the real universe, we test spatially based criteria
to select the protocluster galaxies considered to be members of a given protocluster. 

First, we estimate the effective radius of each structure. <cit.> defined this as the second moment of the member galaxies' positions weighted by their halo masses. Instead, for simplicity when working with a mock galaxy catalog, we define the effective radius as follows:

    R_e = √(1/M_⋆,  tot∑_i M_⋆,i( x_i -  x_c)^2 ),

where M_⋆,i is the stellar mass of a member galaxy located at x_i, M_⋆,  tot is the sum of all M_⋆,i, and x_c is the center of mass of the protocluster at its redshift. 
Another important radial scale, which we will use to define core galaxies, is the virial radius for the
most-massive progenitor halo of a given protocluster, R_200c. We show the evolution of R_e and R_200c as a
function of redshift for the three descendant types in Figure <ref>. 

To investigate potential environmental effects, which should be stronger in the central, highest-density
regions of protoclusters, we distinguish protocluster cores and outskirts.
Core galaxies are all galaxies located within a sphere of radius R_200c centered at the position
of the central (most-massive) galaxy.
We define protocluster outskirts galaxies as all galaxies enclosed in a sphere centered at the structure's center of mass with a radius 2 R_e, excluding core galaxies.[We have confirmed that our results are qualitatively insensitive to the definitions of `core' and `outskirts.']
Figure <ref> shows that for z  1, R_200c < R_e, so this definition of outskirts is sensible. At lower redshift, it would no longer work. Thus, we will focus our analysis at z ≳ 1.5 to avoid the difficulties of mixing core and outskirt galaxies that arises with the spatially based criterion.

To test the ability of the spatially based criterion to select member galaxies,
we compute the purity and completeness of member selection for protocluster cores and outskirts as defined above.
We quantify the purity and completeness as a function of redshift for the three cluster progenitor classes.
We present the results in Figure <ref>.



Figure <ref> shows that as expected, when we use a larger radius (2× R_e) to select the member galaxies, we
obtain higher completeness but lower purity. For this choice of radius, the purity is ∼50-60 per cent at z∼1.5, and the completeness is 60 per cent. For R_e, the purity is ∼60-80 per cent, but
the completeness is 40 per cent. At higher redshift, the completeness
for 2R_e is 90 per cent, whereas for R_e, it is at most
∼50 per cent. We thus opt to use a radius equal to 2R_e to define
protocluster `outskirts', but we have confirmed that the results are
qualitatively the same when R_e is used.




§ RESULTS
 

In the following sections, we explore the dependence of protocluster galaxy populations on redshift and environment. 



 §.§ An excess of SMGs in protocluster cores
 



We first consider the fraction of submm-bright galaxies in different environments to investigate the connection between SMGs
and protoclusters. We analyze mock galaxies with S_870 greater than two different flux limits, 0.5 mJy or 1.5 mJy. The lower limit is motivated by the flux density of the faintest submm-detected members of the SPT2349-56 protocluster <cit.>, as measured using ALMA. 
First, for each protocluster,
we quantify the numbers of SMGs in the core and in the outskirts brighter than a given flux density. Then, we divide by the total number of galaxies in the protocluster core and outskirts to compute the submm-bright fractions for each region, N_ gal(S_870≥ x)/N_ tot, where x is 0.5 mJy or 1.5 mJy. We also compute this quantity for the field (i.e. all galaxies in the mock in a
given redshift bin that do not reside in protoclusters).
The panels of Figure <ref> show how the submm-bright fraction depends on redshift
for the different protocluster types. The top row shows
the results for a flux cut of S_870 > 0.5 mJy, whereas the bottom shows the results for a flux density cut of 1.5 mJy.

The most notable trend in Figure <ref> is that at z  1.5, the submm-bright fraction is higher in protocluster
cores than in both protocluster outskirts and the field.
We have confirmed that this result is qualitatively insensitive to the definition of `cores' (e.g. using R_500c instead of R_200c).
The redshift at which the submm-bright fraction for protocluster cores peaks is higher for more massive clusters.
The peak of N_ gal(S_870≥ 0.5 mJy)/N_ tot for Coma-type protoclusters lies at a higher redshift than the limit of the mock (z>5). In the case of Virgo-type protoclusters, the peak submm-bright fraction is at z ∼ 4, while for Fornax-type protoclusters, it is at z ∼ 3.5. On the other hand, the slope of this fraction for redshifts lower than the peak is higher for low mass cluster progenitors. This implies that the redshift range of the submm phase of protocluster cores is higher for more massive systems.

Galaxies in the outskirts of protoclusters present a slightly higher fraction of SMGs compared to the field over the entire redshift range, but the value is always much closer to that of the field than it is to that for cores. As in the case of the protocluster cores, the redshift at which the fraction of SMGs in protocluster outskirts peaks is slightly higher for the progenitors of more massive clusters.

We find similar trends in the evolution of submm-bright fractions and their environmental dependence for the two different flux density limit thresholds (S_870>0.5 mJy and S_870>1.5 mJy).
Notice that the N_ gal(S_870≥ 1.5 mJy)/N_ tot values for the field and protocluster outskirts are close to zero.
For both flux density cuts, the values for the submm-bright fractions would increase if our model reproduced the total submm
number counts, but we expect that the differences are robust;
see Section <ref> for further discussion.
Given the paucity of sources with S_870 > 1.5 mJy, for the rest of this work, we only consider the S_870>0.5 mJy
definition of `submm-bright'.



We have shown that a random galaxy in a protocluster core is more likely to be submm-bright than in protocluster outskirts or
the field, but it is also worth considering the probability that a random (observationally-identified) SMG is located in a protocluster core.
Field galaxies represent 89 per cent of the mock sample, therefore, although protocluster core members are more likely
to be SMGs, it does not necessarily follow that most SMGs at a given redshift are in located in protocluster cores.
To address this question, we quantify the fraction of SMGs located in different environments as a function of S_870 flux density and redshift in Figure <ref>. At all redshifts considered, at low flux densities, most SMGs are located in the
field, whereas above a transition flux density, most SMGs are located in protocluster cores. This transition flux density decreases
with redshift, ranging from S_870∼ 3 mJy at z ∼ 2 to S_870∼ 1.5 mJy at z ∼ 4.
Protocluster outskirts (as defined in this work, i.e.  galaxies that will reside in clusters at z = 0 but are not in the most massive progenitor halo at the epoch of observation) never dominate the population: at all redshifts and flux densities considered, the fraction of
SMGs in protocluster outskirts is 20 per cent. However, we caution that the above details (e.g. the transition flux)
may be affected by the underprediction
of the overall submm number counts; see Section <ref>.



 §.§ Why is there an excess of submm-bright galaxies in protocluster cores?
 



In this section, we seek to understand the physical reason(s) behind protocluster cores exhibiting a higher submm-bright fraction compared to both protocluster outskirts and the field. As noted above, one potential explanation for the excess of submm-bright sources in protocluster cores is that such environments may have an excess of starbursts due to more frequent interactions and mergers (see
 and references therein). 
It is also possible that this excess
is simply due to a relative overabundance of massive galaxies and thus `oversampling' of the high-mass end of the star formation main sequence (SFMS). A third possibility is that galaxies in protocluster cores tend to be
more dust-rich than those in other environments.

To investigate the first possibility, in Figure <ref>, we quantify the difference between the median SFR of galaxies in the field and those of galaxies in protocluster cores (top) and outskirts (bottom) as a function of stellar mass at z=2, 3, and 4. As in previous plots, the different columns correspond to the three protocluster types considered here. For more detail, the full SFR-M_⋆ distributions for the same redshifts and protocluster types are shown in the Appendix (Figure <ref>).  

From the top row of Figure <ref>, we see that galaxies in protocluster cores above a threshold
stellar mass tend to lie on or slightly above the SFMS defined by field galaxies. 
Below this threshold stellar mass, core members have SFRs that tend to be lower
than those of field galaxies by as much as ∼ 1 dex.
The stellar mass threshold depends on redshift and protocluster type. At z ∼ 4, the stellar mass threshold is
log(M_⋆/) ∼ 10.2. At z ∼ 3, this value is shifted towards higher stellar masses, log(M_⋆/) ∼ 10.7, and at z ∼ 2, it
its ∼ 11.7. At all redshifts considered,
the difference between the median SFRs of field galaxies and those in protocluster cores is greatest at the lowest masses considered.
These results clearly show that the first potential explanation for the excess of SMGs in protocluster cores, that
dense environments feature a greater starburst fraction, does not hold for our model. This is further reinforced by examination
of Figure <ref> in the Appendix.

For galaxies in protocluster outskirts (bottom row of Figure <ref>), at z ∼ 3 and 4, outskirts members typically
lie near the field SFMS. 
At z ∼ 2, low mass (log(M_⋆/) ≲ 10.5) galaxies have SFRs that are suppressed by at most a factor of 2
relative to the field, whereas higher-mass member galaxies have SFRs similar to those of field galaxies. 



We now turn to the second possible explanation, that protocluster cores might exhibit an excess of high-mass galaxies relative to
protocluster outskirts and the field.
To examine this hypothesis, we present the stellar mass probability density functions (PDFs) of core, outskirts, and field galaxies at different redshifts (z∼2, 3, and 4; Δ z = 0.25) for the three protocluster types (Fornax-, Virgo-, and Coma-type progenitors) in Figure <ref>.
The most notable trend is that protocluster cores exhibit an excess of high-mass galaxies (M_⋆ 10^10.5),
i.e. a flatter stellar mass function (SMF), relative to both protocluster outskirts and the field at all redshifts and for all protocluster types.
The difference is more pronounced at higher redshift.
Note that the stellar mass distribution of galaxies in Coma-type protoclusters at z∼4 exhibits a bump at log(M_⋆ / ) ∼ 10.7. This is likely due to statistical fluctuations owing to the small sample of galaxies with M_⋆ 10^10.5 in Coma-type protoclusters
at z ∼ 4. 

The SMFs for the field and protocluster outskirts are similar, though protocluster outskirts exhibit a slightly flatter
SMF than the field. This difference is most pronounced for the outskirts of Coma-type protoclusters
(i.e. the highest overdensities on average) and for Virgo-type protoclusters at z ∼ 2.
Thus, both distributions become different as the redshift decreases.



What is the origin of this excess of high-mass galaxies in protocluster cores? It may be due to baryonic processes that operate
preferentially in protocluster cores, but it could also be a result of hierarchical growth of dark matter halos.
To examine the latter possibility, in Figure <ref>, we plot the PDFs of v_ max values (as a proxy for
halo mass) for galaxies in the three different environments.
We see the same qualitative trends as for the SMF: protocluster cores exhibit flatter v_ max
distributions than both protocluster outskirts and the field, and the difference is more pronounced for Coma-type
protoclusters than for Fornax-type ones (i.e. for higher overdensities). The difference increases with decreasing
redshift. For Coma-type protoclusters and Virgo-type ones at z ∼ 2, the outskirts exhibit slightly flatter v_ max
distributions than the field but are more similar to the field than to protocluster cores. The difference
again increases with decreasing redshift. The results suggest that an excess of high-mass dark matter halos in protocluster
cores results in an excess in high-mass galaxies and thus a higher SMG fraction in cores (as long as the quenched
fraction is low).[We have confirmed that the stellar-to-halo mass relation at each of the redshifts considered is insensitive to environment.]



Finally, we explore the third possibility, that galaxies in
protocluster cores are more dust-rich than galaxies in protocluster
outskirts and the field (which, for fixed SFR, stellar mass, and
redshift, would yield a colder effective dust temperature and thus
higher submm flux density). In Figure <ref>, we
plot the PDFs of the dust-to-stellar-mass
ratio for galaxies in protocluster cores, protocluster outskirts,
and the field for the three different protocluster types at
z ∼ 2, 3, and 4. We see that the distributions are similar,
with a peak at the expected value of ∼ 0.01. Protocluster
cores exhibit a slightly enhanced tail to lower dust-to-stellar
mass ratios, but this tail constitutes a small fraction of the
overall population. We conclude that the dust content is almost
independent of environment, and thus the third potential explanation
does not explain the excess of SMGs in protocluster
cores in our model.



 §.§ Optical counterparts of SMGs
 



We now consider the relationship between submm- and optically selected populations in different environments in our model.
As shown by <cit.>, just 4 out of 14 submm sources in the SPT2349-56 protocluster were observed in optical bands. This highlights the difficulties of identifying the most highly dust-attenuated sources at short wavelengths (see  and recent observational studies concerning optically faint SMGs, e.g. ). In this section, we discuss the augmentation of our mock catalog with predictions for optical photometry and present the fraction of submm-bright sources in our catalog that would have  counterparts in deep optical imaging.

Typically, for observational data, photometric catalogs are constructed by making aperture measurements at the same positions in multiple bands; these positions are defined by a reference image, which is commonly a χ^2 detection image constructed using several bands (; see  for examples). On the other hand, the Hyper Suprime Cam Subaru Strategic Program (HSC-SSP; ) constructs the reference image for source detection using the i-band.

A common practice when using optical data is implementing a magnitude limit to avoid contamination of low signal-to-noise objects.
For instance, <cit.> and <cit.> selected samples of Lyman Break Galaxies using a 5σ magnitude limit in the i-band (also requiring a 3 σ detection in the r-band), which corresponds to 25.9 mag and 26.2 mag, respectively, for those studies. Here, we select optical sources from our mock catalogs using an i-band magnitude limit of 26 mag, similar to the limit applied in these works.

We analyze the fraction of SMGs (S_870≥ 0.5 mJy) that would also be detected in the optical (i ≤ 26 mag). In Figure <ref>, we explore how this fraction depends on redshift and stellar mass for galaxies in the field, protocluster outskirts, and protocluster cores. Here, we do not show the distribution separated by protocluster type because we did not find any trend with this property. As expected, the probability of finding an optical counterpart for an SMG decreases with increasing redshift, since distant sources appear fainter. 
At high redshift (z ≳ 3.0), within a fixed redshift bin, there is an anti-correlation between the fraction of SMGs with optical counterparts and stellar mass, i.e. more-massive
SMGs are less likely to have optical counterparts compared to lower-mass SMGs due to dust obscuration increasing with stellar mass (see the next subsection). This trend appears to be independent of the environment. We note that for a given redshift bin
at high redshift (z ≳ 3.0), the overall optical counterpart probability is slightly lower for protocluster core galaxies compared to those in protocluster outskirts, and the fraction for protocluster outskirts is slightly lower than that for field galaxies. 



 §.§ Fraction of dust-obscured sources
 




To understand the above results, it is worthwhile to investigate the fraction of SFR that is obscured.
Following the definition of <cit.>, we consider dust-obscured sources as all mock galaxies with obscured fraction f_ obs≥ 0.5, where f_ obs = SFR_ IR/SFR. SFR_ IR and SFR denote the star formation rate derived from the total galaxy IR luminosity (light absorbed by dust; see Section <ref>) and the total star formation
rate, respectively.
To obtain SFR_ IR, we use the conversion of <cit.>: 

    SFR_ IR (  yr^-1) = 3.0× 10^-44  L_ IR ( erg  s^-1).

The conversion factor is obtained assuming a <cit.> IMF. However, there is no significant difference compared to a <cit.> IMF <cit.>.

In Figure <ref>, we show the fraction of dust-obscured galaxies as a function of redshift for galaxies in protocluster cores, protocluster outskirts, and the field.
The different rows correspond to different protocluster types. In each panel, for protocluster cores and outskirts, lines indicate the medians taken over the population
of protoclusters in the mock, and the shaded regions denote the 25th-75th percentile range. The line for the field indicates the value for the entire field sample at a given
redshift.

Unlike the redshift evolution of the fraction of submm sources (Figure <ref>), the fraction of dust-obscured galaxies does not statistically depend on redshift or protocluster type. However, it is significantly higher in protocluster cores (N_ gal(f_ obs≥ 0.5)/N_ tot∼ 0.65) compared to protocluster outskirts and the field. In the latter two environments, the fractions of dust-obscured objects are similar (N_ gal(f_ obs≥ 0.5)/N_ tot∼ 0.40).
The reason that the fraction of SMGs depends on redshift but the obscured fraction does not is that the former depends on the absolute values of the SFR and dust mass, whereas the
latter does not. At lower redshifts, there are fewer galaxies with high SFRs (100 yr^-1) because at fixed mass, the SFR decreases with decreasing redshift due
to the redshift evolution of the normalization of the SFMS and quenching of high-mass galaxies (`downsizing').

In order to understand the obtained trend in Figure <ref>, in Figure <ref>, we present the median value of the obscured fraction (f_ obs) versus stellar mass in seven redshift bins from z = 0.2 to 4.5. At all redshifts, the obscured fraction increases with stellar mass, as suggested by some observational studies <cit.>. This trend is also seen in versions of  with explicit dust modelling, which show a strong correlation between dust-to-gas ratio and stellar mass at all redshifts <cit.>. Moreover, at fixed mass, galaxies at higher redshifts exhibit higher f_ obs. For instance, the stellar mass threshold above which 50 per cent of galaxies are classified as dust-obscured (f_ obs≥ 0.5) is log(M_⋆/) = 10.15, 10.04, 9.88, 9.67 at z ∼ 1, 2, 3, and 4, respectively. 



§ DISCUSSION
 



 §.§ Why do protocluster cores differ from less-overdense regions?
 

We have shown that in the  model, galaxies in protocluster cores are more likely to be submm-bright and dust-obscured than galaxies in
protocluster outskirts or the field. Interaction-driven starbursts are not responsible for the
excess of SMGs in protocluster cores. Moreover, there is no clear correlation between environment and inferred dust-to-stellar mass ratios in the model. Instead, the reason that protocluster cores have a higher SMG fraction is simply that they exhibit an excess of high-mass galaxies relative to less-overdense
regions. The submm-bright fraction decreases with decreasing redshift as galaxies at the high-mass end of the SFMS are quenched and thus are
no longer submm-bright.
The relative excess of high-mass galaxies in protocluster cores also results in a higher fraction of dust-obscured galaxies because the fraction of star formation that is obscured increases
with stellar mass. We furthermore showed that protocluster cores have a `top-heavy' dark matter halo mass function relative to less-overdense environments.

Together, these results imply that in our model, the excess of SMGs in protocluster cores is driven by hierarchical growth of dark matter substructure, not baryonic processes.
At fixed redshift, many properties of galaxies (e.g. gas, dust, and black hole masses; SFRs; metallicities) scale with stellar mass, which, in turn,
scales with halo mass. Thus, if the halo mass function depends on environment, so too will distributions of the aforementioned galaxy properties
even if all baryonic processes are independent of environment. Put otherwise, even if a galaxy `knows' only about its own dark matter halo,
the galaxy population can still exhibit significant environmental dependencies purely due to the dependence of the halo mass function on environment.
These environmental dependencies may give a false impression that processes such as merger-induced starbursts, tidal interactions, and ram pressure stripping
are important when in reality the dark matter `backbone' alone causes the differences.

There is some observational support for the above picture. First, we will discuss whether there is observational evidence
that suggests protoclusters have a greater starburst fraction than the field.
<cit.> find an elevated starburst fraction in a z = 2.51 X-ray-detected cluster. <cit.> demonstrated
that in the z ≈ 2.5 protocluster USS 1558-003, massive galaxies
lie along the SFMS, whereas lower-mass galaxies have elevated SFRs.
<cit.> show an enhancement in the SFR-stellar mass relation of HAEs in the most
overdense regions of a z = 2.51 protocluster.
<cit.> find that at 2 < z < 5, the average SFR increases with galaxy overdensity and that this trend
is primarily driven by a relative excess of high-mass in more-overdense environments. <cit.> show
that the SFRs of members of the z = 2.16 Spiderweb protocluster are consistent
with the SFMS. SPT2349-56 <cit.> and the `Distant Red Core' (DRC) <cit.> are considered
two `poster child' high-redshift protocluster cores that are rich in SMGs. In both cases, the member galaxies lie near the SFMS, i.e. there is no evidence
that the member SMGs are starbursts <cit.>.
Given the above, there is not
yet a clear observational consensus
about whether SMGs in protoclusters
tend to lie about the SFMS.

What do observations say about the SMF in protoclusters?
Studies of the SMF in lower-redshift clusters have yielded conflicting conclusions <cit.>. 
<cit.> analysed HAEs in a sample of z ∼ 2 protoclusters, finding top-heavy SMFs
in the most overdense subregions of the protoclusters.
<cit.> analysed the SMFs of 14 protoclusters at 2.0 < z < 2.5 using data from the COSMOS2020
catalog <cit.>. They found that the SMFs of star-forming galaxies do not differ from the field SMF,
whereas quiescent galaxies exhibit a flatter SMF than in the field.
<cit.> find an excess of high-mass galaxies in overdense environments at z ∼ 3.3.
JWST observations should help better characterise the SMF in (proto)clusters and resolve this debate. For example,
based on JWST data, <cit.> show that the z = 2.51 cluster CLJ1001 exhibits an excess of massive galaxies in the
cluster core.

What about simulations?
<cit.> investigated the environmental dependence of the stellar mass-halo mass relation in different environments
using cosmological hydrodynamical simulations. They found that the stellar-to-halo mass ratios of central galaxies in
overdense environments were higher than those in less-dense environments. They suggested that the difference is due to
earlier formation times, more frequent interactions at early times, and a greater number of filaments fueling centrals
in overdense environments. <cit.> noted that although z ∼ 1.5 clusters have higher fractions of quenched
galaxies than the field,
massive quenched galaxies around this redshift have ages that appear to be independent of environment. To understand
this puzzle, they investigated the halo properties of massive quenched galaxies in two cosmological hydrodynamical simulations.
They found that the distribution of v_ max for cluster members is skewed to higher values relative to that for field galaxies,
similar to the results presented in this work. They conclude that secular processes drive the environmental excess of massive quenched
galaxies in high-redshift (proto-)clusters, analogous to what we have argued for the excess of submm-bright galaxies in protocluster
cores.

Further comparisons of the SFR-stellar mass relations, SMFs, and dust-to-stellar mass ratios
between observed protoclusters and the field will help test the physical picture we have proposed and deepen our understanding
of the role of environment in protoclusters.



 §.§ Implications for using SMGs as tracers of protoclusters
 

SMGs are commonly used as beacons of protoclusters <cit.>.
They are intrinsically very luminous, and due to the negative k-correction
in the submm, a given SMG is as easily detected in the epoch of reionisation as it is at z = 1. These aspects make them useful tracers.
Moreover, their high masses imply that SMGs are preferentially associated with overdensities. Indeed, we see that this is the case in our model: Figure <ref>
shows that the majority of bright SMGs reside in protocluster cores.
This plot implies that if one finds even a single bright SMG, it is likely that one has
identified a protocluster in the sense that the z = 0 descendant of the SMG will reside in a cluster (see also ).[We caution that
the exact threshold above which SMGs
are preferentially located in protoclusters may be affected by our model's underprediction of the submm number counts; see Section <ref>
for details.]

SPT0311-58 <cit.> is an example of this phenomenon: initial ALMA observations resolved this
z = 6.9 source to be a merger of two galaxies, one of which is a bright SMG (S_870≈ 15.9 mJy; the companion has 
S_870≈ 2.9 mJy). The inferred dark matter halo mass suggested that this is one of the highest-mass
halos expected under LCDM, thus representing a very rare peak in the matter distribution <cit.>.
<cit.> found that the surrounding field hosts an excess of SMGs.
Recent JWST integral field unit observations revealed ten additional galaxies within a (17 kpc)^2 field of view
<cit.>. Taken together, these data suggest that SPT0311-58 resides in a protocluster.

However, we stress that even if an SMG is in a protocluster according to our theoretical definition,
it does not necessarily follow that the SMG is located in an overdensity at the epoch of observation.
Whether one should see an overdensity around bright SMGs will depend on the redshift, the flux of the SMG,
and the tracer employed (and potentially other factors). Understanding the connection between SMGs and overdensities
of various galaxy populations will require careful modeling. We will investigate this topic in detail in future work.

Our model suggests that bright SMGs are an effective means to identify protoclusters in terms of purity. But, what about completeness? I.e. what fraction of
protoclusters host SMGs? We have not investigated this question quantitatively using the present model because the answer would certainly be affected
by the underprediction of the submm number counts. Nevertheless, the model yields some insight that should be robust. We return to Figure <ref>,
which shows the fraction of galaxies that are submm-bright versus redshift in different environments. Recall that the submm-bright fraction is significantly elevated
in protocluster cores at high redshift, but the enhancement decreases with decreasing redshift due to `downsizing', i.e. the mass above which
galaxies are predominantly no longer star-forming decreases with decreasing redshift. This suggests that SMGs are increasingly incomplete
tracers of protoclusters at lower redshift. This was previously argued by <cit.>, who applied a semi-empirical model in which the galaxy properties are
determined solely by halo mass and redshift to an N-body simulation. We find that this conclusion holds in a SAM that includes
models for environmentally dependent processes (e.g. mergers, ram pressure stripping).



 §.§ Sensitivity of results to the overall underprediction of the submm number counts
 

As shown in Figure <ref>, our model underpredicts the overall submm number counts by a factor of a few. Historically, theoretical
models that assume a standard IMF have underpredicted submm number counts <cit.>,
although the magnitude of the discrepancy has decreased considerably as models have been improved.
To the best of our knowledge, no model can simultaneously
match both the observed submm number counts and the number density of massive quenched galaxies <cit.>.
If the submm counts predicted by our model were consistent with observations, some of the results presented here would be affected.
Importantly, for a fixed flux density threshold, the fraction of SMGs would increase.

However, many of our results
are likely insensitive to this underprediction. Given that the differences between protocluster cores and other environments are primarily driven
by differences in the halo mass function rather than baryonic processes, these differences should be robust to any changes to model parameters
that would be necessary to reproduce the total submm counts.
Moreover, if the underprediction is associated with the treatment of merger-induced starbursts, it is likely that the submm-bright fractions for
protocluster cores would be boosted more than those for the field and protocluster outskirts, further enhancing the difference
between cores and other environments.

Still, it would of course be better if our model predictions better agreed with the observed submm number counts. In subsequent work, we will explore whether
it is possible to simultaneously match the submm number counts and number density of massive quenched galaxies with 
by using parameter values different than those employed here. Should we succeed, we will be able to revisit the analysis presented here
and check whether our primarily results are indeed robust.




§ SUMMARY
 

Using a mock catalog constructed by applying the <cit.> version of the  SAM to the  simulation and then employing the <cit.> scaling relations to predict submm
flux densities, we have investigated the relationship between SMGs and galaxy protoclusters. Our main results are the following:  

    
  * By exploring the dependencies on redshift, environment, and protocluster descendant mass, we found that protocluster core galaxies experience a submm-bright phase, whose peak and duration correlate with the z=0 mass and flux density limit (Figure <ref>). At z  2, protocluster cores exhibit a higher submm-bright fraction than do
    galaxies in protocluster outskirts or the field.
    
    
  * We show that the primary driver of this excess of SMGs in protocluster cores is differences in the halo mass functions in different environments: protocluster cores exhibit a more `top-heavy'
     halo mass function (Figure <ref>), which results in an excess of massive star-forming galaxies relative to other environments (Figure <ref>).
     The excess of SMGs in protocluster cores is not due to a higher starburst fraction (Figure <ref>) or differences in the dust contents of galaxies in different environments
     (Figure <ref>), as protocluster cores are similar to other environments in terms of these two properties.
    
    
  * Most SMGs with S_870≥ 0.5 mJy are in the field rather than protoclusters, but bright SMGs are preferentially located in protocluster cores (Figure <ref>).
    
    
  * Independent of environment, the fraction of SMGs that have optical counterparts decreases with increasing redshift and with stellar mass (Figure <ref>).
    
    
  * Our model predicts a higher fraction of dust-obscured sources in protocluster cores compared to protocluster outskirts and the field independent of redshift.
    (Figure <ref>). The obscured fraction increases strongly with stellar mass and more weakly with redshift (Figure <ref>).
    


Our results add to our understanding of the connection between SMGs and protoclusters. Our mock catalog can be used to optimize the identification, characterization, and interpretation of protoclusters in existing and future surveys.



§ ACKNOWLEDGEMENTS


This work was initiated during the CCA Pre-doctoral Program.
PA-A thanks the Coordenaçõ de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES), for supporting his PhD scholarship (project 88887.596140/2020-00). 
RKC was funded by support for program #02321, provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127. RKC is grateful for support from the Leverhulme Trust via the Leverhulme Early Career Fellowship.
The Flatiron Institute is supported by the Simons Foundation. 
MCV acknowledges the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for supporting his PhD. LSJ acknowledges the support from CNPq (308994/2021-3)  and FAPESP (2011/51680-6). DR is supported by the Simons Foundation.








astropy <cit.>,  L-Galaxies <cit.>





§ SFR – STELLAR MASS RELATION
 


Figure <ref> shows the relationship between SFR and stellar mass for galaxies in the three different environments. 
We see that for all redshifts and protocluster types, the distributions of galaxies in this plane are independent of environment
(as already indicated by Figure <ref>). In particular, galaxies in protocluster outskirts and cores seem to
follow the same (redshift-dependent) SFMS as field galaxies. The most notable difference is that in each panel, there are colored
points at the high-mass tip of the SFMS beyond the region populated by field and protocluster outskirts galaxies. These indicate
that protocluster cores host very high-mass star-forming galaxies that are not found in other environments.





aasjournal



 Paper Title: Tip of the Red Giant Branch Distances with JWST. II. I-band Measurements in a Sample of Hosts of 9 SN Ia Match HST Cepheids.






0000-0002-8623-1082]Siyang Li
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA

0000-0002-5259-2314]Gagandeep S. Anand
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

0000-0002-6124-1196]Adam G. Riess
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA


Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

0000-0001-9420-6525]Wenlong Yuan
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA

0000-0003-3889-7709]Louise Breuval
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA

0000-0002-1775-4859]Lucas M. Macri
NSF's NOIRLab, 950 N Cherry Ave, Tucson, AZ 85719, USA

0000-0002-4934-5849]Daniel Scolnic
Department of Physics, Duke University, Durham, NC 27708, USA

0000-0002-1691-8217]Rachael Beaton
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA

0000-0001-8089-4419]Richard I. Anderson
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL),
 Observatoire de Sauverny, 1290 Versoix, Switzerland

§ ABSTRACT 

The Hubble Tension, a >5σ discrepancy between direct and indirect measurements of the Hubble constant (H_0), has persisted for a decade and motivated intense scrutiny of the paths used to infer H_0. Comparing independently-derived distances for a set of galaxies with different standard candles, such as the tip of the red giant branch (TRGB) and Cepheid variables, can test for systematics in the middle rung of the distance ladder. The I band is the preferred filter for measuring the TRGB due to constancy with color, a result of low sensitivity to population differences in age and metallicity supported by stellar models. We use James Webb Space Telescope (JWST) observations with the maser host NGC4258 as our geometric anchor to measure I-band (F090W vs F090W-F150W) TRGB distances to 7 hosts of 9 Type Ia supernovae (SNe Ia) within 27 Mpc: NGC1448, NGC1559, NGC2525, NGC3370, NGC3447, NGC5584, and NGC5643. We compare these with Hubble Space Telescope (HST) Cepheid-based relative distance moduli for the same galaxies and anchor. We find no evidence of a difference between their weighted means, 0.01 ± 0.04 (stat) ± 0.04 (sys) mag. We produce fourteen variants of the TRGB analysis, altering the smoothing level and color range used to measure the tips to explore their impact.  For some hosts, this changes the identification of the strongest peak, but this causes little change to the sample mean difference producing a full range of 0.01 to 0.03 mag, all consistent at 1σ with no difference. The result matches past comparisons of I-band TRGB and Cepheids when both use HST.  SNe and anchor samples observed with JWST are too small to yield a measure of H_0 that is competitive with the HST sample of 42 SNe Ia and 4 anchors; however, they already provide a vital systematic crosscheck to HST measurements of the distance ladder.






§ INTRODUCTION
 

The `Hubble Tension' refers to a 5-6 σ discrepancy between direct measurements and cosmological inference of the present expansion rate of the Universe, parameterized as the Hubble constant (H_0). Currently, the “gold standard” method to directly measure H_0 utilizes a three-rung ladder to obtain distances to galaxies in the Hubble flow. This method uses geometric distances derived from parallaxes (such as those from ), water masers <cit.>, and detached eclipsing binaries <cit.> to calibrate the luminosities of primary distance indicators such as Cepheid variables (first rung). This calibration is in turn used to measure distances to galaxies that host both Cepheids and Type Ia supernovae to calibrate the luminosities of the latter (second rung), which are then finally used to measure distances to galaxies in the Hubble flow to measure H_0 (third rung). The Supernovae, H_0, for the Equation of State (SH0ES) team, for instance, has used this method to measure H_0 = 73.17 ± 0.86 km s^−1 Mpc^−1 <cit.>. The cosmological inference uses the cosmic microwave background together with a cosmological model such as ΛCDM to infer the present expansion rate. <cit.> used this approach to derive H_0= 67.36 ± 0.54 km s^−1 Mpc^−1, a >5σ difference from the value obtained by <cit.>. Several independent teams and measurements using a wide range of distance indicators have also yielded measurements in tension with those from Planck. No precise direct measurement of H_0 has yielded a value that is lower than that from Planck (see compilations in ). This tension suggests a possible need to revise the standard ΛCDM model, though efforts continue to search for unidentified systematics in the measurements at any level[For an extensive list of studies that have studied systematics related to the tension, we refer the reader to <https://djbrout.github.io/SH0ESrefs.html>.]. 

Independent distance measurements to the same galaxies using multiple standard candles offers one of the best ways to ensure systematics are well accounted for and understood. The tip of the red giant branch (TRGB) refers to the maximum luminosity reached by first-ascent red giant stars before transitioning onto the horizontal branch, and has been used as a standard candle to measure distances <cit.>, and the Hubble constant <cit.>. The TRGB can thus be used as a means to crosscheck systematics of other standard candles, such as Cepheid variables.

The TRGB is commonly measured in the I band, or the Hubble Space Telescope (HST) F814W and James Webb Space Telescope (JWST) F090W equivalents, where the magnitude of the TRGB exhibits the smallest metallicity (and hence color) dependence <cit.>. While it is possible to measure the TRGB in the NIR to take advantage of brighter magnitudes, doing so requires careful calibration of the TRGB's color dependence <cit.> where it rises to ∼ one magnitude per magnitude of measured color, introducing additional systematics. In this study, we focus on measuring the TRGB in the JWST F090W filter, which is most similar to I and F814W used with HST.

The launch of JWST has opened up the possibility of performing extensive crosschecks of Cepheids, TRGB, and other standard candles in unprecedented resolution. In particular, the dual-module configuration of the JWST NIRCam instrument allows for at least three standard candles (Cepheids, TRGB, and Carbon stars) to be simultaneously observed with one set of observations - see for instance, JWST programs GO-1685 <cit.>, GO-1995 <cit.>, and GO-2875 <cit.>, among others.
In a previous study, <cit.> (Paper I), we measured the TRGB with JWST in the maser host NGC4258, which serves as one of four geometric calibrators of the distance ladder, and presented measurements in 2 SN Ia hosts (NGC1559 and NGC5584). The derived luminosity of the TRGB in JWST F090W in Paper 1 matched that independently determined by <cit.>, also in F090W, to ± 0.01 mag, indicating a reliable foundation for distance measurements with JWST in SN Ia hosts.
Here we study an expanded sample using JWST observations of 7 hosts of 9 SNe Ia from Cycle 1 program GO-1685 <cit.> and Cycle 2 GO-2785 <cit.> to measure TRGB-based distances to these galaxies and test their consistency with HST Cepheid-based distances to those same galaxies.



§ DATA
 

We retrieve JWST F090W and F150W observations of NGC1448, NGC1559, NGC5584, and NGC5643 from GO-1685 <cit.> and NGC2525, NGC3370, and NGC3447 from GO-2875 <cit.> using the Barbara A. Mikulski Archive for Space Telescopes (MAST)[<https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html>]. We list observation details in Table <ref> and show galaxy footprints in Fig. <ref>. For NGC2525, we found that the images corresponding to the fourth (and final) dither for each filter were noticeably blurred. Upon further investigation, we found that the guide star had wandered onto some bad pixels in the Fine Guidance Sensor. We thus excluded these dithers from our analysis and generated our own stage 3 image from only the first three dithers for use of mutual image alignment of the underlying stage 2 images with DOLPHOT. 






cccccccc

Galaxy     Program     Observation Number     Observation Date     Filters     Exposure Time [s]      Version
NGC1448     GO-1685     13     2023-08-02     F090W/F277W     418.7 x 4     1215 

NGC1448     GO-1685     13     2023-08-02     F150W/F277W     526.1 x 4     " 

NGC1448     GO-1685     14     2023-18-02     F090W/F277W     418.7 x 4     " 

NGC1448     GO-1685     14     2023-18-02     F150W/F277W     526.1 x 4     " 

NGC1559     GO-1685     1     2023-06-30     F090W/F277W     418.7 x 4     " 

NGC1559     GO-1685     1     2023-06-30     F150W/F277W     526.1 x 4     " 

NGC1559     GO-1685     2     2023-07-15     F090W/F277W     418.7 x 4     " 

NGC1559     GO-1685     2     2023-07-15     F150W/F277W     526.1 x 4     " 

NGC5584     GO-1685     9     2023-01-30     F090W/F277W     418.7 x 4     "  

NGC5584     GO-1685     9     2023-01-30     F150W/F277W     526.1 x 4     "  

NGC5584     GO-1685     10     2023-02-21     F090W/F277W     418.7 x 4     "  

NGC5584     GO-1685     10     2023-02-21     F150W/F277W     526.1 x 4     "  

NGC5643     GO-1685     11     2023-07-07     F090W/F277W     311.4 x 4     "  

NGC5643     GO-1685     11     2023-07-07     F150W/F277W     418.7 x 4     "  

NGC5643     GO-1685     12     2023-07-22     F090W/F277W     311.4 x 4     "  

NGC5643     GO-1685     12     2023-07-22     F150W/F277W     418.7 x 4     "  

NGC2525     GO-2875     1     2023-04-23     F090W/F277W     472.4 x 3     1225 

NGC2525     GO-2875     1     2023-04-23     F150W/F277W     526.1 x 3     " 

NGC3370     GO-2875     2     2023-06-28     F090W/F277W     472.4 x 4     1234 

NGC3370     GO-2875     2     2023-06-28     F150W/F277W     526.1 x 4     " 

NGC3447     GO-2875     12     2023-05-24     F090W/F277W     472.4 x 4     "  

NGC3447     GO-2875     12     2023-05-24     F150W/F277W     622.7 x 4     "  

Summary table for the JWST NIRCam observations of NGC1448, NGC1559, NGC2525, NGC3370, NGC3447, NGC5584, and NGC5643 used in this study. Columns from left to right are: galaxy name, program number, observation number, observation date, filters, exposure time per dither, and context () file version.





§ PHOTOMETRY
 

We follow the general procedures outlined by previous works from our team for photometric reductions <cit.>. In detail, we perform PSF photometry[The photometry for this study is available publicly upon publication in a Zenodo repository, DOI: 10.5281/zenodo.13131990.] using the DOLPHOT[<http://americano.dolphinsim.com/dolphot/>] software package <cit.>, together with the latest (February 2024) version of the JWST/NIRCam module <cit.>. We use the stage 3 F150W  files as reference frames and perform photometry directly on the stage 2  images.  We use the Vega-Vega system to remain consistent with earlier versions of DOLPHOT's JWST module, which gives a ∼0.04 mag offset (in F090W) from the Vega-Sirius system that is currently default in DOLPHOT NIRCam module. We use the “-etctime" option, which allows the package to use () for S/N calculations. We apply the following DOLPHOT quality cuts, similar to those from <cit.>:  < 0.5 (in both bands),  < 0.01 (in both bands), and  ≤ 2. In addition to these quality cuts, we also apply S/N cuts in both bands for each target. For NGC1448, NGC1559, NGC3447, NGC5584, and NGC5643, we adopt a minimum threshold of =5, whereas we choose a value of =3 for NGC2525 an NGC3370 (due to the decreased relative depth of their photometry). 

We also correct for foreground extinction using the Python package  <cit.> and galaxy coordinates from the NASA/IPAC Extragalactic Distance Database (NED)[<https://ned.ipac.caltech.edu/>]. We use the <cit.> reddening law with R_v = 3.1 and A_λ/A_V = 1.4156 and 0.6021 for F090W and F150W, respectively <cit.>. 



§ MEASUREMENT
 

Measuring the TRGB magnitude involves locating the discontinuity or inflection point of the luminosity function consisting of red giant and asymptotic giant branch stars. This can be done many ways; for instance, using a Sobel filter <cit.>, or model-based methods, with either least-squares fitters <cit.> or maximum-likelihood estimation <cit.>. In this study, we measure the TRGB using a Sobel filter using the measurement routine without spatial clipping (which we instead perform using elliptical annuli) from the Comparative Analysis of TRGBs (CATs) team <cit.>, which is publicly available on GitHub[<https://github.com/JiaxiWu1018/Unsupervised-TRGB>]. The CATs team had optimized their measurement parameters (such as smoothing value, color cuts, etc.) by minimizing field-to-field dispersion in the TRGB measurement across multiple fields. At the moment, there are a limited number of JWST fields in each host galaxy, which prevents us from performing a similar optimization. For this study, we adopt a smoothing value of 0.05 mag and unweighted, or `simple' weighting as named in the CATs algorithm (i.e. no further weighting of the output of the edge-detection measurement). We note that without the CATs optimizations in place, this methodology is equivalent to the TRGB measurements adopted by the Carnegie-Chicago Hubble Program <cit.>, but without the additional weighting of the Sobel filter output (which has been shown to cause biases in the outputs; ). We explore the effects of varying the level of smoothing of the luminosity function and the color range used to measure the luminosity function, 14 combinations in all, in the next section. TRGB uncertainties are estimated using bootstrap resampling of the luminosity function with 100 samples.  For NGC 5584, using the smaller smoothing value of s=0.05 mag produces a Sobel response that shows two peaks of nearly the same height. Following <cit.>, if there are two Sobel peaks that are of equivalent height (≤ 2%), we select the brighter peak.  

Before measuring the TRGB, we perform spatial selections to limit contamination from younger stellar populations in these star-forming galaxies. The NIRCam regions used to measure the TRGB are highlighted in Fig. <ref> - in all cases (except NGC3447, described below), only regions exterior to the B=25 mag/sq arcsec isophote (D_25; ) are selected <cit.>. For NGC1559 and NGC5584, the parallel NIRCam module contains a suitable sampling of stars, although only half of the parallel module is used (the far half of each contain too few stars to perform precise empirical PSF adjustments and aperture corrections). The same is nearly true for NGC5643, though we remove a small portion of each parallel module that is interior to D_25. In NGC1448, NGC2525 and NGC3370, a sizeable portion of the main module is outside of D_25, which we include to increase the sampling of stars and for NGC2525 and NGC3370, the parallel modules contain too few stars to perform photometry on. Lastly, NGC3447 is an actively interacting system, often described as two systems, N3447A and B. Here, we use two ellipses centered at RA, Dec = (10:53:23.998, +16:46:26.78) and (10:53:29:3934, +16:47:02.294), major axes of 140 and 50 arcsec, minor axes of 60 and 40 arcsec, and position angles of 80 and 115 degrees, respectively, following <cit.>. A color image of NGC3370 is shown in Fig. <ref>, along with the same D_25 selection region adopted for the spatial cuts. It can be seen that the outer regions of the image used for our analysis are of low stellar density, where stars are easily separated. 






The TRGB in F090W is expected to have minimal variation (<0.02 mag) with color over a range of 1.15 < F090W - F150W < 1.75 mag <cit.>. Here we adopt a color selection of 1.30 < F090W - F150W < 1.75 mag for our baseline result (see Fig. 2 in ), where the tighter range aims to limit the effects of a limited amount of supergiants which remain in our CMDs.









§ DISTANCES
 

We use the TRGB measurements shown in Fig. <ref> to measure distances to the host galaxies. We adopt a TRGB zero-point of M^F090W_TRGB = -4.372 ± 0.033 (stat) ± 0.045 (sys) mag from <cit.> - based on m_TRGB = 25.045 mag, which is the mean of the two simple Sobel measurements using a D > D_25 and outer spatial selections (either being within ± 0.005 of this mean). This calibration uses the geometric maser distance to NGC4258 <cit.>, to calibrate the TRGB in the JWST F090W system and is stable for smoothing values s=0.04 mag to s=0.12 mag due to the absence of weighting (see Fig. 6 in ). This absolute calibration is also highly consistent with the independently derived zero-point of M^F090W_TRGB = -4.36 ±  0.025 (stat) ± 0.043 (sys) mag from <cit.>, after adjusting their value from the Sirius-Vega system to the Vega-Vega zeropoint system (M. Newman, priv. communication).  We list and plot the distances to the host galaxies, compared to Cepheid-based distances from <cit.>. We compare to fit variant 10 from <cit.> for consistency in anchor selection; the distances produced by fit variant 10 are on average greater than those using all anchors (baseline) by ∼0.015 mag, consistent with their differences in H_0 of 72.5 km s^−1 Mpc^−1 for NGC4258 and 73.0 km s^−1 Mpc^−1 using all anchors.


We find a weighted mean difference between the TRGB (baseline results with 1.30 < F090W-F150W<1.75 mag and smoothing of s=0.05 mag) and HST Cepheid distances of 0.01 ± 0.04 (stat) ± 0.04 (sys) mag, which includes the systematic error due to measurement choice listed in Table <ref>, between the TRGB distance moduli measured here and Cepheid distance moduli from HST. We find no statistically significant difference between the two sets of distances measured between the same anchor and SN Ia hosts but with independent distance indicators.  We have not attempted to account for any further population-based differences intrinsic to the TRGB between the field of NGC 4258 and the mean of the SN Ia hosts, but believe these are limited due to the limited metallicity and age differences expected in F090W and our restricted color window <cit.>.


ccccccccccccc



Galaxy    
TRGB    
σ    
TRGB    
σ    
ΔTRGB    
μ_0(TRGB)    
σ    
μ_0(TRGB)    
σ    
μ_0(Cepheid)    
σ (Cepheid)    
σ (var)

    
s=0.10    
s=0.10    
s=0.05    
s=0.05    
(s=0.10-s=0.05)    
s=0.10    
s=0.10    
s=0.05    
s=0.05    
    
     

NGC1448     26.96     0.01     27.01     0.05     -0.05     31.33     0.05     31.38     0.07     31.30     0.05     0.02 

NGC1559     27.12     0.01     27.13     0.01     -0.01     31.49     0.05     31.50     0.05     31.50     0.07     0.01 

NGC2525     27.48     0.03     27.43     0.06     0.05        31.86     0.07     31.81     0.09     32.06     0.11     0.04 

NGC3370     27.83     0.02     27.84     0.08     -0.01     32.20     0.06     32.21     0.09     32.13     0.06     0.02 

NGC3447     27.55     0.03     27.54     0.08     0.01        31.93     0.06     31.92     0.09     31.95     0.05     0.01 

NGC5584     27.58     0.06     27.43     0.10     0.15        31.95     0.08     31.8      0.11     31.77     0.06     0.07 

NGC5643     26.19     0.01     26.20     0.01     -0.01     30.56     0.13     30.57     0.13     30.55     0.06     0.01 

TRGB and Cepheid distances to NGC1448, NGC1559, NGC2525, NGC3370, NGC3447, NGC5584, and NGC5643. Cepheid distances are from <cit.>, fit variant 10. Distance errors do not include an 0.032 mag uncertainty from the maser distance for either Cepheids or TRGB.  TRGB distances include a (correlated across the host galaxies) measurement error for NGC4258 of 0.045 mag from <cit.>. We adopt half the foreground extinction correction, with 0.01 mag added in quadrature to account for potential halo extinction in the host galaxy, as the uncertainty on the foreground extinction correction (as done in ). We also add in quadrature a systematic uncertainty from measurement and peak choices with values and measurement variants listed in Table <ref> and Table <ref>, respectively. Columns from left to right: 1) Galaxy, 2) TRGB measured here with a smoothing value of 0.10 mag, 3) error on that TRGB measurement, 4) TRGB measured here with a smoothing value of 0.05 mag, 5) error on that TRGB measurement, 6) difference between the TRGBs measured with s=0.05 and s=0.10 mag, 7) TRGB distance modulus measured here using a smoothing value of 0.10 mag, 8) error on that TRGB distance modulus, 9) TRGB distance modulus measured here using a smoothing value of 0.05 mag, 10) error on that TRGB distance modulus, 11) Cepheid distance <cit.>, 12) error on the Cepheid distance, 13) dispersion of variants (measurement choices), may be considered as a systematic error on an individual distance measurement <ref>.










The choice of algorithm and selection parameters can impact final TRGB measurements. One compelling approach is to optimize the measurement parameters to minimize scatter in the field-to-field variations (see ), however, the limited number of JWST fields available to measure the TRGB within our host galaxies prevent us from performing such an optimization. To investigate the effects of how different parameter choices can impact our measurements, we explore a fourteen combinations of different luminosity function smoothing, color selection, and zero-point choice. We list the different measurement variants explored in this analysis, together with the weighted mean difference between the TRGB and HST Cepheid distances for each variant, in Table <ref>. We include a thirteenth variant using the zero-point from <cit.>, adjusted for the Vega-Vega photometric system which has differences of ∼0.04 mag in F090W and ∼0.02 mag in F150W. We also add a variant where we use the median of all TRGB measurements (three smoothings, four color ranges) to compare with Cepheids.  We add the standard deviation of the measured TRGBs across the smoothing and color range variants for each galaxy, excluding the variant using the zero-point from <cit.> and median TRGB, as a systematic error to our measurements, listed in Table <ref>. We find that for all variants, the mean differences between the TRGB and Cepheid distances across all galaxies for a given variant are consistent with zero to within their statistical uncertainties with a full range of 0.01 to 0.03 mag.  

In Fig. <ref>, the error in the mean μ_TRGB-μ_Cepheid of 0.03-0.04 mag is a statistical uncertainty.  There is also a systematic uncertainty in the mean TRGB and Cepheid comparison from the measurement uncertainty of the TRGB in NGC4258 of ± 0.04 mag <cit.> which pertains to all calibrated TRGB distances and likewise for Cepheids in NGC4258 of ± 0.02 mag, or ± 0.045 mag when they are combined.  This systematic term due to the measurement of NGC4258 for both methods is the dominant term in the comparison and may only be reduced in the future with the use of additional observations of NGC4258.  The maser distance uncertainty of ± 0.032 mag should not be considered in this distance comparison as it is common to both the Cepheid and TRGB distances.

We can also compare the distances to NGC1559 and NGC5584 from <cit.>, who used the same dataset as here. <cit.> found distances of μ_0 = 31.49 ± 0.07 mag (Δ = 0.01 mag) and 31.80 ± 0.08 mag (Δ = 0.00 mag) to NGC1559 and NGC5584, respectively, when comparing their results to ours from the same smoothing scale (for NGC1559, we now have combined both visits to obtain higher S/N photometry). The TRGB distance for NGC1559 is also in agreement with that measured with Miras in <cit.> of μ_0 = 31.41 ± 0.050 ± 0.060 mag. 

An unavoidable feature of the TRGB method of edge detection is a potential ambiguity when multiple Sobel peaks of similar height are present.  For NGC5584 there are two Sobel peaks separated by 0.2-0.3 mag. Because the peaks are similar in height, different measurement choices may cause changes in which peak is higher. To account for this possibility, we provide an additional individual distance uncertainty listed in Table <ref> estimated from the variation of individual results of all the variants in Table <ref>. This uncertainty should be added for citing a single distance estimate for each host.  A similar situation involving two peaks at similar heights, but at a smaller level, 0.05 mag, is seen for NGC1448 and in the reverse direction for NGC2525. 

The Extragalactic Distance Database  <cit.> and CCHP <cit.> teams have measured HST TRGB distances to NGC1448 and NGC5643, which can provide an interesting comparison with the JWST distances found here. These distances also reflect differences in TRGB measurement methodology; the EDD team uses a model-based approach <cit.>, while the CCHP team uses a Sobel filter applied on a Gaussian-windowed, Locally Weighted Scatterplot Smoothing (GLOESS) smoothed luminosity function <cit.>. We list this comparison in Table <ref>. For NGC1448, these teams independently found distance moduli of 31.38 mag (EDD) and 31.32 mag (CCHP), compared to 31.33 mag and 31.38 mag (different levels of smoothing) found here resulting in a standard deviation of 0.03 mag. For NGC5643, these team found 30.47 mag (EDD) and 30.48 mag (CCHP), compared to 30.57 mag (which agrees well with Cepheids) found here resulting in a standard deviation of 0.04 mag. 


ccc

Galaxy     Reference     μ_0(TRGB)
NGC 1448     <cit.>     31.38  

NGC 1448     <cit.>     31.32 

NGC 1448     Here     31.33 (s=0.05), 31.38 (s=0.10)   

NGC 5643     <cit.>     30.47  

NGC 5643     <cit.>     30.48  

NGC 5643     Here     30.57  

Summary table for distances to NGC 1448 and NGC 5643 from EDD <cit.>, CCHP <cit.>, and here.

 


ccccccc

Smoothing [mag]     Color Cuts [mag]     μ_TRGB - μ_Cepheid [mag]     σ [mag]     Calibration     χ^2     Weighted Scatter [mag]
0.05     1.15, 1.65     0.03     0.04    <cit.>     1.075     0.10 

0.05     1.15, 1.75     0.03     0.04    <cit.>     1.468     0.12 

0.05     1.30, 1.75     0.01     0.04    <cit.>     0.718     0.09 

0.07     1.15, 1.65     0.02     0.04    <cit.>     0.919     0.09 

0.07     1.15, 1.75     0.02     0.04    <cit.>     1.377     0.11 

0.07     1.30, 1.75     0.02     0.04    <cit.>     1.142     0.10 

0.10     1.15, 1.65     0.02     0.03    <cit.>     0.916     0.09 

0.10     1.15, 1.75     0.02     0.03    <cit.>     1.081     0.09 

0.10     1.30, 1.75     0.02     0.04    <cit.>     0.954     0.09 

0.10     1.30, 1.75     0.01     0.04    <cit.>     0.946     0.08 

0.15     1.15, 1.65     0.01     0.03    <cit.>     0.912     0.08 

0.15     1.15, 1.75     0.02     0.03    <cit.>     0.878     0.08 

0.15     1.30, 1.75     0.02     0.03    <cit.>     0.802     0.08 

All Smoothings     All Color Ranges     0.02     0.03    <cit.>    1.063     0.09 

Summary table for the weighted mean differences between the TRGB and Cepheid distances (TRGB - Cepheid) to NGC1448, NGC1559, NGC2525, NGC3370, NGC3447, NGC5584, and NGC5643 across various measurement variants. Cepheid distances are from <cit.>, fit variant 10. The error in the mean difference, TRGB-Cepheid, does not include a systematic uncertainty of 0.03 mag for the TRGB measurement error in NGC4258 from <cit.>. Measurements use `simple' smoothing (i.e. no weighting, see ) and do not include the measurement choice error listed in Table <ref> except for the last variant that uses the median TRGB across all smoothing and color range variants. Bolded values correspond to the baseline variant that uses s= 0.05 mag smoothing with a color range of 1.3 < F090W - F150W < 1.75 mag. For the variant that uses the <cit.>, we use the errors listed in their Tables 4 and 6 added in quadrature with the TRGB measurement and foreground extinction errors. Columns from left to right are: Smoothing value, color cuts, mean difference between TRGB and Cepheid distances, error on the mean difference, chi-squared, and weighted scatter.





§ DISCUSSION
 

We measure F090W TRGB-based distances to NGC1448, NGC1559, NGC2525, NGC3370, NGC3447, NGC5584, and NGC5643 using JWST NIRCam observations and test their consistency with HST Cepheid-based distances to those same galaxies. We find excellent agreement between the two independent sets of distance measurements, which were measured between the same hosts and anchor but using data taken with different telescopes and distance indicators.

Examining the Hubble Tension necessitates close scrutiny of the consistency and systematics of distance indicators. Based on the measurements made in this study, we find no evidence of a bias or systematic difference between the Cepheid and TRGB methods that would cause a difference translatable to H_0 that can solve the Hubble Tension. This finding is in agreement with <cit.>, who find, “the excellent agreement between the published Cepheid distances in Riess et al. (2022) and TRGB distances in Freedman et al. (2021), which in the mean, agree to 0.007 mag". In addition, Fig. <ref> shows a comparison between Cepheid and TRGB distances, both measured with HST, using TRGB and Cepheid distances from <cit.> and <cit.>, respectively. The TRGB and Cepheid distances in Fig. <ref> yield a mean difference of 0.00 ± 0.02 (stat) ± 0.04 (sys) mag, also consistent with no difference even without additional consideration of populations differences in TRGB measurements <cit.>. This comparison will benefit from more JWST TRGB measurements in the future (for instance, from GO-1995; ). As the Hubble Tension corresponds to 5log_10(73/67.5) ∼ 0.17 mag, the demonstrated consistency is meaningful and is inconsistent with providing evidence for a solution to the Hubble Tension at 3σ.






 We do not yet report a value of H_0 from the JWST-calibrated SN subsamples because they are too small and the anchors too few to be competitive with the HST sample of 42 SN Ia and 4 anchors.  The uncertainty in H_0 would be 2.5 times greater with σ∼ 2-2.5 km/s/Mpc vs. 0.9  km/s/Mpc for HST, which would trivially remove the Hubble Tension simply by inflating the error in H_0.  Rather, the greater power of these presently small JWST samples comes from a direct comparison of what they can both measure in common, the distances between the same anchor and SN hosts.  

It will be important to also scrutinize the difference in direct H_0 measurements that arise from different treatments of SNe Ia. <cit.> find that the addition of peculiar flow corrections and cross-calibration of datasets which are included in the Pantheon and Pantheon+ analyses increase H_0 measurements each by 0.5 and 1.1 km/s/Mpc from the <cit.> analysis, bringing it closer in line with the value obtained from Cepheids.  An under recognized source of variations in determinations of H_0 is also the make-up of the SN Ia calibration sample which can produce fluctuations of ∼ 1-2 km/s/Mpc due to small sample statistics.

Crosschecks between standard candles can be made more comprehensive with additional, independent standard candles such as Miras and carbon stars. The carbon star method, also called the J-region Asymptotic Giant Branch (JAGB), originated in the 1980s <cit.> and has since been revived and further pioneered in the 2000s <cit.>. Although the JAGB method still requires further development and standardization (see discussions of asymmetric luminosity functions and metallicity effects in ), the great luminosities of carbon stars in the near-infrared allow the JAGB to reach farther than the I and J-band TRGB, potentially allowing for a more comprehensive crosscheck of Cepheid variables via galaxy distances.

The TRGB measurements made here can benefit from further analysis, such as a future contrast ratio calibration (see CATs, <cit.> or via modelling of the luminosity function <cit.> instead of edge-detection algorithms (Anand et al., in prep). However, even without these additions, the consistency of the TRGB-based distance measurements with those of Cepheid-based distances measurement do not show evidence of a bias or systematic offset in Cepheid distances that would resolve the Hubble Tension. Similar analyses in the future will also benefit from further studies investigating the effects of red giant diversity to improve the accuracy of TRGB distances <cit.>. Future observations of TRGB fields with HST (for instance, from GO-17520;  ), JWST, and the Roman Space Telescope will provide more opportunities to scrutinize the second rung of the distance ladder by providing a more extensive set of observations that can be used to compile a more comprehensive comparison between these distance indicators. Specifically, wide-field JWST observations within the anchor galaxy NGC 4258 will help reduce systematic uncertainties with regards to the absolute calibration of the TRGB, and deep JWST observations of galaxies with the highest levels of mismatch between HST Cepheid and HST TRGB distances (e.g. NGC 3021, NGC 4038/9; ) will help elucidate any individual discrepancies between the two techniques. Lastly, a fully independent distance ladder from the traditional Cepheid+SNe Ia route is also under construction, via the usage of the TRGB combined with Surface Brightness Fluctuations as the final rung <cit.>.



We are indebted to all of those who spent years and even decades bringing JWST to fruition. We thank Yukei Murakami for helpful conversations. SL is supported by the National Science Foundation Graduate Research Fellowship Program under grant number DGE2139757. GSA acknowledges financial support from JWST GO-1685 and JWST GO-2875. DS is supported by Department of Energy grant DE-SC0010007, the David and Lucile Packard Foundation, the Templeton Foundation and Sloan Foundation.  RLB is supported by the National Science Foundation through grant number AST-2108616. RIA is funded by the SNSF through an Eccellenza Professorial Fellowship, grant number PCEFP2_194638.

This research made use of the NASA Astrophysics Data System. This work is based on observations made with the NASA/ESA/CSA JWST. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with programs #1685  and #2875. The JWST data presented in this article were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations analyzed can be accessed via DOI 10.17909/556t-7522.

The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions.





JWST (NIRCam)

astropy <cit.>, 
SAOImage <cit.>, 
DOLPHOT <cit.>


aasjournal



 Paper Title: The most distant HI galaxies discovered by the 500 m dish FAST.



    


















































Bo Peng
pb@nao.cas.cn
Lister Staveley-Smith
lister.staveley-smith@uwa.edu.au

0000-0001-6642-8307]Hongwei Xi
National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China


0000-0001-6956-6553]Bo Peng
National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China


0000-0002-8057-0294]Lister Staveley-Smith
International Centre for Radio Astronomy Research (ICRAR), University of Western Australia

35 Stirling Hwy, Perth, 6009, WA, Australia
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia


0000-0002-0196-5248]Bi-Qing For
International Centre for Radio Astronomy Research (ICRAR), University of Western Australia

35 Stirling Hwy, Perth, 6009, WA, Australia
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia


0000-0002-1311-8839]Bin Liu
National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China
School of Astronomy and Space Science, University of Chinese Academy of Sciences

Bejing, 100049, Beijing, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China
School of Astronomy and Space Science, University of Chinese Academy of Sciences

Bejing, 100049, Beijing, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China



Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science and Technology, Guangxi University

Nanning, 530004, Guangxi, China
Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories,
Chinese Academy of Sciences

Beijing, 100101, Beijing, China



Department of Astronomy, University of California

Berkeley, CA 94720-3411, USA



Department of Astronomy, University of California

Berkeley, CA 94720-3411, USA



Department of Astronomy, University of California

Berkeley, CA 94720-3411, USA



Department of Astronomy, University of California

Berkeley, CA 94720-3411, USA
Physics Department and Tsinghua Center for Astrophysics (THCA), Tsinghua University

Beijing, 100084, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China
Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories,
Chinese Academy of Sciences

Beijing, 100101, Beijing, China



Chinese Academy of Sciences South America Center for Astronomy (CASSACA), National Astronomical Observatories of China, Chinese Academy of Sciences

20A Datun Road, Beijing, 100101, Bejing, China



National Astronomical Observatories (NAOC), Chinese Academy of Sciences

20 Datun Rd.,Chaoyang District, Bejing, 100101, Bejing, China
School of Astronomy and Space Science, University of Chinese Academy of Sciences

Bejing, 100049, Beijing, China
Chinese Academy of Sciences South America Center for Astronomy (CASSACA), National Astronomical Observatories of China, Chinese Academy of Sciences

20A Datun Road, Beijing, 100101, Bejing, China



Purple Mountain Observatory, Chinese Academy of Sciences

No. 10 Yuanhua Road, Qixia District, Nanjing, 210023, Jiangsu, China
School of Astronomy and Space Science, University of Science and Technology of China

No. 96 Jinzhai Road, Baohe District, Hefei, 230026, Anhui, China



School of Astronomy and Space Science, University of Science and Technology of China

No. 96 Jinzhai Road, Baohe District, Hefei, 230026, Anhui, China
CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences

No. 10 Yuanhua Road, Qixia District, Nanjing, 210023, Jiangsu, China



Special Astrophysical Observatory, Russian Academy of Sciences

Nizhnii Arkhyz, Zelenchukskiy region, Karachai-Cherkessian Republic, 357147, Russia



Special Astrophysical Observatory, Russian Academy of Sciences

Nizhnii Arkhyz, Zelenchukskiy region, Karachai-Cherkessian Republic, 357147, Russia















§ ABSTRACT 

    Neutral hydrogen () is the primary component of the cool interstellar medium (ISM) and is the reservoir of fuel for star formation. Owing to the sensitivity of existing radio telescopes, our understanding of the evolution of the ISM in galaxies remains limited, as it is based on only a few hundred galaxies detected in  beyond the local Universe. With the high sensitivity of the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we carried out a blind  search, the FAST Ultra-Deep Survey (FUDS), which extends to redshifts up to 0.42 and a sensitivity of 50 μ Jy · beam^-1. Here, we report the first discovery of six galaxies in  at z>0.38. For these galaxies, the FAST angular resolution of ∼ 4' corresponds to a mean linear size of ∼1.3 h_70^-1Mpc. These galaxies are among the most distant  emission detections known, with one having the most massive  content (10^10.93 ± 0.04 h_70^-2  M_⊙). Using recent data from the DESI survey, and new observations with the Hale, BTA, and Keck telescopes, optical counterparts are detected for all galaxies within the 3-σ positional uncertainty (0.5 h_70^-1Mpc) and 200 km · s^-1 in recession velocity. Assuming that the dominant source of  is the identified optical counterpart, we find an evidence of evolution in the  content of galaxies over the last 4.2 Gyr. Our new high-redshift  galaxy sample provides the opportunity to better investigate the evolution of cool gas in galaxies. A larger sample size in the future will allow us to refine our knowledge of the formation and evolution of galaxies.

    




























§ INTRODUCTION
 

    Hydrogen is the most common element in the Universe. In its neutral form (), it is abundant in spiral galaxies such as our Milky Way. It also indirectly regulates star formation by feeding the molecular clouds that are responsible for initiating star formation <cit.>.  commonly extends far beyond the stellar disk of galaxies, making it an excellent probe for tracing interactions between galaxies, or between galaxies and the circumgalactic medium (CGM).
    
    One of the most significant questions in astronomy is how the Universe evolved into its present form. To answer this, it is necessary to study galaxies over a range of cosmic times and therefore redshifts. The Hubble Space Telescope (HST) reported an oldest galaxy in optical band at z=11.1 <cit.>, which is only ∼ 400 Myr after the Big Bang. Such detections allow measurements of the evolution of the molecular gas fraction of galaxies <cit.>, the evolution of supermassive black holes <cit.>, and tests of the galaxy formation theory inside the standard ΛCDM cosmological framework <cit.>. However, by comparison with the detection of stellar components of galaxies in optical or infrared (IR) bands, detection of cool  is much harder owing to the weakness of the 21 cm emission line. Almost all  detections <cit.> are confined to z<0.35, with only two detections beyond this, the most distant unlensed detection being at z=0.376 from the VLA CHILES survey <cit.>, and the most distant lensed  galaxy detection being at z=1.3 <cit.>.
        
    The FAST Ultra-Deep Survey (FUDS, ) is one of the deepest  surveys, having a sensitivity of ∼50 μJy·beam^-1, a frequency resolution of 22.9 kHz (velocity resolution of 6.76 km · s^-1 at z ∼ 0.4), a redshift limit of z=0.42 (a lookback time of 4.4 Gyr), and an angular resolution of ∼ 4' (physical resolution of 1.3h_70^-1Mpc) at the redshift limit. Hence, it is well-suited to the exploration of gas evolution over 30% of the age of the Universe. Here, we report six  galaxy candidates directly detected in the 21 cm emission line in the pilot survey of FUDS (FUDS0) that have higher redshifts (0.38<z<0.40) than the highest redshift CHILES detections, and are unlensed so that their intrinsic properties are well understood. In this paper, we use the flat universe model with parameters of H_0=70 h_70 km s^-1 Mpc^-1, Ω_ M=0.3, and Ω_Λ=0.7. 



§ DETECTIONS BY FAST
 

    FAST is not only the largest single-dish telescope in the world, but hosts a 19-beam receiver <cit.>, which dramatically boosts its capability to make multiple simultaneous observations and increases its ability to survey and map large areas of sky. For the first FUDS field (FUDS0), a region centred at RA(J2000) = 08^ h17^ m12^ s, Dec(J2000) = +2210480 was observed for a total of 95 hr. This yielded a sensitivity of 50 μ Jy · beam^-1 over an area of 0.72 deg^2. The observations were performed in on-the-fly (OTF) mode from 2019 August 25 to 2020 May 22. More details of the observations, calibration, data reduction, and noise analysis are described in Appendix <ref> and <ref>.

    
    

    We searched for sources with a signal-to-noise ratio (S/N) larger than 7 in the final cube by averaging channels on different scales (25 kHz, 50 kHz, 100 kHz, and 200 kHz) using a custom algorithm (see section 4.1 in ). Our initial study focuses on  detections with z>0.38 (f<1.03 GHz). Candidate signals were visually inspected to remove obvious artefacts — e.g., some discrete ranges of frequency with bad spectral baselines contain an excess of positive and negative signals due to radio frequency interference. The final list consists of six  galaxy candidates with z>0.38. We present  column-density contours overlaid on top of DESI Legacy Imaging Survey[https://www.legacysurvey.org/] <cit.> 3-band optical images and their spectra in Figure <ref>. A two-dimensional Gaussian fit to the column-density maps is used to derive positions with a 1σ uncertainty of 0.52' (based on the offset of 62 FUDS galaxies from their optical counterparts with spectroscopic redshift measurements). The Busy Function <cit.> was employed to derive model spectra, which are overlaid in Figure <ref>. 

    

    In order to further confirm the detections, we split our raw data into two (P1 and P2). The P1 data are from observations performed between 2019 August 25 and 2020 March 01; P2 data are from observations between 2020 March 02 and 2020 May 22. Both sets of data have similar integration times, yielding two independent cubes. Each cube has higher noise by a factor of ∼√(2). Using similar line widths and beam sizes, HI column-density images and spatially integrated spectra were produced from both datasets . All six detections were identified in both P1 and P2 cubes. Cubes from two individual polarization channels also show the reality of the six detections.
    
    The  properties of the six galaxy candidates are listed in Table <ref> (more details in Appendix Table <ref>). They lie in the redshift range of 0.389 < z < 0.402 and have logarithmic  masses, log(M_/h_70^-2  M_⊙), between 10.37 and 10.93. The most -massive galaxy candidate (ID 124) has the largest  mass to date. Considering the 1σ uncertainty, it is slightly more massive than Malin 1 (log(M_/h_70^-2  M_⊙) = 10.82 ± 0.06, ), HIZOA J0836-43 (log(M_/h_70^-2  M_⊙)=10.88, ), or the two highest-mass HIGHz <cit.> galaxies (J160938.00+312958.5, J165940.12+344307.8, both with an  mass of log(M_/h_70^-2  M_⊙)=10.89). A caveat is that the  mass may have contributions from other galaxies at the same redshift within the FAST beam. This requires high angular resolution observations and prohibitively long integration times (e.g., a few hundred hours with the Karl G. Jansky Very Large Array (VLA) to detect them at S/N = 5).



§ DISCUSSION
 

    The comoving volume in the FUDS0 survey at 0.38<z<0.42 is 5.81× 10^4 h_70^-3  Mpc^3. We computed the completeness, cosmic variance, and detectable volume for the six galaxies by following the methods used for the Arecibo Ultra-Deep Survey (AUDS, ). The Σ1/V_ max method <cit.> gives us a higher  mass function () (log(Φ) = -2.85 ± 0.43 at log(M_ h_70^2  M_⊙^-1) = 10.5) than that from local surveys, HIPASS and ALFALFA. This indicates a more extended  at the high-mass end, more massive  galaxies than in the local Universe, and significant evolution over the last ∼ 4.2 Gyr. The full AUDS catalogue <cit.> previously suggested a weak evolutionary trend for an increase of characteristic mass of  with increasing redshift. Our result is consistent with this trend, and may indicate rapid gas consumption following the epoch of peak star-formation density at z ≈ 2. Again, our result is an upper limit on  taking into account the confusing mass.

    
            
    In our sample, all six optical counterparts are found within a spatial separation of 0.5h_70^-1Mpc (the 3-σ uncertainty of fitted  positions) and a velocity separation <200 km · s^-1. Four candidates (ID: 123, 124, 125 and 126) have spectroscopic confirmations from the unreleased data of the Dark Energy Spectroscopic Instrument (DESI, ). The optical counterparts of the two remaining galaxy candidates (ID: 127 and 128) were identified in spectroscopic observations using the Keck[https://keckobservatory.org/] and Hale[https://sites.astro.caltech.edu/palomar/about/telescopes/hale.html] telescopes, respectively. For galaxy 123, our Big Telescope Alt-azimuth (BTA) data reveals a second candidate optical counterpart at a similar redshift. Being further from the beam centre, this is not the preferred counterpart. Nevertheless, it may contribute confusing flux to the  spectrum. The H_α (or [OII], if both Lyman and Balmer series are not detected) emission lines are overlaid on top of  spectra in Figure <ref> (refer to Section <ref> in the Appendix for the whole optical spectra). To derive the stellar mass (M_*) and star-formation rate (SFR), we employed MAGPHYS[http://www.iap.fr/magphys/] <cit.> to fit spectral energy distributions (SEDs). The optical data cover five bands (u, g, r, i, and z) from SDSS, while the IR data cover four bands (W1, W2, W3, and W4) from the Wide-field Infrared Survey Explorer (WISE[https://wise2.ipac.caltech.edu/docs/release/allwise/], ). In Appendix <ref>, we describe the fitting method in more detail. The optical properties are listed in Table <ref> (more details given in Appendix Table <ref>). The optical images and SEDs are also shown in Appendix Figure <ref>.

    We now compare the  properties with the derived stellar properties, namely M_*, SFR, stellar mass surface density (μ_* = M_*/2π R_50^2), and concentration index (R_90/R_50), comparing with galaxies from the extended GALEX Arecibo SDSS survey[https://xgass.icrar.org/index.html] (xGASS, ), CHILES, and the HIGHz <cit.> sample of 39  galaxies with 0.17 < z < 0.25. This gives us an insight into possible evolution in the properties of the most -massive galaxies. Considering possible confusion, our results are upper limits for M_ and gas fraction (f_ = M_/M_*). In the upper panels of Figure <ref>, M_ is shown as a function of M_* and SFR. The FUDS galaxy candidates clearly have large values of M_ and SFR, but consistent with the properties of HIGHz galaxies. Unsurprisingly, the FUDS candidates also have high M_*, though not quite as high as the highest in xGASS. Given the tightness of the M_–SFR correlation, depletion times (the ratio of the two) are also consistent with xGASS and HIGHz galaxies. In the lower panels of Figure <ref>, the gas fraction is shown as a function of μ_* and R_90/R_50. The FUDS candidates show reasonable consistency with the xGASS scaling relations. The gas fractions for the FUDS candidates are high, though well below the most gas-rich galaxies in xGASS. Values for μ_* and R_90/R_50 are low, but consistent with HIGHz galaxies and the trend for xGASS galaxies. Low values for μ_*, indicative of a large halo spin parameter, are also consistent with the ALFALFA HIghMass <cit.> sample. Therefore, the FUDS galaxies appear to be extreme high- mass analogues of galaxies in the local Universe, with properties similar to the lower-redshift, SFR-selected HIGHz sample. The results here indicate that such galaxies are more numerous at z≈ 0.4 than in the local Universe, therefore suggesting significant evolution over the last ∼ 4.2 Gyr. Although there is only a single CHILES galaxy at a similar redshift (z=0.376), it has similar properties to the FUDS candidates, albeit with a higher SFR, and is therefore consistent with this picture.
            
    Furthermore, using the stacking technique at higher redshift (z ≈ 1), optically selected blue galaxies appear to have  masses that are a factor of 3.5 higher for their stellar mass than their z=0 counterparts <cit.>. Depletion timescales have also been reported to be lower at this redshift <cit.> and at intermediate redshifts (z ≈ 0.35) <cit.>. Considering the possible confusion, the real depletion time in our sample could be lower, and more consistent with CHILES. These results therefore also seem consistent with a galaxy evolution picture where gas consumption exceeds gas replenishment for high-mass galaxies following the peak of SFR density at “cosmic noon”, following which there is an almost exponential decrease of their  mass with time and a gradual truncation of the high-mass cutoff in the  mass function from high redshift to low redshift. In the immediate future, the ongoing “blind” FUDS survey will provide even more direct detections of individual galaxies in a larger survey volume, and therefore a more accurate measurement of the evolution of the , allowing further exploration of the cool-gas evolution of galaxies out to z ≈ 0.4. Future observations with the Square Kilometer Array (SKA) will offer the possibility of both high sensitivity and high angular resolution, so will avoid the requirement to confirm optical counterparts through deep optical spectroscopy.



§ SUMMARY


    The FAST Ultra-Deep Survey is a deep blind  galaxy survey designed to explore the evolutionary trend in the cool gas content of galaxies. We have now completed the observation and data reduction for the first of the six target fields, FUDS0. In this paper, we focus on the highest-redshift detections detected in the field. The main findings are summarized below:

    
    
        
  * Six galaxies are discovered through blind detection in 21-cm emission line observations with redshifts z>0.38. These are at the redshift limit of the 19-beam FAST receiver and first such direct detections at this redshift to date, other than through gravitational lensing.

        
  * All have optical counterparts identified using data from  DESI or from new spectroscopic observations, which we conducted with the Hale, BTA and Keck telescopes.

        
  * Comparison with galaxies in xGASS reveals that the six galaxies are extreme high- mass analogues of galaxies in the local Universe.

        
  * The significantly larger HIMF that is implied for high-mass galaxies at z≈0.4 indicates their significant consumption of cool gas over the last ∼4.2 Gyr.
        
    
    










§ ACKNOWLEDGMENTS


    This work made use of the data from FAST (Five-hundred-meter Aperture Spherical radio Telescope). FAST is a Chinese national mega-science facility, operated by the National Astronomical Observatories, Chinese Academy of Sciences. The work is supported by the National Key R&D Program of China under grant number 2018YFA0404703, and the FAST Collaboration. Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.
    This research used data obtained with the Dark Energy Spectroscopic Instrument (DESI). DESI construction and operations are managed by the Lawrence Berkeley National Laboratory. This material is based upon work supported by the U.S. Department of Energy (DOE), Office of Science, Office of High-Energy Physics, under Contract No. DE–AC02–05CH11231, and by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract. Additional support for DESI was provided by the U.S. National Science Foundation (NSF), Division of Astronomical Sciences under contract AST-0950945 to the NSF’s National Optical-Infrared Astronomy Research Laboratory; the Science and Technology Facilities Council of the United Kingdom; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; the French Alternative Energies and Atomic Energy Commission (CEA); the National Council of Science and Technology of Mexico (CONACYT); the Ministry of Science and Innovation of Spain (MICINN); and the DESI Member Institutions[https://www.desi.lbl.gov/collaborating-institutions]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF, the DOE, or any of the listed funding agencies.
    Hu Zou and Suijian Xue acknowledge support from the National Natural Science Foundation of China with grant 12120101003 and the National Key R&D Program of China with grant 2022YFA1602902. J. Wang is supported by the National Natural Science Foundation of China under grants 12173009 and the Natural Science Foundation of Guangxi (2020GXNSFDA238018). Y. Yang appreciates the generous financial support provided to the supernova group at U.C. Berkeley (PI: A.V. Filippenko) by Gary and Cynthia Bengier, Clark and Sharon Winslow, Sanford Robertson, and numerous other donors. A.V. Filippenko's group has received additional financial assistance from the Christopher R. Redlich Fund, Alan Eustace (W.K. Zheng is a Eustace Specialist in Astronomy), Briggs and Kathleen Wood (T.G. Brink is a Wood Specialist in Astronomy), and many other donors. The data presented herein were obtained in part at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration (NASA); the observatory was made possible by the generous financial support of the W. M. Keck Foundation. This research also uses data obtained through the Telescope Access Program (TAP). Z. He would like to acknowledge support received from the CAS Project for Young Scientists in Basic Research (No. YSBR-063). We obtained part of the observed data on the unique scientific facility “Big Telescope Alt-azimuthal" of SAO RAS, as well as reduced and analysed the galaxy spectra with the financial support of grant 075-15-2022-262 (13.MNPMU.21.0003) of the Ministry of Science and Higher Education of the Russian Federation. The authors would like to thank Guo Chen for help with the optical observations by the Palomar P200 telescope, and Dr. Marat Musin for timely coordinating the Director’s Discretionary Time observation using the 6 m BTA telescope at SAO.













FAST, Hale, BTA, Keck






astropy <cit.>, LPipe <cit.>, Pypeit <cit.>, slinefit <cit.>














§ OBSERVATIONS
 
    
    The FUDS survey consists of six target fields aiming at exploring the gas evolution in galaxies. The FUDS0 field covers an area of 0.72 deg^2, and was chosen to overlap with the GAL2577 field of the Arecibo Ultra-Deep Survey (AUDS, ). AUDS has a lower sensitivity (∼ 75 μJy beam^-1) and a smaller redshift coverage (z<0.16) than FUDS, but nevertheless provides a useful comparison with the FAST results in order to verify the calibration and data-reduction methods. An important selection criterion is the avoidance of strong continuum sources. In the NVSS catalogue <cit.>, there are four continuum sources with flux density greater than 50 mJy in or close to the FUDS0 field. The strongest source is located at RA(J2000) = 08^ h17^ m35^ s, Dec(J2000) = +2237119 with a 20 cm flux density of 1.28 Jy.
    
    The observations were taken between 2019 Aug 25 and 2020 May 22, mostly during the FAST commissioning phase. The FUDS0 field was scanned in both the RA and Dec directions with the 19-beam receiver in on-the-fly (OTF) mode <cit.>. The 500 MHz bandwidth (1.0–1.5 GHz) was split into 65,536 channels, which gives a frequency resolution of 7.63 kHz (with equivalent velocity resolution 2.25 km s^-1 at z=0.4). The spectra were recorded with a 1 s integration time. The total observation time was 129 hr, consisting of 15 hr on the calibrator, 95 hr on FUDS0, and 19 hr overhead.



§ DATA REDUCTION
 

    The data-reduction method has been previously described <cit.>. The final cube for the FUDS0 field covers 1 deg × 1 deg, as shown in the left panel of Figure <ref>, with a pixel size of 1' × 1'. The gridded beam size is 4.11' at z=0.4 and its associated frequency dependence is given in our previous study <cit.>. The Hanning smoothed cube has a frequency resolution of 22.9 kHz (6.76 km s^-1 at z=0.4). Since the field is not uniformly sampled, the noise rises from the centre to the edge, with the lowest noise being about 50 μJy beam^-1 in the RFI-free frequency range in the centre of the field.

    

    We used the flagging procedures developed in our previous study <cit.>. Most flagging is associated with external radio frequency interference (RFI), such as radar (∼ 1.09 GHz), GNSS (1.15–1.30 GHz), and the geostationary AsiaStar satellite (∼ 1.48 GHz). FAST also suffered from strong RFI generated by the compressor for the refrigerating dewar before Aug 2021. Our flagging method was carefully designed to be robust against this RFI. The total flagged fraction is about 24%, including the  emission line from the Milky Way.
    
    In order to examine the noise distribution in the final data cube, we followed the procedures described previously <cit.>. For each voxel, we calculated the root-mean square (RMS) over the channels within ± 150 km s^-1, excluding any channels containing detections. The noise cube was then smoothed with a Gaussian function (σ=100 km s^-1) within ± 200 km s^-1. The resulting spatial noise distribution at 1.02 GHz is shown in the left panel of Figure <ref>. The lowest noise is distributed around the field centre. There is excess residual noise from a strong continuum source (S_ν=1.28 Jy) at the upper edge. This impacts the detectability of nearby sources. The right panel shows the central RMS noise as a function of frequency between 1.0 and 1.029 GHz (z=0.38). Internal RFI has a modest impact on the RMS noise level, but its presence causes poor baselines and difficulty in identifying faint sources. Frequencies where source identification was strongly affected are shown in red in the panel.



§ DETECTIONS
 

    The algorithm used for the source finding is similar to that of our RFI finder (see Section 4.1 in ). The finder provides masks for detected signals and flattens the spectral baselines using polynomial functions. Detections with small spatial (<2 pixels in either RA or Dec) or frequency (<5 channels) extent are removed from our candidate list. Criteria for true detections are (1) peak flux density | S_peak|≥ 7σ, where σ is the local RMS in the smoothed spectrum; (2) | S_peak|≥ 5σ plus a distinct double-horn feature in the line profile, or with a beam-sized spatial extent; or (3) | S_peak|≥ 5σ with matched redshifts from other surveys, including SDSS DR16 <cit.>, AUDSOC <cit.>, and AUDS <cit.>. Negative detections that satisfy the above criteria were included for reliability analysis. The source finder did not separate galaxies joined in both spatial extent and frequency. These were later separated manually wherever possible based on their moment-zero maps.

    Many false-negative detections were found around the strong continuum source or close to RFI frequencies. These detections were removed if they were within 5' of the strongest continuum source (the dotted red line in the left panel of Figure <ref>) or within the red bands in the right panel of Figure <ref>, unless they satisfied at least one of these criteria: distinct double-horn features, beam-sized spatial extent, or spectroscopic redshift. Finally, we detected six sources at 0.38<z<0.42. No negative signals satisfying our selection criteria were detected in this redshift range; the reliability for the six galaxies is therefore high. Figure <ref> shows their positions in space and frequency in the FUDS0 field. The contours of column density and spectra of the six galaxies are given in Figure <ref> in the main text.

    

    Since the physical beam size of FAST is about 1.32 h_70^-1 Mpc at z=0.4, it is reasonable to treat these high-redshift galaxies as point sources. We used a two-dimensional (2D) Gaussian function with a fixed full width at half-maximum intensity (FWHM) corresponding to the model beam size in the final cube <cit.> to fit the moment-zero map (see Figure <ref>) to derive the position (R.A. and Dec). The spatial-integrated spectrum is derived from
    
    S(ν) = Σ_ij I_ij(ν) w_ijΔ x Δ y/Σ_ij w_ij^2Δ x Δ y  ,

    where I_ij(ν) is the intensity in pixel with indices of i, j, w_ij is the amplitude of the 2D Gaussian fit, and Δ x Δ y is the solid angle of the pixel. The spatial-integrated spectra are shown in the lower panel of Figure <ref> in the main text.
    
    We used the Busy Function <cit.> to fit the spatially integrated spectrum to derive the integrated flux S_ int, flux density weighted frequency ν_ cen, peak flux density S_ peak(ν), and line width W_50 and W_20. In order to compare with previous work, we correct for the instrumental effect on the line width using
    
    W^ Cor = √(W^2 - f_ ins^2)  ,

    where W^ Cor is the corrected line width, W is the line width in units of Hz derived by fitting the Busy function, and f_ ins is the frequency resolution (22.9 kHz; equivalent velocity resolution 6.76 km s^-1 at z=0.4).

    
    
    Considering that some galaxy candidates are detected close to RFI where the spectral baseline may not be flat, the Busy function can underestimate parameter uncertainties. Hence we employed the following jack-knife method to estimate their uncertainties by taking into account thermal noise and baseline noise around the galaxy spectral profiles:
    
    
    
        
  * The noise spectrum is extracted by subtracting the best-fit Busy function from the spatially integrated spectrum. 
                
        
  * The noise spectrum is fractionally shifted by 1/30 of its length. An artificial spectrum is generated by summing the noise spectrum and the best-fit Busy function.
        
        
  * The artificial spectrum is refitted with a Busy function. 
        
        
  * The above process is repeated 30 times to generate a set of 30 values for each parameter. The parameter uncertainty is estimated from the standard deviation of each set.
        
    
    For flux uncertainties, we conservatively introduce a further uncertainty of 10% to account for other sources of error, including calibration, gridding, and frequency dependence. The relative errors of flux parameters (including S_ int and S_ peak(ν)) are given by
    
    σ_ rel' = √(σ_ rel^2+(10%)^2)  ,

    where σ_ rel' is the relative error after correction and σ_ rel is the relative error derived by the noise-shift method.

    The  masses for the detections are derived with <cit.>:
    
    M_ = 49.7   D_ Lum^2   S_ int ,

    where M_ is the  mass in h_70^-2  M_⊙, D_ Lum is the luminosity distance of the galaxy in h_70^-1  Mpc, and S_ int is the integrated flux in Jy Hz. The derived properties of the  galaxies are listed in Table <ref>.

    
    
    
    
    
    
    

    
    
    
    
    
    
    



§ OPTICAL COUNTERPARTS
 

    The Dark Energy Spectroscopic Instrument (DESI) is a multiplexed spectroscopic survey to explore dark energy by employing the Mayall 4 m telescope at Kitt Peak National Observatory and 5000 robotic fiber positioners <cit.>. The survey observes galaxies and stars selected from the DESI Legacy Imaging Surveys <cit.>. The target selection was validated during the DESI Survey Validation phase <cit.>. The DESI experiment necessitates multiple supporting software pipelines and products <cit.>. The data are processed and analysed by an extensive spectroscopic reduction pipeline and a template-fitting pipeline to derive classifications and redshifts for each targeted source <cit.>.

    
    
    We found the optical counterparts of four  galaxy candidates (ID: 123, 124, 125, and 126) in  DESI survey data. The optical spectrum for galaxy candidate 127 was obtained with the Keck-I 10 m telescope and the Low Resolution Imaging Spectrometer (LRIS, ) on 2023 Oct 19. The 5600 Å dichroic, the 600/4000 blue grism (dispersion 0.63 Å pixel^-1), and the 400/8500 red grating (dispersion 1.20 Å pixel^-1) provided a wavelength coverage of 3150–10,270 Å. The slit width was set to be 1” during the observations and the exposure time was 900 s. The raw data were reduced by using the  pipeline <cit.>, which performs a completely automated, end-to-end reduction of LRIS spectra. A linear combination of a linear local continuum and two Gaussian profiles (H_α and [N II] λ 6583 is adopted to model the emission-line profile in the H_α region. Galaxy candidate 128 was observed on 2023 Oct 16 with the long-slit Double Spectrograph (DBSP) on Palomar P200 telescope. A total of 35 min on target exposure time yielded an optical spectrum, in which the H_α, H_β, and [O III] λ 5007 emission lines were detected at S/N = 41.0, 5.6, and 3.9, respectively. The spectroscopic data were reduced following the  pipeline <cit.>, and the redshift is derived using  <cit.>. 
            
    In our spectroscopic observations with the BTA, we discovered a second optical source (R.A.: 08:17:48.26, Dec: +22:17:50.7) with a similar redshift to galaxy 123 within the FAST beam. The spectrum was captured using SCORPRIO-2 (Spectral Camera with Optical Reducer for Photometric and Interferometric Observations, ) at the 6 m BTA telescope of the Special Astrophysical Observatory (SAO) on 2023 Dec 20. The [O II] λλ 3726, 3729 emission and H&K Ca II absorption corresponding to a redshift of 0.3894 (5) was clearly identified. Although it is at a larger separation (∼ 1^'), it may contribute additional flux to the  spectrum. All of the galaxies in our sample are confirmed with optical spectroscopic redshifts. Methods used in the SDSS survey[https://classic.sdss.org/dr7/algorithms/speclinefits.php] were employed to remove continuum and fit the emission/absorption lines. Figure <ref> displays the whole optical spectra of the optical counterparts with detected lines marked. We did not detect any Lyman or Balmer lines in the spectra of the galaxies with IDs 123 and 126, which indirectly implies less ionized gas. Our measurements from radio observations also shows lower  masses for these two galaxies.

    

    We employed MAGPHYS[http://www.iap.fr/magphys/] <cit.> to fit optical/IR photometry from SDSS (u, g, r, i, and z) and WISE (W1, W2, W3, and W4) to derive the stellar mass (M_*), star-formation rate (SFR), and specific SFR (sSFR). MAGPHYS is designed for fitting the spectral energy distribution (SED) in the ultraviolet, optical, and near-IR bands. The code takes into account the stellar component, as well as the dust component which attenuates stellar-population spectra with emission at IR bands. In our data, we removed the bands with relative uncertainties larger than unity. The Milky Way extinction at each band was removed by using a dust-reddening map <cit.> and a dust-extinction function <cit.>. Considering the possibility of contamination of the W4 band of WISE by active galactic nuclei, we performed a refit without this band when the fit failed. This happened when best-fit parameters with an uncertainty of zero were derived, or when the boundary of parameter space was reached. The final fit results are given in Figure <ref>. The best-fit parameters of the optical counterparts are listed in Table <ref>.

    

    











aasjournal












 Paper Title: FAST observations of neutral hydrogen in the interacting galaxies NGC 3395/3396.



firstpage–lastpage
New lower bound for the optimal congruent geodesic ball packing density of screw motion groups in 𝐇^2×𝐑 space. 
[Mathematics Subject Classification 2010: 52C17, 52C22, 53A35, 51M20. Key words and phrases: Thurston geometries;  geometry; geodesic ball packing; tiling; space group;]
    Arnasli Yahya and Jenő Szirmai 

Department of Algebra and Geometry, Institute of Mathematics,

Budapest University of Technology and Economics, 

Műegyetem rkp. 3., H-1111 Budapest, Hungary 

arnasli@math.bme.hu, szirmai@math.bme.hu

    August 5, 2024
=========================================================================================================================================================================================================================================================================================




§ ABSTRACT 
We report on high-sensitivity neutral hydrogen observations toward the gas-rich interacting galaxies NGC 3395/3396 with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Compared to previous observations carried out by the Very Large Array (VLA) and the Westerbork Synthesis Radio Telescope (WSRT),  a more extended HI envelope around this system has been detected. The total HI gas mass of the NGC 3395/3396 system is estimated to be 7.8 × 10^9 M_⊙. This value is 2.7 times more than that reported based on the VLA interferometric maps. Previous observations found a large HI tail extending to the south-west and a minor tail emerging from the north of this peculiar galaxy pair. Based on the high-sensitivity observations of FAST, an extended HI plume to the north-west and a gas plume to the north-east have been detected for the first time. Neutral hydrogen of the two smaller galaxies IC 2604 and IC 2608 on the south of the system have also been detected. We discuss the origins of these extra gas and possible tidal interactions between these galaxies. NGC 3395/3396's most prominent tidal feature, the south-west tail combined with the new detected north-west plume behaves like a large ring. We suggest the ring might be formed by the previous fly-by interaction between NGC 3395 and NGC 3396 which happened 500 Myr ago. Our study shows that high-sensitivity HI observations are important in revealing low column density gas, which is  crucial to a deeper understanding of this interacting system.





galaxies: individual: NGC 3395 - galaxies: individual: NGC 3396 - galaxies: individual: IC 2604 - galaxies: individual: IC 2608 - galaxies: interactions








§ INTRODUCTION

It is widely accepted that galaxy interactions such as collisions and mergers play an important role in galaxy evolution. These processes can change the morphology of a galaxy and maintain the stable star formation rate inside (e.g. Sancisi et al. 2008; Richter 2017). Atomic hydrogen (HI) is the most abundant component of the interstellar medium (ISM). In gas-rich galaxies, the extent of the HI emission could be several times larger than their optical  diameters (D_25), making it a very good tracer of tidal interactions, cold gas accretions and/or mergers (e.g. Sancisi et ai. 2008; Serra et al. 2012; Xu et al. 2021). Neutral hydrogen 21cm line surveys of large samples of galaxies indicate that at least one out of four galaxies shows signs of merger or accretion events in the recent past (Sancisi et al. 1999). The interaction history between a galaxy and its environment could be studied by gathering information of extended HI structures such as tails, bridges, plumes and ring-like structures in galaxy surroundings. Many authors have also attempted to explain these complex HI features by means of simple dynamical models (e.g. Toomre & Toomre 1972; Barnes 1992; Durrell et al. 2003; De Looze et al. 2014). Numerical simulations predict that mergers between two gas-rich disk galaxies could trigger gaseous inflows and starbursts (e.g. Hernquist 1989; Mihos et al. 1991; Mihos & Hernquist 1996). NGC 3395/3396, also named Arp 270 (Arp 1966), is a pair of closely interacting late-type starburst galaxies. NGC 3395 (the west galaxy) and NGC 3396 (the east galaxy) are classified as Sc and Sm by HyperLeda[https://leda.univ-lyon1.fr]. The distance to the system is 21.8 Mpc (Tully, Shaya & Pierce 1992). The optical image shows NGC 3395 is almost face-on, and NGC 3396 is almost edge-on. Their systemic velocities are 1605 and 1678 km s^-1 respectively according to Garrido et al. (2002), indicating the merger is occurring in a plane almost perpendicular to the line of sight. The system is an approximately equal-mass merger, with a mass ratio of 1.5:1 (Zaragoza-Cardiel et al. 2013). Using the high-resolution Chandra X-ray observation, Brassington et al. (2005) detected sixteen X-ray point sources in the two galaxies, seven of which are classified as ultraluminous X-ray sources. By comparing the luminosities and galaxy properties, they suggest NGC 3395/3396 is in a later stage of evolution than NGC 4485/4490, but earlier than the Antennae and NGC 3256.  Zaragoza-Cardiel et al. (2013) made Hα observations of the system. Outflows, characteristic of galactic superwinds and gas inflow toward the centre were detected. They speculate the presence of an active galactic nuclei (AGN) in NGC 3396. Radio continuum observations also found evidences for recent star formation both in the two galaxies (Huang et al. 1994). Using the observations of VLA, Clements et al. (1999) detected a large HI tail extending to a projected distance of 63 kpc south-west of NGC 3395. Besides, a much weaker HI tail emerging from the north of the pair has also been detected (Fig. 1). Smith et al. (2010) discovered a candidate tidal dwarf galaxy at the western extremity of the large tail with moderate optical and UV colors. They also found a faint diffuse emission near the middle of this tail. A comparison with the Mice highlights the absence of any gaseous outflows from the NGC 3395/3396 system (Read 2003).These studies suggest that this interacting galaxy pair is at an earlier stage of evolution than the 11 ongoing mergers listed by Toomre (1977). By means of N-body simulations, Clements et al. (1999) conclude that the galaxies are before or after 50 Myr of their second perigalactic passage, with the first approach occurring approximately 500 Myr ago. The current star formation activity is due to the second close approach. They also suggest the NGC 3395/3396 system will merge within 100 Myr. 

Although the NGC 3395/3396 system has been studied in a wide range of wavelengths, we make deeper HI observations of this region with FAST. FAST high-sensitivity observations have revealed many new structures of galaxies in the local universe, such as extra-planar HI clouds and an HI tail in the M101 galaxy group (Xu et al. 2021), a long HI accretion stream toward M106 (Zhu et al. 2021), a 0.6 Mpc HI structure associated with Stephan's Quintet (Xu et al. 2022), and new tidal features in M51 (Yu et al. 2023). In this paper, we report the high-sensitivity HI observations of the interacting galaxies NGC 3395/3396 by FAST. This paper is organized as follows: in Section 2, we introduce our observations and data reduction. Results and analysis are in Section 3, and finally we summarize in Section 4.

 




§ OBSERVATIONS AND DATA REDUCTION

We have carried out the FAST All Sky HI Survey (FASHI), which is a new survey of HI emission covering the whole FAST sky between -14^∘ and +66^∘ of declination over the frequency range of 1.0 - 1.5 GHz. The scientific goal of FASHI is to take advantage of the high-sensitivity of FAST to make a complete census of the HI gas in the nearby universe.  The aperture of FAST is 500 m, and its effective aperture is about 300 m. The sensitivity of this telescope reaches 2000 m^2/K and the system noise temperature has been controlled below 20 K and the pointing accuracy is ∼ 7.9^'' (Jiang et al. 2019, 2020). It is the most sensitive single dish telescope in this frequency range, allowing us to take sensitive observations for various scientific goals, such as studies of pulsars (e.g. Feng et al. 2021; Pan et al. 2021), fast radio burst (e.g. Li 2021), and galaxy evolution (e.g. Zhu et al. 2021; Xu et al. 2022) . From August 2020 to January 2023, more than 7500 square degrees of the sky have been observed, and more than 40000 extragalactic HI galaxies have been detected by FASHI. More information of FASHI is described by Zhang et al. (2023). 



In order to increase the sensitivity and confirm the weak detections, we have further used the Multibeam on-the-fly (OTF) mode to map the NGC 3395/3396 region twice during 2022 January and February. The the 19-beam receiver system in dual polarization mode was used as front-end and the half-power beam width is 2.9 arcmin at 1.4 GHz for each beam. For the digital back-end system, we chose the Spec(W) spectrometer which has a bandwidth of 500 MHz and 65 536 channels, resulting in a velocity resolution of 1.67 km s^-1 at 1.4 GHz. The data were reduced mainly using the FAST spectral data reduction pipeline HiFAST (Jing et al., 2024; Xu et al., 2023). The HiFAST pipeline combines several useful data reduction packages including antenna temperature correction, baseline correction, RFI mitigation, standing-waves correction, gridding, flux correction, and generating fits cubes. More detailed procedures are described in the HiFAST pipeline cookbook online[https://hifast.readthedocs.io/].

 


 



 





§ RESULTS AND ANALYSIS

An integrated HI flux of 23.2 Jy km s^-1 is detected in the central region of NGC 3395. This value is consistent with previous observations by Arecibo and the Nançay Radio Telescope (NRT), whose values are 20.2 and 22.0 Jy km s^-1 respectively (Lewis 1985; van Driel et al. 2001). At a velocity resolution of 6.7 km s^-1, the noise of our data is 0.5 mJy beam^-1. At this noise level, the 5σ column density threshold within one velocity resolution element is 7.5 × 10^16 atoms cm^-2. This value is about two orders of magnitude lower than that of VLA, which enable us to detect new features in this system. The obtained 21-cm HI image of the NGC 3395/3396 region with FAST, VLA and WSRT are shown in Fig.1. The VLA and WSRT HI images show an extended S-shaped structure around the pair, with a large tail in the south-west (we call it “tail 1" hereafter in this paper) and a minor tail (hereafter “tail 2") emerging from the north of the system. The nearby company galaxies IC 2604 and/or IC 2608 are also detected by VLA and WSRT. It can be noticed that the HI emission detected by FAST is more extended. The HI gas of IC 2604 and IC 2608 seems to be connected with the envelope of NGC 3395/3396. The most prominent detected HI features are the gas in the north-west and north-east of NGC 3395/3396. These structures have been detected for the first time. The discussions of these structures are in the following subsection 3.2. The total gas mass of the envelope of NGC 3395/3396 could be estimated by equation

    M = 2.35 m D^2 ∫ N(x,y) dxdy

where the factor 2.35 is the mean atomic weight, m is the mass of atomic hydrogen, D is the distance, dx and dy are the pixel sizes, N(x,y) is the HI column density which could be calculated through

    N (x,y) = 1.1 × 10^24∫ S_v dv/θ_beam^2

where S_v is the flux density in unit of Jy, and θ is the beam size of FAST in arcsec. The obtained gas mass of the envelope is 7.8 × 10^9 M_⊙, about 3 times higher than that found by Clements et al. (1999), indicating more diffuse cold gas has been detected.



 §.§ The south-east tail and north tail

Previous HI observations have already found two HI tails in the gas-rich interacting system of NGC 3395/3396. Fig.2 shows our FAST HI channel maps of this region superimposed on the WSRT moment-0 image. We can see that tail 1 has an HI velocity range of 1554.8 km s^-1 to 1684.4 km s^-1, and tail 2 has a velocity range of 1660.1 km s^-1 to 1692.5 km s^-1. This is consistent with the observations of VLA (Clements et al. 1999) and WSRT (van der Hulst et al. 2001). Clemens et al. (1999) first discovered these tails. According to their study, tail 1 has been stripped from NGC 3395 during a prograde encounter with NGC 3395, although it appears to be joined with NGC 3396 in the VLA map. By means of N-body simulations, they further found NGC 3395/3396 is within 50 Myr of its second close approach, which may have just occurred or will occur in the near future. The FAST integrated HI emission of the south-east tail is shown in the top left panel of Fig.3. The presence of tail 1 is wider and longer than those revealed by VLA and WSRT, indicating the existence of more diffuse and faint gas. Using the above two equations and the integrated velocity range shown in table 1, we estimate the HI gas mass of tail 1 to be 1.8 × 10^9 M_⊙, which is 4.1 and 2.3 times higher than those detected by VLA and WSRT, respectively. The mass of tail 1 is 23 percent of the total envelope of NGC 3395/3396. This value is much lower than that found in the tails of the Antennae, where 70 percent is found (van der Hulst 1979).

Tail 2 is a much weaker HI tail emerging from the north of the NGC 3305/3396 system (Clemens et al. 1999). This tail is more obvious in the HI image of WSRT (Fig.1). In our observations, this tail is hardly resolved owing to the large beam of FAST. By comparison with the HI and optical images, Clemens et al. (1999) suggest that this minor tail is the extension of an HI ridge which coincides with an optical tidal feature in the south of NGC 3395. This tidal feature could also be reproduced in the simulations of Clemens et al. (1999), but needs slight changes to increase the projected length.



 §.§ The north-west and north-east plumes

 


These two HI features are detected by FAST for the first time. In the channel maps of Fig.2, we notice that from the velocity range of 1587.2 km s^-1 to 1643.9 km s^-1, there is an extra plume of HI gas to the north-west of NGC 3395/3395. This plume seems to stem from the western extremity of tail 1 and connects to the north-west of the envelope of NGC 3395/3396. The bottom left panel of Fig.3 displays the integrated flux density map of this extra plume. It looks like a tail on the opposite side of tail 1. Fig.4 is the moment-1 map (velocity field) of the NGC3395/3396 system. The envelope of NGC 3395/3396 has a velocity gradient from north-east to south-west. The velocity fields of tail 1 and the north-west plume are almost symmetrical, with a symmetric axis from northeast to southwest, suggesting the two tails might be two halves of a large gas ring. Ring like structures are common around interacting galaxies (e.g. Schneider et al. 1989; Malphrus et al. 1997; Ryder et al. 2001). According to the models of Toomre (1978), ring morphology could be produced by an off-center collision between two galaxies, and the far side of the ring will soon open up into extended tidal tails. The N-body simulation of Clemens et al (1999) suggests that a weak fly-by interaction between NGC 3395 and NGC 3396 has taken place about 500 Myr ago. The bottom panel of Fig.4 shows the position–velocity (PV) diagram cut through the center of the ring. The velocity in the center of the ring is lowest (∼ 1587 km s^-1), and increases towards the two tails, indicating the ring is expanding. The expanding velocity (v_exp) of the ring could be estimated by measuring the deviation of the velocity of the ring seen in the PV diagram (Pokhrel et al. 2020). We calculate v_exp as the difference between the systemic velocity of the ring and the gas velocity at the center (where the gas is deviating from the surroundings). We adopt 1627 ± 8 km s^-1 as the systemic velocity of the ring as the ring feature is clearest in the velocity range between 1619.6 and 1635.8 km s^-1 in the channel maps of Fig. 2. The expanding velocity of the ring is thus estimated to be about 40 ± 8 km s^-1. The expansion age of the ring could thus be estimated by equation t_exp = R/v_exp, where R = 29.8 kpc is the radius of the ring. The derived value is 725 ± 145 Myr, which is roughly consistent with the simulation of Clemens et al (1999). We thus speculate that tail 1 and the north-west plume are two half parts of a ring which was produced by the first encounter of NGC 3395 and NGC 3396 about 500 Myr ago. 

From the channel maps of Fig.2, we found another new structure on the north-east of NGC 3395/3396 in the velocity range of  1708.7 km s^-1 to 1741.1 km s^-1. Its integrated flux density is also shown in the bottom right panel of Fig.3. The HI gas mass is 1.1 × 10^8 M_⊙, which is the lowest among the four structures. We check the optical images from Sloan Digital Sky Survey (SDSS)[https://dr12.sdss.org/fields], the Dark Energy Spectroscopic Instrument (DESI) legacy imaging surveys[https://www.legacysurvey.org/decamls/] and ultraviolent images from the Galaxy Evolution Explore (GALEX)[https://galex.stsci.edu/GR6/],  which are all publicly available on line. Emission in these wavelengths by the north-east plume is extremely deficient. No previously catalogued galaxy matches with this HI feature. A search in this region on the NED/IPAC extragalactic database (NED) also yields no findings.



 §.§ Possible tidal interactions with IC 2604 and IC 2608

 


 


 The HI emission of the two smaller galaxies IC 2604 which is 14 arcmin to the south-west, and IC 2608 which is 14 arcmin to the south-east have also been detected by VLA and FAST (Fig.1). The HI emission of IC 2608 is undetected by WSRT. The HI velocities of the two galaxies range from 1546 km s^-1 to 1708 km s^-1 and 1587 km s^-1 to 1757 km s^-1, respectively, indicating they lie at the similar distance as the NGC 3395/3396 system. IC 2604 is classified as a barred spiral by de Vaucouleurs et al. (1991). The optical image of this galaxy appears asymmetrical with a large HII region at the extremity of its southern arm. Its HI morphology is also asymmetrical with the peak emission in this optical arm (Clemens et al. 1999). IC 2608 is an Sc-type galaxy (Vaucouleurs et al. 1991). The optical disk of this galaxy appears almost edge-on. The HI peak emission is coincident with the optical center, with a small tail extending to the south-east (see the Fig.2 of Clemens et al. 1999). The asymmetrical HI structures of IC 2604 and IC 2608 indicate possible tidal interactions with the NGC 3395/3396 system. From Fig.1, we notice the HI emissions of IC 2604 and IC 2608 detected by FAST are more extended, and seem to be connected with the envelope of NGC 3395/3396. From Table 1, it could also be noticed that the gas mass of these galaxies calculated from the observations of FAST are 20 percent and 42 percent more than those detected by VLA, indicating more diffuse gas has been detected. IC 2604 and IC 2608 may be physically connected to the envelope of NGC 3395/3396 by neutral hydrogen. Clemens et al. (1999) suggested IC 2604 and IC 2608 have at most a minor influence on the dynamics of NGC 3395/3396, as it is not necessary to include them in their N-body simulations to reproduce the HI morphology of tail 1 and tail 2. As is shown above, our FAST observations have detected more diffuse gas and new structures in the envelope of NGC 3395/3396, indicating slight changes of their models are needed. 

We now discuss the possible tidal interactions between NGC 3395/3396 and IC 2604/2608. The top panel of Fig.5 shows the PV diagram cut through IC 2604, tail 1, NGC3395/3396 and the north-east plume. The positions and directions of the two PV diagrams are shown as the two red arrows in Fig.3.  It can be noticed the IC 2604 contours are asymmetrical with an HI bridge connecting to tail 1 in the PV diagram, implying they are interacting. The north-east plume might be a tidal tail on the opposite side of NGC 3395/3396 caused by IC 2604. Fig.6 shows the composite color images of IC 2604 and IC 2608 from the DESI legacy imaging surveys (Dey et al. 2019). The star distribution of IC 2604 is asymmetrical and seems more extended to the north-east, which is the direction to the NGC 3395/3396 system. Our study suggests tidal interaction with IC 2604 should be considered in the study of the evolution of the NGC 3395/3396 system. More gas is stripped toward tail 1 by the tidal force of IC 2604, making this tail  much denser and more massive than the north-west plume. This may be the reason the mass of the north-west plume is only a quarter of tail 1. The bottom panel of Fig.5 shows the PV diagram cut through IC 2608, tail 1, NGC3395/3396 and tail 2. The IC 2608 contours look symmetrical, even though there is also a weak HI bridge connecting to tail 1. The deep optical image of IC 2608 (Fig. 6) is also symmetrical. Consistent with the study of Clemens et al. (1999), we regard tidal interaction between NGC 3395/3396 and IC 2608 is weak, although 40 percent more diffuse gas has been detected in this galaxy.

In gas-rich interacting galaxies, material could be pulled from the system and forms gaseous filaments that can harbour second generation tidal knots and tidal dwarf galaxies (TDGs).
Clements et al. (1999) noticed a distinct clump of HI in the western extremity of tail 1 (Fig. 1). Dynamical analysis indicates the clump is in virial equilibrium and unable to collapse to form stars. They thus suggest this clump represents another example of TDG. Based on the images from GALEX and SDSS, Smith et al. (2010) found the source near the end of tail 1 has moderate optical and UV colors, indicating star formation activities inside tail 1. Dynamical simulations suggest tidal interactions could trigger starburst by compressing the gas of a galaxy (e.g. Linden & Mihos 2022).  To quantify the effect of tidal interactions with this TDG, we calculate the tidal index Θ defined by Karachentsev & Makarov (1998) as
 
    Θ = log_10 (M_∗ [×10^11M_⊙]/D_project^3 [Mpc])

where M_∗ is the stellar mass of the NGC 3395/3396 system (2.4 × 10^10 M_⊙ according to Zaritsky et al. 2014), IC 2604 (6.3 × 10^8 M_⊙ according to Leroy et al. 2019) and IC 2608 (4.7 × 10^8 M_⊙ according to Leroy et al. 2019) respectively. D_project is the projected distance from the TDG to these galaxies. A higher Θ indicates a stronger influence. The derived values of Θ are 3.2, 2.0 and 1.3 for the NGC 3395/3396 system, IC 2604 and IC 2608, respectively. Pearson et al. (2016) found if a dwarf galaxy pair has a tidal indices Θ > 1.5, the pair is most likely affected by tidal and/or ram-pressure stripping from the host galaxy. Our study suggests the TDG in tail 1 is affected by tidal interactions mainly from the NGC 3395/3396 system, but the influence from IC 2604 should not be ignored. IC 2608 has at most a minor influence on the dynamics of the NGC 3395/3396 system. Simulations are beyond the scope of this paper. But a new model involving three galaxies (NGC 3395, NGC 3396 and IC 2604) is required to obtain a fully matched result in the future. 
 


§ SUMMARY

We report the high-sensitivity HI observations toward the gas-rich interacting galaxies NGC 3395/3396 with FAST.  More diffuse cold gas and new structures around this system have been detected. The total HI gas mass of the envelope of NGC 3395/3396 is 2.7 times more than that reported previously. An extended HI plume on the north-west and a new gas plume on the north-east have been detected for the first time. Neutral hydrogen of the two smaller galaxies IC 2604 and IC 2608 on the south have also been detected. We discuss the origins of these extra gas and possible tidal interactions between these galaxies. NGC 3395/3396's most prominent tidal feature, the south-west tail combined with the north-west plume look like a large ring. The ring might be formed by the previous fly-by interaction between NGC 3395 and NGC 3396. IC 2604 probably has tidal interactions with the NGC 3395/3396 system. Our study shows that high-sensitivity HI observations are crucial in revealing low column density features in nearby galaxies.



§ ACKNOWLEDGEMENTS

We thank the anonymous referee and scientific editor for insightful comments and constructive suggestions. We acknowledge supports from the National Key R&D Program of China No. 2018YFE0202900. We thank Clemens M.S. for sharing their VLA observation on the web. This work was supported by the Youth Innovation Promotion Association of Chinese Academy of Science (CAS), the National Natural Foundation of China No. 12373001, and also supported by the Open Project Program of the Key Laboratory of FAST, NAOC, Chinese Academy of Sciences.



§ DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the corresponding author.


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 Paper Title: An all-sky catalogue of stellar reddening values.

 


T_ eff
km s^-1
log g
ξ_ t
ζ_ RT
v_ r
vsin i
E(B-V)
Kepler

   


Department of Theoretical Physics and Astrophysics, Masaryk University, Kotlářská 2, 611 37 Brno, Czechia, epaunzen@physics.muni.cz
Kuffner Observatory, Johann-Staud-Straße 10, A-1160 Wien, Austria
Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, 917 24 Trnava, Slovakia





 
  
  
   When observing astronomical objects, we have to deal with extinction (i.e. the absorption and scattering of the emitted radiation by dust 
   and gas between the source and the observer). Interstellar extinction depends on the location of the object and the wavelength. The different extinction laws describing these effects are difficult to estimate for a small sample of stars.
  
   Many sophisticated and automatic methods have recently been developed for estimating astrophysical parameters (age and metallicity, for example) depending on the reddening, which is normally treated as a free parameter within the corresponding estimations. However, many reddening values for stars have been published over the last few decades, most of which include observations in the ultraviolet, which are essential for a good estimation but are essentially no longer taken into account. 
  
   We searched the literature through the end of 2022 for published independent reddening values of stellar objects based on various methods that exclude estimates from reddening maps. In addition, we present new reddening estimates based on the classical photometric indices in the Geneva, Johnson, and Strömgren-Crawford systems. These are based on well-established and reliable calibrations.
  
   After a careful identification procedure and quality assessment of the data, we calculated the mean reddening values of 157 631 individual available measurements for 97 826 objects. We compared our results with the ones from recent automatic pipeline values, including those from the Gaia consortium. In addition, we chose star cluster members to compare their mean
   values with estimates for the corresponding aggregates. Within the different references, we find several statistically significant offsets and trends and discuss possible explanations for them.
  
         Our new catalogue can serve as a starting point for calibrating and testing automatic tools such as isochrone and
  spectral energy distribution fitting. Our sample covers the whole sky, including the Galactic field, star clusters, and Magellanic Clouds, and so can be used for a variety of astrophysical studies.

   

   An all-sky catalogue of stellar reddening values
    E. Paunzen1
        M. Netopil2
        M. Prišegen3
                                N. Faltová1
        
    
=============================================================================================================








§ INTRODUCTION
 


Extinction and reddening caused by interstellar dust affect the detected radiation
from most observable astronomical sources. The problem worsens when objects lie close to the
Galactic plane due to the high dust density <cit.>. An error in determining the 
reddening will have severe consequences, for example for drawing colour-magnitude diagrams and 
determining astrophysical parameters such as the effective temperature, luminosity, mass, and age
<cit.>. 

However, <cit.> conducted multi-colour photometry of O- and B-type stars 
and found no unique reddening law. In addition, they concluded that there is a minor variation in the total-to-selective extinction ratio (R_ V) with Galactic longitude. This was later confirmed by <cit.> from the spatial variation in the wavelength of maximum polarisation. Finally, <cit.> summarised the knowledge
about the interstellar reddening law, R_ V, varying for different sight lines.
As a further complication, the interstellar extinction is variable depending on the wavelength <cit.>.
The combination of these two effects leads to different extinction coefficients for
different photometric filters for a specific reddening law. This must be considered 
for the ultraviolet (UV) and infrared region <cit.>, which is normally not accessible from the ground.
An excellent overview of the relevant processes and methods can be found in <cit.>. 

Reddening measurements for the interstellar medium in the past relied on three techniques: (1)
star counts <cit.>, (2) spectroscopic and photometric measurements with their calibrations
<cit.>, and (3) main sequence fitting of colour-colour and
colour-magnitude diagrams <cit.>. Each of these techniques has its own advantages and disadvantages.

With the availability of precise photometric data from the UV to infrared
region, spectral energy distribution (SED) fitting techniques <cit.> 
are now widely used to build 3D reddening maps. This technique needs, in addition to a good knowledge
of the stellar astrophysical parameters, a set of stellar flux models that introduces another
source of uncertainty <cit.>.   

The astrometric results from the Gaia satellite <cit.> open a new
window for the determination of astrophysical parameters based on
precise parallaxes. The corresponding final catalogue will include ultra-precise parallaxes
(and thus distances) and auxiliary measurements such as photometry and spectroscopy, which
makes the reddening determination a critical issue.  

In this paper we present a catalogue of mean reddening values compiled from the literature,
which, to our knowledge, does not exist elsewhere.
It provides a source of standard values for future calibration purposes, especially as a starting
point for the SED fitting procedures and new Gaia data releases. 






§ SAMPLE SELECTION AND DATA SOURCES
 



Besides the inclusion of references already known to us, the literature was searched until the end of the year 2022 for reddening estimates of stellar objects based on various methods, and no time limit was set for the past. Almost all larger catalogues are already available from the CDS/VizieR, and we used some reddening related keywords of the unified content descriptor – such as phot.color.excess or phys.absorption – to identify appropriate papers. A pre-selection based on the catalogue title was made because of the many returned references. Furthermore, we do not cover works that include reddening estimates for fewer than ten objects. This certainly results in an incomplete list, but a complete census cannot be gathered anyway. The remaining references were checked to see if these include independent reddening estimates – thus, we excluded works that adopt estimates of others that are, for example, already included in our list. The compiled references and the number of studied objects are listed in Table <ref>. We do not cover results of reddening maps or Gaia data, as we intend to provide a catalogue for their validation.

The reddening values are not always listed as E(B-V) but also in the Strömgren-Crawford 
<cit.> and Two Micron All Sky Survey <cit.> photometric
systems. For the transformation to E(B-V), we used the following transformations 
<cit.>:


    E(B-V)    =    1.35E(b-y) = 0.36E(V-K_ S) =  
       =    2.00E(J-K_ S) = 0.32A_ V = 2.78A_ K_ S.


The errors for the colour excess ratios of the different photometric bands 
listed in <cit.> are typically below 0.04 mag. We also
considered a non-standard reddening law if listed in the individual references.
In addition to the references from the literature, we also calibrated reddening values in the 
Geneva seven-colour, Johnson, and Strömgren-Crawford photometric systems. In the following,
we overview the corresponding calibrations and data sources.

The Geneva photometric sample: The Geneva photometric catalogue <cit.>
belongs to one of the most homogeneous datasets, based on a unique instrumentation 
and reduction procedure in both hemispheres <cit.>. The about 43 000 measured stars in the General Catalogue of 
Photometric Data <cit.> cover all spectral types and luminosity classes. 
For O/B type stars, the reddening free X/Y parameters <cit.> enable an estimate of the reddening in E[B-V] that can be transformed to the Johnson UBV equivalent E(B-V) = 0.842 × E[B-V].
In the first step we used the parameter space -0.3 ≤ X ≤ +1.4 and -0.07 ≤ X ≤ +0.15 to extract the most likely 
O- and B-type stars population <cit.>. The sample was then refined by a cross-match with SIMBAD and a check of available spectral classifications. This was done on the basis of coordinates (a
search radius of ten arcseconds was used) and apparent magnitudes.
The final cleaned sample includes 10 233 stars with a reddening based on Geneva photometric data.

The Johnson photometric sample: We employed the Q parameter, which is usable for early-type (i.e. hotter than B9) stars.
It utilises the colours U-B and B-V and their ratio <cit.>. It has been widely applied, especially for young open clusters <cit.>. For this work, the mean Johnson UBV 
measurements from the GCPD were taken. As the next step, the Q values for different spectral types were calculated, and all 
relevant hot objects were identified.
For this, the spectroscopic data compilation by <cit.> and further spectroscopic data from the SIMBAD database
were used. If no spectroscopic information was available, objects were deleted from the list rather than introducing wrong
reddening values for highly reddened cool-type objects, for example. The final list of reddening values based on the Q-method
includes 9878 stars.

The Strömgren-Crawford photometric sample: The uvbyβ photometric system has been widely and successfully used since its introduction almost 60 years ago <cit.>. Multiple calibrations for different stellar groups have been published since then.
We used the catalogue of mean uvbyβ values by <cit.>. It includes 60 668 stars with unweighted mean 
indices and their errors. From this compilation, only stars with the complete set of uvbyβ measurements were considered.
This results in a list of 32 529 stars in total.
We used the program TEMPLOGG <cit.> to calculate the reddening values. 
This program is a menu-driven application written in C-Shell script. It provides convenient access to the different Fortran
codes that perform the inversions from observed colour indices to fundamental
parameters, and it also enables the user to process tables of photometric data for a
list of stars in batch form. It applies the calibrations from
<cit.>, <cit.>, and <cit.> and covers the whole spectral type range.

The identifications in the references (Table <ref>) are manifold. They 
range from commonly known IDs (for example, HD and HIP numbers) to coordinates in several 
epochs. Especially the Lausanne code numbering system (LID) used in the GCPD, is sometimes
troublesome. However, a common object identification must be done before the final means can be calculated.
Our primary source for this task is the 2MASS catalogue. It is 
deep enough for our purpose but also covers the brightest stars. All objects were carefully
checked within the 2MASS survey. If no unambiguous identification was possible, we skipped the
measurements. In total, only about 1700 data points were skipped. This is a small number compared
to the over 120 000 measurements in the final catalogue.

In the last step, we calculated unweighted mean values and their standard deviations. Finding criteria
for introducing meaningful weights on a justified basis was impossible. As expected for many objects and references, some mean reddening values exhibit large errors up to 2 mag. 
The reasons for that could be wrong identifications or simply very divergent measurements.

The final catalogue includes 157 631 individual available measurements for 97 826 objects and will be available in electronic form, an excerpt is listed in Table <ref>.








§ ANALYSIS
 

Our primary source for common identification is the 2MASS catalogue. For the further analysis,
we cross-matched it with the Gaia Data Release 2 and 3 (DR2 and DR3) catalogues <cit.> using the coordinates
and J as well as G magnitudes. Again, we were conservative, rather than excluding a 
Gaia source instead of including a false identification. We could identify 96 549 from
the 97 826 objects (or 98.69%) of our catalogue.

The final catalogue represents a sample of stars distributed over the whole sky, as shown in Fig. <ref>.
Several important Galactic features, such as the disk, the central and Bulge region, and the north
and south poles, are seen. However, the Magellanic Clouds are also visible.

In Fig. <ref> the histogram of the G magnitudes is shown. Our sample includes objects with magnitudes of 1.7 to 21.2,  with maxima at 8.5 and 16.5 magnitudes. The 16.5 magnitude maximum is caused
by objects from the Galactic Bulge <cit.>. It shows a statistically
significant number of stars in all magnitude bins, which can be used for calibration.



 §.§ The references for assessing the results
 

We selected six recent and widely used sources
of reddening values to compare and analyse our values with the literature: <cit.>, <cit.>, <cit.>, <cit.>, <cit.>, and <cit.>.
From these, the work by <cit.> presents a 3D map, whereas the other three
sources list reddening values for individual stars.

We included a comparison with results from the Gaia DR2 <cit.> because many papers devoted to star clusters and stellar astrophysics are based on it. Most of them use reddening values for the analysis.

For all six references, we have to emphasise that no filter in the UV region (bluewards of 400 nm)
was used for the reddening estimates. It is well known that indices such as Johnson (U-B) and 
Strömgren (u-b) are most efficient for such a purpose. This is a severe drawback. We note that
the G and G_ BP filters of the Gaia photometric system measure the flux down to about 330 nm, with a minimal efficiency compared to the other, redder regions. Furthermore, the filters are much too broad (blue cutoffs at
680 and 1000 nm, respectively) to be useful for the reddening estimate.

We also notice that the StarHorse <cit.> and 
StarHorse2021 <cit.> compilations include negative reddening values. It is
written in the papers that these values must be treated with caution, but no other comments
for the reasons are given.



<cit.>: They presented a 3D interstellar dust reddening map of the Galactic plane
based on Gaia DR2, the Two Micron All Sky Survey (2MASS), and the Wide-Field Infrared Survey Explorer <cit.> photometry. The filters range 
from 400 nm to 2400 nm.
It covers the whole
Galactic longitude range with Galactic latitudes | b | < 10. They applied a machine
learning algorithm called random forest regression to derive E(G-K_ S), 
E(G_ BP-G_ RP), and E(H-K_ S). In doing so, they built an empirical
training sample of stars selected from several large-scale spectroscopic
surveys, including the APO Galactic Evolution Experiment <cit.>
Large Sky Area Multi-Object Fiber Spectroscopic Telescope <cit.>, and
Sloan Extension for Galactic Understanding and Exploration <cit.> surveys.
Together with the photometry, reddening values were derived with
the star-pair technique. They state that a comparison with results in the literature
shows good agreement and that their results have typical uncertainties of about 0.07 mag
in E(B-V). We used the three listed reddening values for the individual Gaia DR2 stars and
computed a mean reddening and its standard deviation using the following relations 
<cit.>:

    E(B-V) = 0.45E(G-K_ S) = 6.09E(H-K_ S)                
    .

There are 37 045 stars that are also on our target list. 

Gaia DR2 catalogue <cit.>: It includes both the G-band extinction,
A_ G, and the E(G_ BP-G_ RP) reddening. They were first derived using the parallaxes and photometric 
data to get each passband's effective temperature, absolute magnitudes, and reddening
values. Then, an interpolation routine within the PARSEC evolutionary models <cit.>
for solar metallicity (Z_⊙ = 0.0152), and a standard reddening law was applied. The authors state that
the extinction estimates are inaccurate on a star-by-star level but mostly unbiased
and so are applicable at the ensemble level.  
We transformed the reddening of (G_ BP-G_ RP) according to <cit.>:

    E(B-V) = 0.77E(G_ BP-G_ RP)   
    .

The standard deviation was derived by the given upper and lower limits for E(G_ BP-G_ RP). 
In total, we have 51 356 stars in common.

Gaia DR3 catalogue <cit.>: In addition to more precise astrometric parameters, 
this data release also includes low-resolution BP/RP spectra for 219 million sources. They cover the wavelength range 330 to 1050 nm with a resolution between 13 and 85. This resolution does not permit the measurement of individual spectral lines but can be used similar to spectrophotometry. The overall method
has not changed <cit.>. We note that the filter curves have been altered
compared to the Gaia DR2. With these new data sources, the individual
reddening estimates should be expected to be closer to the already published ones, as compiled in this work.



StarHorse <cit.>: They combined parallaxes and photometry from the Gaia DR2 together 
with the photometric catalogues
of Pan-STARRS 1, 2MASS, and AllWISE <cit.> in order to derive
Bayesian stellar parameters, distances, and extinctions. For this purpose, the StarHorse code <cit.> was
applied. It is a Bayesian
parameter estimation code that compares many observed
quantities to stellar evolutionary
models. Given the set of observations plus several priors, it finds the posterior probability over a
grid of stellar models, distances, and extinctions. A mean precision of 0.20 mag for A_ V was achieved.
Our analysis used the listed line-of-sight extinction 50th percentile for 67 437 stars in common.

StarHorse2021 <cit.>: For this version, they significantly updated the
StarHorse algorithm in the context of the Gaia DR3. Furthermore, the photometric data from 
SkyMapper DR2 <cit.> without the u filter were included. It was
concluded that the systematic
errors of the astrophysical parameters are smaller than the nominal uncertainties for most objects.

Bayestar2019 <cit.>: This is a 3D map of interstellar dust 
reddening that covers three-quarters of
the sky (i.e. declinations of δ > -30). It is based on the 
Pan-STARRS 1
and
2MASS colours ranging from 400 nm to 2400 nm. Including the astrometric data from the
Gaia significantly improved the accuracy compared to the prior version of the 
maps <cit.>.
They group stars into small angular 
patches in the sky. Based on the available photometric measurements of each
star, its spectral type and the parallax from Gaia (if available), they compute a probability distribution over the star's
distance and foreground dust column. Each star puts a constraint
on the line-of-sight distance versus dust column relation.
Assuming a constant reddening law, a significant number of stars
is needed along a single sight line  
to put a strong constraint on the dust density as a function
of distance. We used the distances from <cit.> as well as Galactic
coordinates
to estimate mean reddening values. 



 §.§ Comparison with the references
 

We statistically analysed the differences in the reddening
values of the individual references among each other and our catalogue.
We expect a normal distribution centred at zero with a certain width
or standard deviation. Two other important quantities are the third and fourth
standardised moments, the skewness and kurtosis <cit.>. 



The skewness is a measure of symmetry
around the zero point or the lack of symmetry. In the ideal case,
the skewness for a normal distribution is zero (mean is equal to median), and any symmetric data should have a value near zero. 
Negative values indicate data that are skewed left in the sense that the left tail of the 
distribution is long relative to the right one. Values between -0.5 and +0.5 for a large
sample, as ours can be considered symmetric. 
The kurtosis measures whether the data are tailed relative to a normal distribution. The value for an
ideal normal distribution is three. Excess kurtosis is often used, subtracting a value of three. 

Table <ref> presents all statistical values for the
different references, whereas Fig. <ref> shows the data graphically. 
The histograms are shown in Figs. <ref> to
<ref>.
It has to be kept in mind that these characteristics are for
the extinction in (B-V).

All the investigated datasets' mean and median values are compiled 
around zero. There are no apparent outliers. 
The standard deviations for the datasets of the literature vary between 0.12 and 0.23 mag. 
These values also seem to limit the global statistical accuracy for any of these references.
The comparison with our datasets yields slightly higher standard deviations (up to 0.3 mag).
We think that the reason is the use of UV data within our compilation. As stated before, it is
essential to include this wavelength region, especially for early-type stars <cit.>.
Looking at the skewness and kurtosis values, we find that only two datasets <cit.>
qualify as being close to normal distributions. All others deviate significantly,
especially when it comes to kurtosis. We
also calculated all values for those 8500 objects common in all datasets to exclude selection effects. The results
are the same, with slightly lower standard deviations. 

Figure <ref> presents more detailed structures of the individual differences with our catalogue.
The asymmetry of the different distributions is visible, especially for the upper main sequence stars (which are, in general, at
more considerable distances from the Sun). For the cool-type stars, there is, in four cases, a similar effect in the other
direction evident. 

In general, we advise the users of the published reddening values to search all
available sources and to compare them. The object's location in the Milky Way needs to be checked for significant deviating values. 
De-reddening procedures using reddening-free indices, for instance those described in Sect.
<ref>, are always preferable.



 §.§ Reddening values of open clusters
 

As the next step, we investigated the members of star clusters in our sample. The releases of the Gaia data brought a flood of newly
discovered star clusters based on astrometric and photometric data. However, wrongly identified or already known aggregates make a
homogeneous analysis difficult. 
We used the star cluster membership lists from the catalogue of <cit.> to identify possible open cluster members among the studied stars.
This catalogue contains the parameters (age, reddening, and distance) of 7167 star clusters, with more than 700 newly discovered high-confidence star clusters. In addition to this,
they also include a list of cluster members with membership probabilities for each star. For example, they performed several cross-checks with already published
catalogues and found offsets for the extinction (see Fig. 7 therein). We must emphasise that determining the cluster parameters is 
still challenging, although, from the Gaia datasets, we already get a reasonable estimate of the distances <cit.>.
We cross-matched our sample with the lists by <cit.> and identified
4270 high-confidence (P>0.7) star cluster members. For the comparison, we only took star clusters for which more than two members are included in
our sample, leaving us with 786 aggregates. In Fig. <ref>, we present the comparison result with the published values by 
<cit.>. Plotting star clusters with more than five members does not change the results.
The skewness and
kurtosis of the corresponding distribution are -1.99 and +8.50.
We see a wide spread of differences with a clear trend for E(B-V) < 0.2 mag. This means that their Bayesian neural network technique generally 
overestimates the reddening. 
This might be a result of the applied binning by <cit.> of 
0.11 mag in (G_ BP-G_ RP).
For larger reddening values, the effect reverts. 
This conclusion is also valid using mean reddening values from the six sources
we used for our comparison.
Determining the cluster parameters is still very much limited by the choice of reddening. At the same time,
the distance can be accurately estimated using the Gaia data (which will improve further with forthcoming releases). We also now have very good
metallicities from the Gaia-ESO <cit.> and Galactic Archaeology with Hermes <cit.> surveys, for example, which could serve
as a starting point for fitting isochrones to get the age. But still, the fitting techniques need to consider all these starting values
to derive homogeneous cluster parameters <cit.>.





 §.§ Variable extinction of stellar objects
 

It has been well documented that several star groups show variable extinction. Most of
these objects, like the classical T Tauri and UX Ori stars show this effect because of a
varying circumstellar environment <cit.>.

On a larger scale, such effects have also been observed for Hii regions 
and the Galactic centre <cit.>. In general, it
can be said that reddening varies in regions with rapid variations in dust and gas content.

Intrinsically variable stars are at the centre of many scientific studies <cit.>. The periods, amplitudes, and light curve characteristics <cit.> are as manifold as the underlying physical mechanisms <cit.>. For example, Cepheid variables and their period-luminosity-relations <cit.> have allowed us to start constructing a distance ladder, which helped us explore large regions of the Universe. For such studies, the knowledge of a precise extinction
value is essential. Therefore, our catalogue can help identify possible outliers and offsets
due to incorrect reddening values.



§ CONCLUSIONS
 

Compiling mean reddening values of stellar objects is essential for calibrating and testing observations
and models. The interstellar and inter-cluster absorption must be considered for various aspects of astrophysical
studies. Its wavelength dependence and different reddening laws due to multiple mixtures of interstellar
gas and dust make it necessary to work with a statistically sound sample of objects. We present a catalogue
of mean reddening values for 97 826 objects distributed across the visible parts of the Milky Way and the Magellanic
Clouds.

A comparison with published reddening values derived via sophisticated automatic fitting procedures reveals
systematic offsets for both Galactic field objects and star clusters. Therefore, estimating the reddening using well-established techniques and datasets, especially observations
in the UV region, is still essential. Future satellite missions such as the Quick Ultra-VIolet Kilonova surveyor <cit.>
will help improve this situation significantly. Also, a (re-)analysis of photometric
UV observations available in scientific archives is very much needed <cit.>.


We are grateful to the referee for the constructive input.
This work was supported by the grant GAČR 23-07605S and the European Regional Development Fund, project No. ITMS2014+: 313011W085 (MP).
This research has made use of the SIMBAD database,
operated at CDS, Strasbourg, France and of the Two Micron All Sky Survey (2MASS), 
which is a joint project of the University of Massachusetts and the Infrared 
Processing and Analysis Center/California Institute of Technology, funded by 
the National Aeronautics and Space Administration and the National Science Foundation.
This work presents results from the European Space Agency (ESA) space mission 
Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis 
Consortium (DPAC). Funding for the DPAC is provided by national institutions, 
in particular the institutions participating in the Gaia MultiLateral Agreement 
(MLA). The Gaia mission website is https://www.cosmos.esa.int/gaia. 
The Gaia archive website is https://archives.esac.esa.int/gaia. 


aa





§ HISTOGRAMS OF THE REDDENING DIFFERENCES















 Paper Title: The mass-metallicity relation as a ruler for galaxy evolution: insights from the James Webb Space Telescope.











































                                       
                                       
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    > ∼< ∼.5ex.5ex∝∼.5ex.5ex.5exAlthæaz &NatureNew AstronomyPhys. Rev. APhys. Rev. BPhys. Rev. BPhys. Rev. DMNRASApJApJLApJSA&AA&A Supp.A&A Rev.ARA&AAJQJRASPhys. Rep.Ap&SSP&SSPubl. Astr. Soc. AustraliaPubl. Astr. Soc. Pac.J. Chem. Phys.Pub. Astron. Soc. JapanSpace Science ReviewsGeophysical Research LettersJournal of Geophysical ResearchNew Astronomy ReviewsJCAPFundamentals of Cosmic Physicsplots_png/,plots/t_ dA_100σ_ SFRσ_ZThe MZR as a ruler for galaxy evolution: insights from the JWSTPallottini et al.
        Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
         Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA
         INAF-Osservatorio di Astrofisica e Scienza dello Spazio, via Gobetti 93/3, I-40129, Bologna, Italy
        
        Galaxy evolution emerges from the balance between cosmic gas accretion, fueling star formation, and supernova feedback regulating metal enrichment of the interstellar medium. Hence, the relation between stellar mass (M_⋆) and gas metallicity (Z_g) is fundamental to understand the physics of galaxies. High-quality spectroscopic JWST data enable accurate measurements of both M_⋆ and Z_g up to redshift z≃ 10.
        
        Our aims are to understand (i) the nature of the observed mass-metallicity relation (MZR), (ii) its connection with the star formation rate (SFR), (iii) the role played by SFR stochasticity (flickering), and (iv) how it is regulated by stellar feedback.
        
        We compare the MZR obtained by the JADES, CEERS, and UNCOVER surveys, which comprise about 180 galaxies at z=≃ 3-10 with 10^6  M_⋆ 10^10, with ≃ 200 simulated galaxies in the same mass range from the serra high-resolution (≃ 20) suite of cosmological radiation-hydrodynamic simulations.
        
        To interpret the MZR, we develop a minimal, physically motivated, model for galaxy evolution that includes: cosmic accretion, possibly modulated with an amplitude  on 100 timescales; a time delay  between SFR and supernova feedback; SN-driven outflows with a varying mass loading factor ϵ_ SN, that is normalized to the FIRE simulations predictions for ϵ_ SN=1.
        
        Using our minimal model, we find the observed mean MZR is reproduced for relatively inefficient outflows (ϵ_ SN=1/4), in line with findings from JADES.
        
        Matching the observed MZR dispersion across the full stellar mass range requires a delay time =20, in addition to a significant modulation (= 1/3) of the accretion rate.
        
        Successful models are characterized by a relatively low flickering (≃ 0.2), corresponding to a metallicity dispersion of ≃ 0.2. Such values are close but slightly lower than predicted from serra (≃ 0.24, ≃ 0.3), clarifying why simulations show no clear trend for the MZR, and show some tension with the observations especially at M_⋆≃ 10^10.
        
        As the MZR is very sensitive to SFR stochasticity, models predicting high r.m.s. values (≃ 0.5) result in a chemical chaos (i.e. ≃ 1.4), virtually destroying the observed MZR. As a consequence, invoking a highly stochastic SFR (≃ 0.8) to explain the overabundance of bright, super-early galaxies leads to inconsistencies with the observed MZR. 
        The mass-metallicity relation as a ruler for galaxy evolution:
         insights from the James Webb Space Telescope
            
        A. Pallottini 0000-0002-7129-57611mailto:andrea.pallottini@sns.itandrea.pallottini@sns.it A. Ferrara 0000-0002-9400-73121 S. Gallerani 0000-0002-7200-82931 L. Sommovigo 0000-0002-2906-22002 S. Carniani 0000-0002-6719-380X1 L. Vallini 0000-0002-3258-36723 M. Kohandel 0000-0003-1041-78651 G. Venturi 0000-0001-8349-30551
            Received July 31, 2024; accepted XX XX, XXXX
        ====================================================================================================================================================================================================================================================================================================================================
        
        
        
        § INTRODUCTION
        
        
        
        
        The baryon cycle plays a pivotal role in regulating the galaxy formation and evolution process through cosmic time. As cosmic gas accretes in the dark matter halo potential well, it can cool and eventually form stars; massive stars explode as supernovae, enriching the surrounding interstellar medium with metals, that can potentially be ejected from the galaxy. Therefore key information regarding the star formation and enrichment history is encoded in the relation between stellar mass (M_⋆) and gas metallicity (Z_g), the so called mass-metallicity relation (MZR), making it effectively a standard ruler for galaxy evolution <cit.>.
        
        
        
        Over the past 20 years, it has become possible to measure the MZR from z≃ 0<cit.> up to the beginning of cosmic noon <cit.>, mostly by using the oxygen to hydrogen abundance ratio [O/H] as a proxy for Z_g.
        
        Locally, these observations have shown that Z_g increases with stellar mass up to M_⋆≃ 10^10 and beyond that point it flattens.
        
        
        This can be understood as due to the fact that low mass galaxies are prone to metal ejection due to their shallower potential well, while massive galaxies can retain most of the metals they have produced <cit.>. In this view, galaxy evolution is guided by a bathtub equilibrium <cit.> which determines the metallicity by balancing infall and outflows <cit.>.
        
        Further, observations have highlighted that Z_g and M_⋆ are tightly connected with the star formation rate (SFR) in the so-called fundamental mass-metallicity relation (FMR, ), which seems to be redshift-independent up to z≃ 3<cit.>; other factors as galaxy size <cit.> and molecular gas content <cit.> might also play some secondary role in connecting Z_g to M_⋆.
        
        
        The MZR evolution at z4 has been predicted via semi-analytical models <cit.> or cosmological simulations <cit.>. Most models predict almost no evolution or a very weak redshift dependence for z>3<cit.>; some others suggest a break down of the relation at z 9-12<cit.>.
        
        
        Thanks to the exquisite spectroscopic capabilities of JWST, we can accurately infer Z_g for galaxies well within the Epoch of Reionization (EoR, z>6). At present, surveys like JADES <cit.> and CEERS <cit.>, have provided metallicity measurements at z≃ 3-10<cit.> and z≃ 4-10<cit.>, for a combined sample of about 170 galaxies in the 5× 10^6  M_⋆ 10^10 stellar mass range.
        
        These JWST observations suggest that the MZR is already in place in the EoR, albeit downshifted by 0.5 dex with respect to the local one. The evolution in the z≃ 3-10 range is very mild, as relatively low mass (M_⋆≃ 10^9-10) galaxies can be chemically mature (Z_g≃ 0.3) already at z≃ 6. The MZR shows a r.m.s. dispersion σ_Z = 0.3 dex, and possibly a hint of flattening at z 6<cit.>.
        
        Furthermore, multiple line detections in the same target can be used to constrain abundance patterns of individual elements <cit.>. Resolved observations are beginning to probe the presence of metallicity gradients up to z≃ 8<cit.>, which should provide deeper insights into the formation process of the galaxy and the history of the stellar mass buildup <cit.>.
        
        Observations targeting lensed fields <cit.> are uncovering the metallicities of even the fainter galaxies <cit.>, which is key in order to explore the infall/outflow interplay due to stellar feedback in the less massive objects.
        
        Importantly, using observations of lensed targets at z≃ 3-9, <cit.> suggest that the 0.5 dex shift of normalization and the higher scattering (0.3 dex) w.r.t. the local MZR can be caused by the high level of burstiness of the SFR expected in high-z galaxies <cit.>.
        
        
        Indeed, as we move from the local Universe to high z<cit.>, galaxies are expected to become more bursty, as a consequence of the increase of specific SFR <cit.> combined with a decrease in size <cit.>, which can make the stellar feedback more effective <cit.> in maintaining a higher level of turbulence <cit.>.
        
        
        With the recent availability of JWST observations <cit.>, the time varying stochastic SFR behavior (in short, flickering or burstiness), has been invoked as a possible mechanism <cit.> to explain the overabundance of bright galaxies at z10<cit.>.
        
        However, some works predict that r.m.s. amplitude of the SFR variability falls short of explaining the said overabundance <cit.>. Thus, it is unclear if flickering alone can explain the phenomenon, particularly since the required high level of variability <cit.> is apparently not seen in the data <cit.>.
        
        
        Studies of the SFR flickering have experienced a recent surge, as stochastic SFR variations can have an impact on our ability to observe distant galaxies <cit.> and affect the possibility of detecting Population III stars <cit.>. In addition, the flickering can modify the UV spectral slopes of high-z galaxies and the escape fraction of ionizing photons <cit.>, ultimately controlling the cosmic reionization history <cit.>.
        
        Analyzing the amplitude and temporal variation of SFR flickering provides unique insights into the various feedback processes that regulate the formation and evolution of early galaxies <cit.>.
        
        On the one hand, high-amplitude and high-frequency flickering, on timescales shorter than the delay between SFR and SN explosions (≃ 20-40) are invoked <cit.> to explain the observed abrupt quenching of SFR in ≃ 10^9 galaxies already at z≃ 7<cit.>.
        
        On the other hand, the presence of disks observed in M_⋆≃ 10^9-10 galaxies up to z≃ 7<cit.> implies a limited level of stochasticity, as otherwise the disk would be disrupted <cit.>.
        
        In the present work, we aim to clarify the effects of SFR flickering and feedback regulation of high-z galaxies by using the MZR as a standard ruler.
        
        The paper is structured as follows; in Sec. <ref> we present the serra simulation suite and compare it with MZR observations from JADES, CEERS, and UNCOVER; in Sec. <ref> we develop a minimal model to give a physical interpretation to the MZR; in Sec. <ref> we discuss the discrepancies found between simulations and data in the light of the analytical model; conclusions are given in Sec. <ref>.
        
        
        
        § THE MASS-METALLICITY RELATION AT HIGH REDSHIFT
        
        
        To study the MZR at high-z, firstly we adopt the data from SERRA, a suite of cosmological zoom-in simulations that follows the evolution of z 6 galaxies <cit.>.
        
        In SERRA we use the code RAMSES<cit.> to evolve DM, gas, and stars. We enable the module RAMSES-RT<cit.> to track radiation on-the-fly by coupling it <cit.> with KROME<cit.>, in order to account for non-equilibrium chemistry up to H_2 formation <cit.>.
        
        Stars are formed using a <cit.>-<cit.> like relation based on H_2. Once formed, stars produce UV radiation that ionizes the gas, photo-dissociates H_2, and builds a radiation pressure in the gas. Massive stars generate stellar winds and explode as SNe. Depending on the kind of feedback, energy injection in the gas can be of thermal (subject to radiative losses) and/or turbulent (later dissipated) nature <cit.>.
        
        Adopting a ≃ 1.2× 10^4 (≃ 20  pc) gas mass (spatial) resolution, with music<cit.> we initialize cosmological initial conditions[We adopt a ΛCDM model with vacuum, matter, and baryon densities in units of the critical density Ω_Λ= 0.692, Ω_m= 0.308, Ω_b= 0.0481, normalized Hubble constant h =  H_0/(100  km  s^-1  Mpc^-1) = 0.678, spectral index n=0.967, and σ_8=0.826<cit.>.] generated at z=100, and follow the evolution of galaxies down to z=6 (and z=4 for a sub-sample, see ).
        
        For this work, we select ≃ 200 central serra galaxies at z=7.7 with stellar mass 10^6 M_⋆ 10^10; we compute the gas metallicity as Z_g = M_g^Z/M_g by considering the total gas (M_g) and metal (M_Z) mass contained within 3 stellar effective radii from the galaxy center, which is close to the gas half-mass radius[Different assumptions on the integration radius produce only small changes in the inferred metallicity.].
        
        Note that, for a more direct comparison with observation, we should compute line and continuum emission from serra galaxies; then, we could infer M_⋆ from synthetic SED fitting and combine line emission to prepare metallicity calibrators. Such an approach would reduce potential mismatches due to uncertainties in using different calibrators <cit.>, e.g. to relax the single zone model assumption <cit.> and correct for biases in the comparison <cit.>, also avoiding potential issues in the M_⋆ determinations <cit.>.
        
        While this kind of forward modeling approach is very powerful, also allowing to prepare novel observational strategies <cit.>, here it hinders the possibility to compare with most of the other models, as the MZR is usually computed integrating metal, gas, and stellar masses; thus we avoid it in the present work.
        
        The prediction for serra are plotted in Fig. <ref>, along with JWST data from <cit.>, <cit.>, and <cit.>, for a total of about 180 galaxies at z≃ 3-10 with 10^6  M_⋆ 10^10.
        
        The bulk of serra galaxies is between 10^7 M_⋆ 10^9; these galaxies have 10^-1.5 Z_g  10^-0.5, which is broadly consistent with the observed JWST galaxies.
        
        However, at 10^7 M_⋆ 10^8 some serra galaxies show Z_g ≃ 0.25 dex higher than the observed vales; moreover, for M_⋆≃ 10^10, Z_g is on average lower than observed, up to extreme cases of 0.5 dex. In general, serra galaxies show no clear MZR trend and their dispersion appears to be somewhat larger than the observed one.
        
        Interestingly, with respect to <cit.> and <cit.>, the lensed galaxies from <cit.> seem to indicate lower values of Z_g at M_⋆ 10^7; the lensed data seems consistent with SERRA, but only a handful of simulated galaxies and observations are in that mass range.
        
        As noted by <cit.>, the lack of a clear trend and the large scatter in the SERRA relation resemble the behavior of their 6<z<10 sample. However clear differences are present, such as the relatively metal rich galaxies at M_⋆≃ 10^8 and low metallicity galaxies at M_⋆≃ 10^10.
        
        Further, the lack of a clear trend might be partially due galaxy sample selection, as most of the SERRA data has 10^8 M_⋆ 10^9 and only a small fraction of galaxies has M_⋆≃ 10^7. Thus, the observed galaxy mass range is not uniformly covered by serra galaxies, whose sample is drawn from a collection of zoom-in simulations focusing on M_⋆≃ 10^10 galaxies and their close environment. Indeed, some of the M_⋆ 10^9 mass galaxies form in a highly pre-enriched environment, which explains their relatively high metallicities (Z_g≃ 10^-0.5, see ). Note that considering different redshift intervals[We have checked the SERRA data at z=7 ,8,  and  9.] yields qualitatively similar results.
        
        
        Thus, in summary, the normalization of the MZR of serra is roughly similar to the observed galaxies, but no trend is clearly visible and some discrepancies are present, especially in the M_⋆≃ 10^10 range.
        
        Similar (or larger) tensions are present also when a comparison with other models is performed. These can be noted, e.g. from the fit obtained by the fire-2 simulations <cit.>. fire-2 data are close to the observed Z_g at M_⋆≃ 10^9.5, but the predicted slope of the MZR is different, thus the tension with <cit.> increase with decreasing M_⋆. Finally, fire-2 galaxies present a much higher scatter, that increases with decreasing stellar mass up to ≃ 1 dex at M_⋆≃ 5× 10^7.
        
        An in depth comparison between observations and simulations is presented in <cit.>, which, in addition to serra, considers the zoom-in simulations from firstlight<cit.> and FIRE<cit.>, the IllustrisTNG cosmological simulations <cit.>, and the Astraeus semi-analytical models <cit.>; as detailed in <cit.>, most simulations seem to reasonably match the Z_g data at ≃ 10^9 but have steeper slopes and underpredict the metallicities at lower M_⋆.
        
        Interestingly, some of the simulations seem to be consistent with what observed by <cit.>, which however have only eight targets, thus it is unclear if there is a change of slope of the MZR for M_⋆ 10^7.
        
        
        
        
        § A MINIMAL PHYSICAL MODEL TO EXPLAIN THE MZR
        
        
        
        Given the very contrived match between simulations and observations, it seems worthwhile to step back and try to understand the trend and dispersion of the MZR using basic physical models. The advantage of the approach consists in simplifying the complexity of numerical simulation while retaining the most important physical processes shaping the MZR. 
        
        To this aim we devise a minimal, physical model describing the evolution of DM (M_dm), gas (M_g), star (M_⋆), and gas-phase metal (M_g^Z) mass of a galaxy, following <cit.>.
        
        As in <cit.>, we introduce an explicit feedback delay resulting in a modulation of the star formation history (SFH).
        
        
        
        
         §.§ Model setup
        
        
        
        We assume that the DM halo increases as a result of cosmological accretion, which on average can be written as in <cit.>
            Ṁ_dm = 71.6 (M_dm/10^12) (0.7/h)  E(z)  ,
        
        where E(z) = [-0.24 + 0.75 (1+z)]√(Ω_m(1+z)^3 + Ω_Λ).
        
        We allow stars to form (eq. <ref>) and include stellar feedback via SNe, exploding after a delay time . SN cause mass outflows with a rate Ṁ_out (eq. <ref>), enrich the gas of metals with a yield y, and have a return fraction R.
        
        Thus, the stellar mass increases because of SFR and decreases after  because of SN explosions:
        
            Ṁ_⋆ =  SFR(t) - R  SFR(t-) ,
        
        which for t_d=0 (no-SN-delay) would give an instantaneous recycling approximation as in <cit.>.
        
        The gas mass increases because of cosmic accretion and return from stars, and it decreases because of the SFR process and SN driven outflows:
        
            Ṁ_g = f_bṀ_dm(t) + R  SFR(t-) -  SFR(t) - Ṁ_out(t-) ,
        
        where f_b = Ω_b/Ω_m is the cosmological baryion fraction.
        Finally, the gas metal content increases because of the SN yields while it decreases because of astration and outflows:
        
            Ṁ_g^Z = f_b Z_inṀ_dm(t) + y  SFR(t-) - Z_g [ SFR(t) -Ṁ_out(t-)] ,
        
        where Z_g = M_g^Z/M_g is the gas metallicity, and we include the possibility for the cosmic gas to be already enriched at Z_in, which we set to Z_in=10^-7, i.e. virtually metal free.
        
        
        
        To solve the system in eq.s <ref>, we need to specify a functional form for Ṁ_out and SFR.
        
        We take the outflow rate as in <cit.>:
        
            Ṁ_out = 3.6 ϵ_ SN  SFR(M_⋆/10^10)^-0.35 ,
        
        with ϵ_ SN an efficiency parameter that we use to calibrate the mass loading factor; ϵ_ SN=1 correspond to the results from <cit.>. Note that ϵ_ SN=1 yields a loading factor consistent with what <cit.> observes for HZ4 <cit.>. Further, using ϵ_ SN=1 in eq. <ref> would match the results from <cit.> for z≃ 5-6 ALPINE galaxies <cit.> which feature a spatially extended gas component <cit.>. However, ϵ_ SN≃ 1/3 is needed to match the loading factor inferred from z≃ 3-9 JADES galaxies <cit.>.
        
        
        We assume that the SFR is proportional to the gas mass:
        
            SFR = M_g/t_⋆ ,
        
        and we select a constant t_⋆ = 1  Gyr as our fiducial star formation time scale[In the model, galaxy evolution is self-regulated by feedback, thus the sensitivity of the results from t_⋆ is limited in our case, and null in the =0 case with constant loading factors for infall and outflow <cit.>. A posteriori, we note that the fiducial t_⋆ = 1  Gyr gives specific star formation rates sSFR =  SFR/M_⋆ which are consistent with SERRA galaxies, i.e. ≃ sSFR≃ 100-1   Gyr^-1 for galaxies with masses M_⋆=10^6 - 10^10.]. The choice of t_⋆ is roughly consistent with the upper limits of the depletion times reported by <cit.> for ALPINE galaxies, and it is discussed in more detail in Sec. <ref> (see also App. <ref>).
        
        To complete the model, we assume that halos can form stars after they reach a virial temperature for atomic cooling to be effective (10^4  K); similarly to serra, we assume return fraction and yields appropriate for a <cit.> IMF and adopting <cit.> tracks with a Z_⋆= stellar population[Changing the metallicity of the stellar population does modifies the yield and return fraction, but gives only minor modifications to the upcoming results.], which gives y≃ 0.0228 and R≃ 0.3242.
        
        
        The system (eq.s <ref> and <ref>) is solved along with z=z(t) using an embedded 5th/6th order Runge-Kutta method <cit.> with adaptive timestep, which is selected in order to have a fractional (absolute) precision of at least ≤ 10^-5 (≤ 10^2) for M_dm, M_⋆, M_g, and M_g^Z. The delayed SFR and stellar mass used to evaluate the stellar feedback are computed using a 7 points time stencil.
        
        
        
        
         §.§ Overview of the minimal physical model
        
        
        The delay between SFR and feedback  and the amplitude of the outflow (ϵ_ SN) regulate the burstiness of the galaxy in our single zone model <cit.>.
        
        To understand the impact of burstiness on galaxy evolution, it is instructive to consider a halo with mass M_dm = 3× 10^10 at z=6 and set the outflow efficiency to the standard value of ϵ_ SN=1.
        
        In Fig. <ref> we compare the evolution of the stellar, gas, and metal mass content for = 0 (no-SN-delay, dashed lines) and = 10  Myr (solid lines).
        
        By construction, the halo mass growth (eq. <ref>) is unaffected by , thus the two models follow the same DM evolution, which smoothly grows from M_dm≃ 10^7 at z ≃ 18, when the universe was t≃ 200 old.
        
        At that time, for =0 the gas and stars has ≃ 10^5 and ≃ 10^2, respectively, and both grow reaching approximately ≃ 5× 10^7 at t≃ 800, with M_⋆/M_dm≃ 5× 10^-3 broadly consistent with what expected from abundance matching models <cit.>.
        
        In the case with = 10  Myr, the secular trends are qualitatively similar, but the system experiences a series of bursts on time scales of ≃ 20  Myr=2.
        
        Let us focus on a single burst cycle around z≃ 10, when the halo has M_dm≃ 10^9 and M_⋆≃ 10^6. In the first half period of the cycle (0-), cosmic accretion quickly replenish the gas (gas infall rate is ≃ 0.5 from eq. <ref>), reaching M_g≃ 10^7 in a few Myr. Stars form at a modest rate SFR≃ 10^-2 (eq. <ref>) under feedback-free conditions <cit.>. After , the feedback kicks in, first enriching the galaxy and eventually (≃ 2) becoming powerful enough to expel both gas (gas outflow is ≃ 1 using eq. <ref>) and metals <cit.>.
        
        However, in the example the impact of SFR flickering is limited already after z≃ 15, when the galaxy has M_⋆≃ 10^5 or 10× lower if no delay is considered. At z≃ 6, the final stellar mass is M_⋆≃ 10^7 within a factor of 2 for the two models.
        
        For the gas and metals, the model with SN delay starts to converge to the no-SN-delay case at z≃ 8, when M_⋆≃ 10^7; oscillations for the gas and metals are still present up to z≃ 7, but they are milder.
        
        As in <cit.>, it is convenient to quantify the burstiness of the SFR by defining the variable δ expressing the log of the stochastic SFR variation with respect to its mean (in short: flickering)
        
            δ≡log SFR/⟨ SFR⟩ ,
        
        where log⟨ SFR/⟩ is a second order polynomial fit in the time variable t. The low order fit is needed to factor out the smooth behavior of the functions without removing time modulations <cit.>.
        
        Similarly to the flickering, we define the analog variable for the gas metallicity
        
            δ_Z≡logZ_g/⟨ Z_g⟩ ,
        
        where log⟨ Z_g /⟩ is a second order polynomial fit in the variable log M_⋆/. For both δ and δ_Z we can define the typical variation as the root mean square (r.m.s.) deviation, i.e.  and , respectively.
        
        Adopting eq.s <ref>, we find that the = 10  Myr case has a flickering ≃ 0.3 before the two models start to converge, which is slightly higher than the ≃ 0.24 obtained for SERRA galaxies <cit.>.
        
        For different  the qualitative behavior is very similar, as the model is off-balance and oscillates around the no-SN-delay case, that is similar to a bathtub solution <cit.>. For shorter (longer) ,  can be smaller (higher), as galaxy with a smaller (higher) M_⋆ can be off-balanced.
        
        The balance between infall and outflow rates is critical, since the dynamical system (eq.s <ref>) modeling the galaxy evolution give rise to exponentially increasing/decreasing trends; introducing a ≠ 0 can efficiently break the balance, causing cycles of complete gas and metal depletion.
        
        To explore the MZR variations induced by the flickering, in Fig. <ref> we plot the tracks of the selected M_dm = 3× 10^10 at z=6 with t_d from 5 to 25 Myr.
        
        Because of the longer , the SFR becomes increasingly bursty. Specifically, for the selected model the flickering ranges from ≃ 0.1 to ≃ 0.6 for =5 Myr to =25 Myr, respectively.
        
        
        The the MZR modulations induced by the flickering are highly non linear.
        
        With =5-10, the MZR dispersion is negligible-small (≃ 0.05-0.2), as the flickering can affect galaxies only up to M_⋆≃ 10^5-7.
        
        For =15, the full M_⋆ range experience flickering with a ≃ 0.5, yielding an high ≃ 0.8.
        
        Cases with >15 Myr do not show a higher stochasticity, as an increasing delay only regulates which M_⋆ can be affected by the feedback unbalance[Note that an higher/lower level of flickering can be induced by changing the infall/outflow rates, as shown later in Sec. <ref>.]. Qualitatively, the behavior is similar with higher M_dm, but the convergence to the bathtub solution is faster.
        
        In summary, a feedback delay induces a stochastic, bursty star formation behavior that becomes progressively more enhanced as t_d is increased. Such SFR flickering corresponds to analog Z_g fluctuations which act to decrease the mean metallicity as gas and metals are effectively ejected from the galaxy by outflows. 
        
        
        
        
        
         §.§ The impact of a stochastic SFR on the MZR
        
        
        We run sets of models that at z=6 have a M_dm from 10^9 to 10^13 with a logarithmic binning of 0.1 dex, in order to cover the mass range 10^5  M_⋆ 5× 10^10.
        
        We analyze different variations of the minimal models, reporting the results in different panels of Fig. <ref>, where they are compared with data from JWST observations <cit.>.
        
        
        
          §.§.§ Base models
        
        
        Let us start by discussing the base models analyzed in Sec. <ref>, i.e. with ϵ_ SN=1, consistent with fire simulations <cit.>, and selecting =20, so that most of the explored stellar mass range is expected to have a stochastic SFR.
        
        In the upper left panel of Fig. <ref> we report both the individual tracks of the base models and their M_⋆ average trends.
        
        For the base models, the median case falls significantly below the observed average MZR. Also, the dispersion is much larger than seen in JWST data, that can be barely matched by the upper envelope of the predicted curves. 
        
        The base models have a ≃0.5 flickering, that induces a 1 almost in the entire stellar mass range (M_⋆ 10^9, Fig. <ref>).
        
        The flickering is due to cycles of infall/outflow which determine an oscillatory behavior of the evolution around the =0 control case, that is largely independent of the hosting M_dm.
        
        The Z_g-M_⋆ normalization is determined by the strength of the outflows, that completely devoids the galaxy of gas and metals, not allowing the metallicity to rise to the observed level. Even for =0 the outflow seems too extreme, as only part of the lensed galaxy data can be matched <cit.>.
        
        
        In summary, the efficient feedback (ϵ_ SN=1) combined with a =20 generates a SFR flickering of ≃ 0.5, inducing MZR variations of ≃ 1.4 resulting in a chemical chaos that is not observed. Barring the option that observations are tracing only the tip of the Z_g-M_⋆ relation, in order to explain the observed MZR we modify the base models as follows.
        
        
        
          §.§.§ Weak feedback
        
        
        
        First, we reduce the impact of stellar feedback by decreasing the outflow rate from <cit.> (eq. <ref>), i.e. setting ϵ_ SN=1/4; such a loading factor is closer to what <cit.> infer for 10^7.5 M_⋆ 10^9 JADES galaxies.
        
        As shown in the upper right panel of Fig. <ref>, this modification increases the average metallicity of the modeled galaxies, matching the observed mean trends in the whole 10^6 M_⋆ 10^10 mass range. Comparing to the =0 control case, it is evident that the outflow efficiency is the main driver of the mean Z_g-M_⋆ trend.
        
        
        Note that, reducing the outflow efficiency while maintaining a fixed =20 results in ≃ 0.1 modulation of the MZR, i.e. too low with respect to the observed (≃ 0.25, see Fig. <ref>).
        
        This effect is induced by the suppression of the amplitude of the SFR flickering, especially at the high mass end.
        
        Indeed the models show a small flickering, with ≃0.15 for M_⋆ 10^8, and even slightly lower values for higher stellar masses (Fig. <ref>).
        
        As discussed in <cit.>, M_⋆ 10^9 galaxies show SFR fluctuations with characteristic periods of ≃ 20-40, which correspond to the typical evolutionary times of SNe.
        
        Such flickering timescale increases to ≃ 80-150 in more massive galaxies which are more sensitive to mergers and accretion rate modulation. The latter effects are not accounted for in our minimal model (eq. <ref>). The next step is then to heuristically incorporate them in our treatment.
        
        
        
        
          §.§.§ Weak feedback, modulated accretion
        
        
        To incorporate the extra stochastic behavior expected from variation in the cosmic accretion in a simple manner, we impose a sinusoidal modulation on a 100 timescale
        
            Ṁ_dm^mod= Ṁ_dm[1 + sin(t/100  )] ,
        
        with Ṁ_dm being the average cosmic accretion from eq. <ref> and with  scaling the amplitude of the modulation[Note that small halos should be relatively less affected by modulation on long timescales (≃ 100), since the hosted galaxies have shorter SFH. However, cosmological accretion variations can be coherently combined with the SN delay to give a higher  also in the low mass range.].
        
        
        As feedback determines the mean trend of the MZR, we keep the reduced outflow efficiency (ϵ_ SN=1/4 in eq. <ref>) and compute the evolution of a minimal model by setting the amplitude of the oscillation to =1/3, which should yield a scatter below the 0.3 dex dispersion expected for the distribution of growth rates of DM halos <cit.>.
        
        The results from these modified models are shown in the lower left panel of Fig. <ref>: both the mean trend and scatter of the observed MZR are recovered (Fig. <ref>).
        
        Such a matching set of modified models yields a roughly constant ≃ 0.2 and ≃ 0.3, satisfactorily matching the JWST data.
        
        
        
        
          §.§.§ Weak feedback, modulated accretion, no-SN-delay
        
        
        As a final check, in the lower right panel of Fig. <ref> we show the effect of removing the SN-delay from the best matching model just discussed.
        
        While the mean MZR trend is recovered, the metallicity dispersion (≃ 0.05) is much smaller than observed (≃ 0.25). Also, the median of the models fails to reproduce the relation for most of the low mass lensed galaxies <cit.>.
        
        With no-SN-delay, the SFR flickering is induced only by modulation of the cosmic accretion, which fails to unbalance the system through the ejection of a substantial fraction of the contained gas.
        
        With the selected =1/3 and =0, the model reach ≃0.1 for M_⋆ 10^8, while the flickering gets to ≃0.2 only for M_⋆≃ 5× 10^8 galaxies.
        
        
        Compared to the control case (=0), the average Z_g is slightly higher; practically, SFR flickering induced by the accretion modulation can increase Z_g since a higher gas mass can be converted into stars without efficiently ejecting the gas via outflows, i.e. the opposite outcome with respect to SFR flickering induced via SN-delay.
        
        Interestingly, despite the relatively high SFR flickering (average of ≃ 0.2), the metallicity variation is the lowest of all considered cases (≃ 0.05): only a delayed SN feedback can efficiently off-balance the system and induce modulations on both SFR and Z_g.
        
        We note that the serra cosmological simulations show a relatively modest SFR flickering <cit.>, and close to the expectations for z≃ 6 galaxies <cit.>. Yet, given the sharp sensitivity of  to SFR variations, such time variability results in a  larger than observed. 
        
        
        To summarize, our analysis shows that: (i) a weak feedback, and (ii) a relatively mild stochasticity given by (iii) SN-delay combined with a long term accretion rate modulation are critical to simultaneously match both the mean and dispersion of the observed MZR relation in the entire stellar mass range of galaxies sampled by JWST at z=3-10.
        
        Finally, we note that invoking stochasticity to explain the overabundance of bright JWST galaxies requires >0.5 (more specifically, ≃ 0.8, ≃ 0.7, and ≃ 0.6 according to , , and , respectively; see Fig. <ref>).
        
        However, such extreme flickering amplitudes are (i) higher than that recovered from SED fitting allowing for SFH variability <cit.>, and (ii) would induce a chemical chaos (1.4) that is not present in the observed MZR at z=3-10<cit.>.
        
        
        
        
        
        § DISCUSSION
        
        
        The minimal models presented here can also be useful as a tool to guide the development and compare complex cosmological simulations, particularly when focusing on relations that - like the MZR - are very sensitive to small variations of the underlying physics, that is included via sub-grid models in galaxy simulations <cit.>.
        
        
        
        
         §.§ Comparing numerical simulations
        
        
        
        
        
        In galaxy simulations, ejective feedback, such as outflows caused by mechanical/kinetic prescriptions, can effectively suppress the SFR activity as much as preventative feedback, such as turbulence/delayed cooling prescriptions <cit.>, leading to similar SFR histories when the same initial conditions are considered <cit.>.
        
        Despite similar SFR histories, other properties can differ significantly <cit.>, such as the dynamical state of a galaxy.
        
        For instance, <cit.> show that FIRE-2 galaxies <cit.> have a much lower incidence of disks compared to serra galaxies <cit.>.
        
        Additionally, SERRA galaxies tend to have higher Z_g and lower MZR scatter compared to fire-2<cit.>, especially in the M_⋆≃ 10^9 mass range. 
        
        Both effects are likely caused by the higher SFR flickering of fire-2<cit.> with respect to serra<cit.>, which is ultimately regulated by the efficiency and kind (e.g. ejective vs preventative) of included stellar feedback. Violent outflows are present in fire-2<cit.>, while the suppression of SFR due to the photo-dissociation of molecular hydrogen in serra<cit.> can more gently can modulate the SFR activity without drastically modifying the galaxy dynamics.
        
        Similar considerations hold when comparing successive improvements of simulations suites. For instance, the loading factor from fire-2<cit.> are lower by a factor of ≃ 2 with respect to fire<cit.>; this difference dictates that the MZR from fire-2<cit.> is about 0.3 dex higher than the MZR from fire<cit.>; in both cases the slope is steeper (normalization is lower) than what observed by <cit.> and is instead more consistent with <cit.>.
        
        Despite the simplicity of the minimal model presented, hints of such differences in the simulations can be highlighted and explained.
        
        
        
        
        However, it is difficult to directly quantify the differences in the simulations with the presented models.
        
        
        
        For instance, the loading factor in our simplified models (but also in relatively more complex ones as  and ) is a scalar quantity used as an input value for each galaxy, while in simulations is usually defined as an output that has a spatial dependence <cit.>. 
        
        Additionally, when dealing with simulation snapshots, quantifying both the SFR event and the consequent outflows is tricky because of the time-delay between SFR and feedback <cit.>, particularly for galaxies far from a quasi-equilibrium situation.
        
        
        
        
        Further, the simplifications done in our minimal model impose we can only capture part of the complexity present in simulations.
        
        For instance, while the SN-feedback delay is uniquely defined, simulations finds a distribution of  that depend on the underlying physical models included <cit.>; thus, trying to find the set of parameters of a minimal model that gives the best match to a simulation will only give effective parameters, a sort of summary statistic that can be used to compare different simulations.
        
        
        Apart from these difficulties, a systematic parameter fitting procedure should give a better quantification of the comparison between different simulations, and can also be used to enable an even better match between the data and the minimal models. However, such models are lacking a few ingredients that prevents reproducing the full connection between metal build up and star formation history of galaxies.
        
        
        
        
         §.§ Caveats of the minimal model
        
        
        The limitations of the presented minimal models can be appreciated by considering the fundamental mass-metallicity relation (FMR), i.e. the link between Z_g, M_⋆, and SFR that is observed to be redshift independent up to z∼3<cit.> and seems to break down at z5<cit.>.
        
        We adopt the parameterization from <cit.>
            μ≡log(M_⋆/) - 0.65 log( SFR/) ,
        
        which is obtained by minimizing the Z_g dispersion for the high sSFR sub-sample from the Sloan Digital Sky Survey (SDSS, , z 2).
        
        In Fig. <ref> we show the FMR for the minimal models matching the mean MZR and its dispersion, i.e. the weak feedback (ϵ_ SN=1/4) set with modulated accretion (= 1/3).
        
        These models are below the SDSS relation by about 0.5 dex at μ 7, with the separation that decreases with increasing μ, down to 0.1 dex at μ 9, almost connecting with the FMR trend observed at low z.
        
        As expected <cit.>, JWST galaxies are offset below the SDSS relation.
        
        The best matching models for the MZR only partially match the JWST data in the FMR plane; the minimal models are closer to the JWST data when considering the lensed galaxies from <cit.>.
        
        Further the minimal models only produce downward deviation with respect to the FMR from the SDSS.
        
        Instead, serra galaxies manage to better recover the trend for JWST galaxies around μ≃ 8, reproducing both downward and upward deviations with respect to the FMR from the SDSS; however, serra galaxies show an overabundance of low Z_g galaxies at μ≃ 8.5-9.0, which is not seen in the JWST data.
        
        
        In an equilibrium model <cit.>, the shape of the MZR is independent from the SFR, which uniquely determines the speed a galaxy can climb up the Z_g-M_⋆ curve.
        
        
        Note that the simplified model seems to deviate more from the data at low μ, i.e. a combination of relatively high SFR and low M_⋆; the adopted feedback increases in efficiency for lower M_⋆ (eq. <ref>).
        
        Thus, the observed FMR deviation might be recovered by the minimal model if we consider not only ejecting but also a preventing feedback, e.g. photodissociation of molecular hydrogen, which can suppress the star formation without affecting the gas mass (e.g. see Alyssum, a serra galaxy described in ) and can play a role in explaining some of the bright blue monsters seen by JWST <cit.>.
        
        As an alternative to keep matching the MZR and recovering the offset from the FMR, we could try to change the simplified SFR prescription (eq. <ref>); this can be done for instance by adopting as the time scale for star formation a redshift dependent depletion time <cit.>, which are typically shorter than the selected t_⋆=1  Gyr by about a factor ≃ 10, similar to what <cit.> report for z≃ 7 galaxies by using GLAM<cit.> determinations, thus promoting a faster galaxy evolution at high-z.
        
        Indeed, by adopting the depletion time from <cit.> as the time scale for SFR (see App. <ref>, in particular Fig. <ref>), the stellar mass build up is faster at M_⋆ 10^6, while later saturates to values similar to those resulting from the t_⋆=1  Gyr case as both SFHs become feedback regulated, approaching a bathtub equilibrium.
        
        
        However, on the one hand, the modifications affect the predictions of the minimal model mostly in the M_⋆ 10^6 range; on the other hand, a z average depletion time is sensitive to the population of the sample, e.g. for main sequence is ≃× 5 lower than for starburst <cit.>, and the results from <cit.> are mostly relying on the data of M_⋆ 10^8-10 galaxies from the ALPINE <cit.> and REBELS <cit.> surveys.
        
        To summarize, while trying to reconcile the FMR behavior is an interesting perspective and there are a few options, some care should be taken in extending/modifying the prescriptions for the minimal models; we leave such a possibility for a future work.
        
        
        
        
        § CONCLUSIONS
        
        
        
        
        
        
        The exquisite spectroscopic data collected by JWST allow for the first time to derive the mass-metallicity relation (MZR) in galaxies up to redshift z≃ 10.
        
        
        
        
        In this work, we considered the MZR data for a combined sample of about 180 galaxies with stellar mass 10^6  M_⋆ 10^10 at z=3-10 given <cit.>, <cit.>, and <cit.>, and obtained from the CEERS <cit.>, JADES <cit.>, and UNCOVER <cit.> surveys, respectively. 
        
        We compared the observations with the predictions from the serra simulations <cit.>, finding a broad agreement with the observed MZR. However, simulations show a lack of a clear metallicity trend, and some tension, particularly at M_⋆≃ 10^10.
        
        
        
        
        To better understand the observed high-z MZR and to clarify the behaviour of the simulations, we have devised a minimal physical model for galaxy evolution in which star formation is fueled by cosmic gas accretion <cit.> and is regulated by supernova driven outflows (eq. <ref>), with a loading factor from <cit.> that is controlled by an efficiency ϵ_ SN; additionally, we incorporated an explicit delay () between star formation and supernova feedback, inducing a stochastic SFR behavior. Some models also explore the possible modulation of cosmic accretion (eq. <ref>). s are:
        
          ∙ To recover the average trend of the MZR observed at high-z, outflows must be less efficient (ϵ_ SN = 1/4) than predicted in <cit.>. However, this evidence is consistent with the mass loading factors inferred for JADES galaxies <cit.>.
          
          
          ∙ To match the MZR dispersion in the full stellar mass range, both a delayed (=20) SN feedback, and a modulation of the cosmic accretion (= 1/3) are required.
          
          
          ∙ The r.m.s. variation of the MZR () is very sensitive to the SFR flickering (). The weak feedback necessary to reproduce the average MZR trend (ϵ_ SN = 1/4) also results in a low-amplitude SFR flickering (≃ 0.2). This prescription correctly reproduces the moderate MZR scatter (≃ 0.25) observed by JWST.
          
          
          ∙serra galaxies have slightly higher ≃ 0.24<cit.>, resulting in a metallicity scatter of ≃ 0.3, higher than observed. Differently from the analytical model, serra galaxies also overpredict the number of low metallicity (Z_g≃ 0.2) galaxies at M_⋆≃ 10^10.
          
          
          ∙ In general, any model predicting 0.5 is likely to overshoot the observed metallicity r.m.s. scatter, possibly leading to a chemical chaos (1.4) that is it not present in JWST data, for which ≃ 0.25).
          
        
        
        
        
        
        The last point also entails that simultaneously explaining the observed MZR <cit.> and the overabundance of bright galaxies observed by JWST <cit.> through high SFR flickering <cit.> is very challenging, considering that a ≃ 0.8 is required to explain z>10 observations <cit.>.
        
        We note that while both the SN-feedback delay and cosmic accretion modulation induce SFR flickering, the latter tends to give a gentler modulation of Z_g, since high feedback efficiency and a delay are needed in order to off-balance the MZR generated from a bathtub-like equilibrium <cit.>.
        
        However, variation of cosmic accretion can only go up to 0.3 dex <cit.>. Thus, alternative explanations <cit.> seem more favored to solve the overabundance problem.
        
        
        
        
        While we showed that the presented minimal model can also be used to guide our intuition in comparing complex cosmological simulations, we recall that such a simplified model does not fully capture the physical complexity of the connection between galaxy formation and metal enrichment, as highlighted by the poor match with the JWST data when analyzing the off-set from the fundamental mass-metallicity relation.
        
        
        
        Combining insights from such models with further analysis of ongoing observations, and more complex numerical simulations is crucial for understanding the galaxy formation and evolution process at high-z.
        
        
        
        We acknowledge the CINECA award under the ISCRA initiative, for the availability of high performance computing resources and support from the Class B project SERRA HP10BPUZ8F (PI: Pallottini).
        
        AF acknowledges support from the ERC Advanced Grant INTERSTELLAR H2020/740120 (PI: Ferrara).
        
        SC and GV acknowledge support support from the ERC Starting Grant WINGS H2020/101040227 (PI: Carniani).
        
        Any dissemination of results must indicate that it reflects only the author's view and that the Commission is not responsible for any use that may be made of the information it contains.
        
        Partial support (AF) from the Carl Friedrich von Siemens-Forschungspreis der Alexander von Humboldt-Stiftung Research Award is kindly acknowledged.
        
        We gratefully acknowledge computational resources of the Center for High Performance Computing (CHPC) at SNS.
        
        We acknowledge usage of the Python programming language <cit.>, Astropy <cit.>, Cython <cit.>, Matplotlib <cit.>, Numba <cit.>, NumPy <cit.>, pynbody<cit.>, and SciPy <cit.>.
        stile/aa_url
        
        § MODIFICATIONS TO THE SFR TIME SCALES
        
        
        In bathtub models <cit.>, the shape of the MZR is mostly independent from the functional form of the SFR, as the equilibrium solution is determined by the balance between infall and outflow, while the SFR uniquely determines the speed a model climbs the MZR from low to high M_⋆.
        
        Instead, the SFR prescription can be important if a stochastic behavior is present in the system and when analyzing the FMR.
        
        In the fiducial model presented in the paper we assumed that the SFR is proportional to the gas mass and is regulated by a fixed time scale for star formation, i.e. t_⋆ = 1  Gyr. As a natural alternatively for a fixed t_⋆, a model can consider to adopt t_⋆ via empirical determinations <cit.> or model-based predictions <cit.> of the depletion time, which is expected to decrease with redshift, thus giving a faster star formation rate at higher z.
        
        As a test, we modify our models by changing t_⋆ in our SFR prescription (eq. <ref>) by adopting the scaling suggested by <cit.>
            t_⋆^mod   ≃8.95   Gyr/E(z)
               = 8.95   Gyr/ [-0.24 + 0.75 (1+z)]√(Ω_m(1+z)^3 + Ω_Λ) ,
        
        and setting the proportionality constant in order to match <cit.> determinations at z=0.
        
        As a reference, t_⋆≃ 20  t_⋆^mod at z≃ 10, thus a faster stellar mass build is expected for the modified model. 
        
        As a benchmark, we select the halo with M_dm=3× 10^10 at z=6 analyzed in Sec. <ref> (see Fig. <ref>), evolve it with t_⋆ = 1  Gyr and t_⋆^mod from (eq. <ref>), and plot the results in Fig. <ref> for both =10 and a reference no-SN-delay case.
        
        The largest differences between the t_⋆ = 1  Gyr and t_⋆^mod models are present for the stellar mass build up at z 10, when the galaxy has M_⋆ 10^7,
        
        The t_⋆^mod model promotes a faster build up, particularly when a SN-delay is present, as the lack of feedback combined with the short SFR timescales make he galaxy reach M_⋆ 10^6 during the first burst.
        
        As the time progresses, differences between the models tend to wash out, as the galaxy approaches M_⋆≃ 10^8, the SFH starts to become feedback-regulated, and at z≃ 6, stellar, gas, and metal masses are roughly similar in all cases. 
        
        Interestingly, while the amplitude of the flickering is similar (≃ 0.5), the modulation acts on slightly shorter time scales for the t_⋆^mod model, as a consequence of the faster SFR rise and the heavier off-balance caused by the stellar feedback.
        
        This implies that the t_⋆^mod model at z 7.5 gives an even enhanced dispersion for the MZR (from ≃ 0.7 to ≃ 1.7).
        
        Note that when no-SN-delay is present, the SFH evolution is feedback regulated from the start, and the main difference is an increased gas fraction for the t_⋆ = 1  Gyr model.
        
        Note that adopting <cit.> implies a depletion time with a ∝ z^-2.5 redshift dependence, i.e. steeper with respect to the ∝ z^-1.5 dependence from <cit.>. Thus, by assuming <cit.> instead of <cit.> to modify the SFR timescale, we expect smaller variation with respect to the fiducial t_⋆=1  Gyr model.


 Paper Title: FNet II: Spectral Classification of Quasars, Galaxies, Stars, and broad absorption line (BAL) Quasars.



firstpage–lastpage
Dirac eigenvalues and the hyperspherical radius
    Christian Bär
    August 5, 2024
===============================================




§ ABSTRACT 
In this work, we enhance the FNet, a 1-dimensional convolutional neural network (CNN) with a residual neural network (ResNet) architecture, to perform spectral classification of quasars, galaxies, stars, and broad absorption line (BAL)-quasars in the SDSS-IV catalog from DR17 of eBOSS. Leveraging its convolutional layers and the ResNet structure with different kernel sizes, FNet autonomously identifies various patterns within the entire sample of spectra.  Since FNet does not require the intermediate step of identifying specific lines, a simple modification  enabled our current network to classify all SDSS spectra. This modification involves changing the final output layer from a single value (redshift) to multiple values (probabilities of all classes), and accordingly adjusting the loss function from mean squared error (MSE) to cross-entropy. FNet achieves a completeness of 99.00% ± 0.20 for galaxies, 98.50% ± 0.30 for quasars, 99.00% ± 0.18 for BAL-quasars, and 98.80% ± 0.20 for stars. These results are comparable to those obtained using QuasarNET, a standard CNN employed in the SDSS routine, comprises convolutional layers without the ResNet structure with equal kernel sizes, and is utilized for redshift measurement and classification by identifying seven emission lines. QuasarNET, in order to overcome the problem of finding a CIV emission line with broad absorption which is slightly more challenging than that of detecting emission lines requires to add BAL CIV line to the list of lines that the network learns to identify. However, this procedure is not necessary in FNet as it learns the features through a self-learning procedure.






stars—galaxies—quasar: individuals— software: simulations — techniques: spectroscopic  — surveys










§ INTRODUCTION


Classifying astrophysical objects—such as stars, galaxies, and quasars—based on their spectral and photometric properties is crucial for advancing research and understanding the Universe's origin and evolution <cit.>. 

Paradoxically, the substantial quantity of data generated in astrophysical surveys renders the manual inspection of each spectrum unfeasible. For instance, the seventeenth data release (DR17) from the Sloan Digital Sky Survey (SDSS) encompasses over 623 TB of data on the Science Archive Server (SAS), containing approximately 1.5 million unique spectra and objects <cit.>. The SDSS catalog from DR17 of the main survey extended Baryon Oscillation Spectroscopic Survey (DR17-eBOSS) <cit.>, from which we derive data for our current research, contains 1.4 million spectra. Therefore, automated methods must be implemented to achieve classification with the same precision as human experts.

As of 2023, approximately ten distinct and intermediate methods have been recognized for the classification and identification of stars, galaxies, supernovae, dwarfs, and quasars <cit.>:

1. Template Matching (TM): Constructs a template database for each class and associates new data with the closest matching template <cit.>. This method is used in various applications, such as the redrock pipeline classifier in the Dark Energy Spectroscopic Instrument (DESI) quasar survey <cit.>. See also <cit.>.

2. K-Nearest Neighbor (KNN): Determines the label for an object based on the majority labels of its K closest objects in the feature space <cit.>.

3. Support Vector Machine (SVM): Determines decision boundaries to distinguish between various data classes <cit.>.

4. Decision Trees (DT): Utilize leaves to represent classification results and nodes to serve as criteria for distinguishing objects <cit.>.

5. Ensemble Learning: Connects numerous classifiers to form a robust classifier <cit.>.

6. Artificial Neural Networks (ANN): Mimic the functionality of the human brain to perform machine learning tasks <cit.>.

7. Gaussian Naive Bayes: Manages features characterized by a Gaussian distribution, with the outcome determined by the maximum posterior probability <cit.>.

8. Bayesian Logistic Regression (LR): Derives posterior probability distributions from linear regression <cit.>.

9. Partial Least Squares Discriminant Analysis (PLS-DA): Addresses data within the same cluster, as opposed to data in different clusters <cit.>.

10. Ranking-based (RB) Classification: Utilizes graph-based ranking methods. An example is the locally linear embedding classifier, which transforms data from its high-dimensional space to a lower-dimensional space based on the manifold <cit.>.



 A comprehensive study by <cit.> on spectra in their observed cosmological frame has shown that convolutional neural networks (CNNs) outperform other methods in classifying observed spectra. Since DR16 <cit.>, SDSS has officially adopted QuasarNET <cit.>, a CNN used to infer redshifts and identify candidates that are likely to be misclassified by the standard pipeline. However, CNNs can face challenges such as overfitting and prolonged computation times due to their strong feature selection capabilities. For optimal classification of stars, galaxies, and quasars, conducting the analysis in the observed cosmological frame is advisable to minimize redshift impact and gain a comprehensive understanding.

Other methods usually perform worse than human-expert classification <cit.>. In contrast, deep learning (DL) methods, with their ability to recognize patterns and identify spectral features such as emission/absorption lines and spectral breaks, achieve accuracy comparable to visual inspection <cit.>. For example, <cit.> showed that principal component analysis (PCA) <cit.> produces extreme redshift estimations for quasars, which are not consistent with visual inspection or DL-based networks like FNet <cit.> and QuasarNet <cit.>.

Efficient optimization procedures in DL and CNN-based networks have enabled the solution of previously unseen problems <cit.>. The successful application of CNNs in large surveys has made them increasingly applicable to astronomical tasks <cit.>.

In this paper, we enhance the previously implemented network FNet <cit.> to classify quasars, galaxies, stars, and BAL quasars in the DR17 eBOSS dataset. FNet is a CNN with a residual neural network (ResNet) structure, designed to be trained using the observed optical spectra/flux of quasars. Initially, it was created to estimate the redshift of quasars in the SDSS-IV quasar catalog from DR16 eBOSS <cit.>. FNet achieves an accuracy of 97.0% for the velocity difference in redshift, |Δν| < 6000  km/s, and 98.0% for |Δν| < 12000  km/s.

FNet provides similar accuracy to QuasarNET but is applicable to a wider range of SDSS spectra, especially those lacking the clear emission lines exploited by QuasarNET <cit.>. In DR16Q, around 8600 spectra were not recognized by QuasarNET due to the absence of at least two emission lines necessary for its line finder units. After visual inspection, approximately 5000 of these spectra were flagged as quasars, and their visual inspection (VI) redshifts were subsequently reported in the DR16Q catalog. FNet predicts the redshift of these VI quasars with an accuracy of 87.4% for |Δν| < 6000  km/s (see Fig. 4 in ).

Unlike QuasarNET, FNet does not require identifying specific lines, allowing straightforward modification to classify all SDSS spectra. This involved changing the final output layer of FNet from a single value (redshift) to multiple values (class probabilities) and adapting the loss function from mean squared error (MSE) to cross-entropy. Further details can be found in Sec. <ref>.

Both FNet and QuasarNET are CNN-based networks but have different designs. QuasarNET consists of 4 convolutional layers with kernel sizes of 10, following the traditional procedure to identify emission lines as local patterns hidden in spectra using its "line finder" units. FNet, on the other hand, consists of 24 convolutional layers with a ResNet structure and kernel sizes of 500, 200, and 15, enabling it to find both “local” and “global” patterns in spectra through a self-learning procedure. This makes FNet applicable to ambiguous spectra and a larger range of redshifts; further details can be found in Sec. <ref>.

In this work, we utilize the SDSS catalog from DR17 of the main survey eBOSS <cit.>, which comprises 1.4 million observations.

In Sec. <ref>, we briefly review the basics of quasar spectroscopy, the structure of their optical spectra, and the description of SDSS and eBOSS surveys.

In Sec. <ref>, we describe the CNN structure developed for this work.

In Sec. <ref>, we present the results of our training and compare them with similar works in the literature.

Finally, in Sec. <ref>, we present the conclusions of the paper.





§ DATA



The dataset used in this study is derived from the Sloan Digital Sky Survey IV (SDSS-IV) quasar catalog from Data Release 17 (DR17) of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) <cit.>. Notably, there have been no changes in the primary eBOSS survey data since DR16; consequently, both DR16 eBOSS and DR17 eBOSS contain the same number of spectra <cit.>. Data is gathered using 500 fibers on a 2k CCD associated with each spectrograph, with wavelength coverage spanning approximately 361 to 1014 nm <cit.>.

The data in this sample is annotated with class identifiers for each spectrum: Star (CLASS_PERSON = 1), Galaxy (CLASS_PERSON = 4), Quasar (CLASS_PERSON = 3), or BAL-Quasar (CLASS_PERSON = 30). In total, there are 1,367,288 spectra classified with these identifiers. The distribution is as follows: Stars = 233,859, Galaxies = 39,054, Quasars = 396,843, and BAL-Quasars = 39,501. Additionally, 658,020 objects were designated as CLASS_PERSON = 0, indicating they were not inspected. Eleven spectra with high flux and continua matching an archetypal quasar continuum shape, but without recognizable absorption or emission features, have been marked as possible blazars (CLASS_PERSON = 50) <cit.>. See Fig. <ref>.


A vital aspect of data selection for training neural networks is the preparation of a training/test data sample that maximizes confidence, ensuring the neural network is trained with the most accurate training set possible. The (DR16Q/DR17Q)-eBOSS dataset includes automated classifications determined by version v5_13_0 of the SDSS spectroscopic pipeline <cit.>. The quasar-only sample is estimated to be contaminated by non-quasar objects at a rate of approximately 0.3%–1.3% <cit.>. Furthermore, it is affected by low-confidence quasars, stars, and galaxies labeled by a confidence rating recorded in the column Z_CONF, with 0 representing the lowest confidence and 3 indicating the highest confidence (a value of -1 indicates the object was not visually inspected). Consequently, due to incorrect pipeline classification and redshift estimation, the DR17Q-eBOSS dataset contains stars and galaxies that have been misclassified as quasars and vice versa <cit.>. To address this, we apply the following criteria to ensure the dataset is as confident as possible:


    

  * High Confidence Level: Each class is selected based on Z_CONF = 3, indicating the highest confidence level.
   

  * BAL-Quasar Probability: To ensure the inclusion of nearly all confident BAL-Quasars, we use BAL_PROB ≥ 0.9. The BAL_PROB represents the probability assigned to each quasar based on the statistical significance of the troughs associated with the C IV line and the quality of the χ^2 fit to the quasar continuum <cit.>.
   

  * Visual Inspection: To include only visually inspected sources for Galaxies, Quasars, and BAL-Quasars, we use Z_VI > 0.
   

  * Quasar Classification: For quasars, we use IS_QSO_FINAL = 1, while for Galaxies and Stars, we use IS_QSO_FINAL ≠ 1. The IS_QSO_FINAL parameter, introduced in DR16, takes integer values from -2 to 2. Quasar spectra have a value of 1, and questionable quasar spectra have a value of 2. All values of 0 or less denote non-quasars <cit.>.
    


Moreover, in addition to visually inspected quasars from DR7Q <cit.> and DR12Q <cit.>, some spectra in the dataset were classified by the automated classifier in DR14Q <cit.>. Some of these entries were flagged for visual inspection when automated methods failed to recognize their classifications, indicated by the flag AUTOCLASS_DR14Q = VI. This subset comprises 35,268 spectra. Many of these spectra exhibit low SNRs or display strong/weak absorption lines, which can confound the pipeline (see Sec. 3 of <cit.> and Sec. 3 of <cit.>). A small DELTA_CHI2, which is the case for many spectra flagged as AUTOCLASS_DR14Q = VI, indicates that they are unlikely to be useful for scientific study.

Consequently, these spectra of flag AUTOCLASS_DR14Q = VI have been excluded from the  dataset since they cannot provide the ground true for training and testing. The final dataset in this study comprises 639,906 spectra, consisting of 229,647 stars, 28,688 galaxies, 359,609 quasars, and 21,962 BAL-quasars (see Fig. <ref> (A).

It is important to highlight that the application of the aforementioned criteria does not impose any constraints on the signal-to-noise ratio (SNR) of our test and training sets. The distribution and range of SNR in the confident data used for the training and test sets are representative of the broader dataset, as illustrated in Fig.<ref>(B). 



 






 §.§ Prepossessing the data



To enable deep learning (DL) networks to process data effectively, data preprocessing plays a crucial role. We follow the same procedure presented by <cit.>. The observed spectrum, representing wavelength versus flux, is akin to a one-dimensional vector. In the DR16Q/DR17Q dataset, each observed spectrum contains nearly 4500 flux data points in the logarithmic space of wavelength. To create trainable data, we fit and extrapolate each spectrum to a one-dimensional row of 4618 data points uniformly distributed in the logarithmic space of wavelength in the range of 360  nm to 1032.5  nm. 

Due to significant variability in the observed flux of the objects, and to accelerate the network and enhance processing accuracy, we normalize the data of each spectrum using zero-mean normalization and unit-norm normalization <cit.>. The reduced, normalized data is then stored in an N × M matrix, where N represents the total number of objects in different classes and M = 4618 is the number of wavelength resolutions. Specifically, after applying the criteria to ensure a confident dataset, N = 639,906.






§ CONVOLUTIONAL NEURAL NETWORK (CNN)








 

 §.§ Model Selection



Convolutional Neural Networks (CNNs) have been widely utilized in machine learning <cit.>, demonstrating substantial improvements in computer vision <cit.>, and have become the most widely adopted architecture <cit.>. The architecture of FNet was initially presented in <cit.>. In this work, we provide an overview of FNet and highlight the significant modifications that enable it to excel in classification tasks.

As Residual Networks (ResNets) were employed in the architecture of FNet, we first examine whether this structure can be enhanced using novel and more complex methods. Introduced by <cit.>, ResNets are an advanced form of CNNs that incorporate "skip connections." These improvements allow inputs to bypass certain layers and be added directly to the outputs of later layers, mitigating the vanishing gradient problem and enabling the training of much deeper networks. Currently, ResNet serves as a baseline in many neural network applications and comparisons <cit.>.

 

Compared to more complicated or newly introduced architectures, such as Transformers <cit.>, ResNets often maintain competitive performance for simpler tasks <cit.>. In our tests of the transformer model with different numbers of headers (2, 4, and 8) and layers (2, 4, and 6), after training with the same data as FNet, the overall accuracy achieved was always below 95%, falling short of the performance achieved by the simpler ResNet-based FNet architecture. It is observed that beyond a certain model complexity, the improvements in accuracy tend to be marginal, especially in scenarios where the data characteristics do not demand such complexity, as is the case for some 1D data <cit.>. Additionally, complexities can sometimes lead to overfitting, particularly when not properly regularized or when the dataset is not sufficiently large <cit.>. The choice to move to a more complex architecture should be driven by specific needs that cannot be met by simpler models and should be justified by empirical evidence showing clear benefits.

Moreover, the accuracy of any machine learning model is highly dependent on the quality of the input data <cit.>. High-quality data are well-curated, balanced, and reflective of real-world scenarios. This includes comprehensive representation of all classes in classification tasks, minimal noise, and high precision. Often, efforts and resources are better spent on improving data quality through enhanced collection methods and rigorous cleaning processes. As shown in Sec. <ref>, we have carefully preprocessed and selected the data.

Building upon our previous work, where our earlier model achieved high accuracy, as demonstrated by our comparison with the Transformer and supported by the reasoning above, we continue to utilize FNet based on ResNet in this article, with some minor modifications for classification instead of regression. Below, we outline the architecture of FNet.



 

 §.§ FNet



FNet differs from the officially adopted SDSS QuasarNET <cit.>, a CNN-based model that mimics the traditional human method by identifying prominent spectral lines, classifying the spectrum, and calculating redshifts from these lines. In contrast, FNet is designed to autonomously uncover hidden patterns in the data without relying on predefined information. These patterns could include prominent and weak lines, global patterns, and specific patterns of different classes. This distinct design results in different outcomes and application scopes.

The architecture of FNet is demonstrated in Fig. <ref>. FNet employs a one-dimensional ResNet architecture designed for classifying spectral data. This architecture features 8 residual blocks, each containing 3 convolutional layers with small (15), medium (200), and large (500) kernel sizes to capture both local and global patterns in a spectrum. This design aligns with our tests, where we evaluated training efficiency and prediction accuracy using randomly selected kernel sizes (10 to 500 pixels) and model depths (8 to 72 layers). Our designed architecture represents an optimized balance of efficiency and accuracy.


For each residual block, the input spectrum x is processed through three convolutional layers initialized by the He Normal initializer <cit.>. Batch normalization is applied after each convolutional layer to maintain network stability. The ReLU activation function <cit.> is used following the first two batch normalization steps to introduce non-linearity, enabling the model to capture complex patterns. The output of each residual block H(x) is then added to the input x to form H(x) + x, ensuring gradients remain within an appropriate range during training. After the residual blocks, the network flattens the output and passes it through fully connected layers, culminating in the classification of the spectrum.



 

 §.§ Training



A crucial aspect of training a neural network for a particular task is choosing the right loss function and optimization method. For classification tasks, "Cross Entropy" is commonly used, whereas "Mean Squared Error" is often preferred for regression tasks <cit.>. In the earlier version of the FNet model, we employed mean squared error since the task involved predicting the redshift of quasars <cit.>. In this work, "Cross Entropy" <cit.> is used as the loss function for this classification problem, along with the AdamW optimizer to optimize the loss function.

AdamW, or Adam with weight decay <cit.>, is a modification of Adam, which combines the best properties of the AdaGrad <cit.> and RMSProp <cit.> algorithms to handle sparse gradients on noisy problems. AdamW retains the benefits of Adam’s adaptive learning rate and momentum while incorporating weight decay separately rather than adding it to the gradient as in Adam. This small but critical change helps in better regularization and often leads to better training outcomes. AdamW typically converges quickly and is effective in cases with large datasets and/or high-dimensional spaces. Experimental results demonstrate that AdamW leads to improved training loss and enhanced generalization compared to models trained with Adam <cit.>.

We also performed a comparison by testing FNet on 40,000 spectra from the DR17Q catalog over 100 epochs (see Fig. <ref>). The results clearly exhibit the advantage of using AdamW, which converges faster than other optimizers.





Optimizing a neural network model with the AdamW optimizer requires the right selection of hyperparameters. Experimentation with hyperparameter configurations is pivotal in identifying the optimal settings for achieving superior optimization and generalization outcomes. This includes fine-tuning the learning rate (lr), adjusting beta coefficients for gradient averaging, setting weight decay for regularization, and contemplating the utilization of AMSGrad <cit.>. 

In this work, specific parameter values were employed to obtain highly optimized results, including an initial learning rate of lr_1=0.00024, beta coefficients of (0.9, 0.999), weight decay of 1 e-6, and amsgrad=False to use the standard Adam update rule. Notably, the implementation of learning rate scheduling strategies, such as reducing the learning rate after designated epochs, can enhance convergence <cit.>. Techniques like L2 penalty weight decay play a crucial role in mitigating overfitting, particularly in datasets characterized by a profusion of features <cit.>.


 
We utilized the PyTorch framework for training and testing our neural network model <cit.>. The source code for our model is available at: https://github.com/AGNNet/FNet.githttps://github.com/AGNNet/FNet.git, and the dataset used can be accessed at: https://www.kaggle.com/ywangscience/sdss-iii-ivhttps://www.kaggle.com/ywangscience/sdss-iii-iv. Training of the FNet model was performed on an Nvidia Tesla V100 graphics card, with each training epoch taking approximately 90 minutes. The inference time for predicting the redshift of an SDSS spectrum is around 14 milliseconds.



 



§ RESULTS



As detailed in Sec. <ref>, we used confident quasars, galaxies, stars, and BAL-quasars from the DR17Q catalog to train and test FNet.

We quantify the precision of the predictions using the metric of completeness <cit.>, defined as the ratio of correctly predicted spectra to the total number of spectra in each class. This metric is assessed on the test sample.




 §.§ Imbalance in Data


Highly imbalanced data presents a significant challenge, as most networks tend to prioritize the majority class. In extreme cases where the minority class constitutes less than 1%, it may be completely disregarded. Addressing class imbalance in deep learning is an active area of research, and finding effective approaches for specific tasks and imbalance scenarios is challenging <cit.>. However, traditional methods such as data sampling and cost-sensitive learning have shown applicability in deep learning contexts in recent years <cit.>.


In our sample, most spectra belong to quasars (approximately 390,000) and stars (approximately 230,000), while fewer spectra are attributed to BAL-quasars (approximately 26,000) and galaxies (approximately 30,000). This creates a moderate imbalance, with only 9% of the data representing the less common classes. Testing the FNet model on this imbalanced data yielded expected results: galaxy completeness was 86.9%, BAL-quasar completeness was 78.8%, star completeness was 98.8%, and quasar completeness was 98.3%. As anticipated, training the network with this imbalanced sample prioritized quasars and stars while neglecting BAL-quasars and galaxies. We attempted oversampling the minority classes and using weighted cross-entropy to address the imbalance, but these methods did not significantly improve the results.


Fortunately, the number of minority class spectra (approximately 30,000 for each class) in our sample is sufficient to establish a confident training set. To mitigate data imbalance, we equalized the number of spectra for each class to N = 26,667, the total number of BAL quasars, which is the smallest class.




 §.§ Problem of BAL-quasar identification



It is widely acknowledged that detecting quasars with broad absorption line (BAL) features <cit.> is more complex than detecting emission lines at the human-expert level. Quasars with BAL features display a distinct absorption trough blueward of the emission lines, which must be sufficiently separated from the line center and possess adequate width. The balnicity index (BI), an automated measurement of the strength of the BAL feature in the CIV line, annotated in the SDSS survey as BI_CIV, quantifies this characteristic. The primary challenge in determining whether a spectrum exhibits a BAL feature, whether through visual inspection or automated methods, lies in accurately assessing the level of the unabsorbed continuum.


For example, in this context, QuasarNET <cit.> addresses the problem of identifying a CIV emission line with broad absorptions by treating it as equivalent to detecting any other emission line. To achieve this, they incorporate a BAL_CIV line into the list of lines that the network is trained to recognize. QuasarNET, which consists of a network with four convolutional layers followed by a final fully-connected layer, includes "six line finders" to detect Lyα (121.6 nm), CIV (154.9 nm), CIII (190.9 nm), MgII (279.6 nm), Hβ (486.2 nm), and Hα (656.3 nm) emission lines. Additionally, it is enhanced with a seventh “line finder” unit specifically designed to identify the CIV line with a broad absorption feature.


On the other hand, FNet utilizes a ResNet structure with 24 convolutional layers and kernel sizes of 500, 200, and 15. This design enables FNet to recognize both “global” and “local” patterns in spectra through a self-learning procedure, independently discovering hidden features and training on all spectra uniformly. The presence of the larger kernels, particularly the size 500, effectively bypasses complexities in detecting BAL features and eliminates the need to incorporate external information, such as the BAL_CIV threshold, for spectral classification. 

We tested FNet using only smaller kernel sizes of 100 and 10, and 200 and 17, instead of 500, 200, and 15. The completeness decreased with the smaller kernels, especially for BAL-quasars, suggesting that some broad features were overlooked by the network.



 §.§ training results


Eighty percent of the spectra were allocated to the training set, while 10% were reserved for validation using k-fold cross-validation <cit.>. The remaining spectra were designated for the test set, ensuring they were not used to train the CNN.





After exclusively using the training/test set primarily sourced from our criteria introduced in Sec. <ref> and excluding those labeled with AUTOCLASS_DR14Q = VI, consistent with the approach employed in QuasarNET <cit.>, the classification completeness achieved by FNet improved to 99.00% ± 0.20 for galaxies, 98.50% ± 0.30 for quasars, 99.00% ± 0.18 for BAL-quasars, and 98.80% ± 0.20 for stars. The uncertainty in completeness percentages reflects tests conducted over multiple data batches. This method of evaluating a model is particularly useful for ensuring robustness and understanding the consistency of the model's performance, with validity ensured by choosing large batches that include randomly selected test samples of all classes. The confusion matrix evaluating FNet's classification is depicted in Fig. <ref>. Figure <ref> and Figure <ref> show examples of both successes and failures of the final test. In order to reduce noise in the data and make underlying spectral features, such as emission or absorption lines, more pronounced, we used Gaussian smoothing on all spectra in the above figures only for presenting purpose.


Indeed, when training on imbalanced data (as illustrated in Sec. <ref>), the high number of misclassified rare sources indicates that the network tends to confuse rare sources with dominant ones, reducing the completeness for dominant sources. Conversely, using balanced data yields more accurate results for rare sources. This improvement in completeness for rare sources subsequently increases the overall number of correctly predicted sources, as there are fewer instances of rare sources being confused with dominant ones.












 §.§ Training result for less confident spectra and potential application to other datasets
 


In Sec. <ref>, we used only data with the highest confidence redshifts (Z_CONF = 3), the most secure BAL probabilities (BAL_PROB ≥ 0.9), and no ambiguity about quasar classification (IS_QSO_FINAL = 1). Relaxing these conditions to include sources with low redshift confidence (Z_CONF ≠ 3), less secure BAL probabilities (0.5 ≤ BAL_PROB < 0.9), and ambiguously classified quasars (IS_QSO_FINAL ≠ 1) adds an extra 2% of spectra to the main data for the training-test procedure. These spectra are mostly related to sources with too low SNRs to be confidently classified by human experts <cit.>.


We performed training and testing on the dataset with ambiguous data included and observed a slight decrease in completeness compared to using only clean data. Specifically, FNet achieves a completeness of 98.30% ± 0.40 for galaxies, 98.00% ± 0.40 for quasars, 98.50% ± 0.40 for BAL-quasars, and 98.20% ± 0.30 for stars. These results remain acceptable for scientific use.


For example, when testing QuasarNet on the sample of spectra without confident annotations (Z_CONF < 3), which represents about 2% of the spectra <cit.>, it classifies 20% of the spectra as quasars with reliable redshifts. In comparison, FNet achieves a completeness of 45% for quasars, 72% for BAL-quasars, and 62% for stars. For galaxies, the number of sources with Z_CONF ≠ 3 is negligible, so we do not consider them for this test. Fig. <ref> shows the confusion matrix for this 2% of ambiguous spectra.



In general, FNet learns to classify spectra not only by recognizing prominent emission and absorption lines but also by identifying subtle patterns that may not be immediately apparent <cit.>. Consequently, even after incorporating the 2% of train/test sets with less confident classifications, FNet still achieves high classification completeness. This robustness suggests that FNet has significant potential for application to other datasets. However, careful data preprocessing is essential when applying FNet to datasets other than SDSS-IV.






§ CONCLUSIONS
 


Accurate spectral classification in astrophysics requires reliable methods. With the increasing volume of data from current and forthcoming surveys, relying solely on visual inspection is impractical. Research into statistical approaches for analyzing spectra within their cosmological context <cit.> has shown that convolutional neural networks (CNNs) outperform other methods in classifying observed spectra. Therefore, developing automated methods that achieve human-expert accuracy has become essential.


In this study, we adapted and modified the previously introduced network, FNet, a 1-dimensional CNN with a ResNet architecture, to classify the spectra of quasars, galaxies, stars, and BAL-quasars in the SDSS-IV catalog from the DR17 superset of eBOSS. This network was previously successful in predicting the redshift of quasars in DR16 of eBOSS, achieving a velocity difference accuracy of 97.0% for |Δν| < 6000   km/s, 98.0% for |Δν| < 12000   km/s, and 98.9% for |Δν| < 30000   km/s when compared to visually inspected redshifts <cit.>.


As FNet does not rely on identifying specific lines, a simple modification enabled our current network to classify all SDSS spectra without external information about emission/absorption lines. This modification involves changing the last output layer of FNet from a single value (redshift) to multiple values (probabilities of all classes) and adjusting the loss function from mean squared error (MSE) to cross-entropy.

From a total of 1,367,288 spectra of quasars, stars, and galaxies in the SDSS-IV quasar catalog from DR17 of eBOSS, we selected 639,906 spectra (Stars: 229,647; Galaxies: 28,688; Quasars: 359,609; BAL Quasars: 21,962) for the classification training set. This subset represents the highest confidence level of source selection in this catalog.


Utilizing its convolutional layers and the ResNet structure, FNet autonomously discerns both “local” and “global” patterns within the spectra. The CNN employs convolutional layers with kernel sizes of 500, 200, and 15 to detect various patterns in the flux of quasars. The flux is then processed through 24 residual blocks: the first 21 blocks have a channel size of 32, followed by three blocks with channel sizes of 64, 32, and 16, respectively. This self-learning capability is crucial for classifying spectra from diverse astrophysical objects.


It is worth noting that detecting quasars with broad absorption lines (BALs), as in the case of BAL quasars, is slightly more challenging than detecting emission lines. Unlike QuasarNET, which addresses this by adding the BAL CIV line to the list of identifiable lines to find a CIV emission line with broad absorptions, this step is unnecessary in FNet due to its self-learning feature acquisition process.

FNet achieves a completeness of 99.00% ± 0.20 for galaxies, 98.50% ± 0.30 for quasars, 99.00% ± 0.18 for BAL quasars, and 98.80% ± 0.20 for stars. These results are comparable to those obtained using QuasarNET <cit.>, a standard CNN used in the SDSS catalog for redshift measurement and classification <cit.>.





§ ACKNOWLEDGMENT


We acknowledge the support from Dr. Jie Jiang and Prof. Yifu Cai from USTC for providing the Nvidia DGX Station. We would like to thank the anonymous referee for their comments, which have enhanced the scientific credibility of the paper, leading to more comprehensive discussions and clearer explanations. R. Moradi acknowledges support from the Institute of High Energy Physics, Chinese Academy of Sciences (E32984U810).




§ DATA AVAILABILITY


The catalog underlying this article is available in The Sloan Digital Sky Survey Quasar catalog: sixteenth data release (DR16Q), at https://www.sdss.org/dr16/algorithms/qso_catalog/https://www.sdss.org/dr16/algorithms/qsocatalog/. The code can be found in the public domain: https://github.com/AGNNet/FNet.githttps://github.com/AGNNet/FNet.git and the prepared data set can be found in https://www.kaggle.com/ywangscience/sdss-iii-ivhttps://www.kaggle.com/ywangscience/sdss-iii-iv.

mnras



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 Paper Title: Cloud Collision Signatures in the Central Molecular Zone.









^*email: rb5132@princeton.edu

School of Physics and Astronomy, Cardiff University, Queen’s Buildings, The Parade, Cardiff CF24 3AA, UK
Department of Physics, Princeton University, Princeton, NJ, USA




§ ABSTRACT 

Molecular cloud collisions are a prominent theory for the formation of stars.  Observational studies into cloud collisions identify the collision via a bridging feature: a continuous strip of line emission that connects two intensity peaks that are related in position space and separated in velocity space.  Currently, most observations of collisions and these bridging features take place in the Milky Way disc.  They are also theorized to take place in the Central Molecular Zone (CMZ), where temperatures and densities are both significantly higher than in the disc.  For studies in the Milky Way Disc, the most commonly-used tracer tends to be .  However, for studies in the CMZ, where the density and temperature are significantly higher,  becomes so abundant that it loses its ability to adequately highlight the bridging feature of cloud collisions.  As a result, studies have begun using other tracers, whose physical and chemical behavior has not been studied under CMZ conditions. We perform combined hydrodynamical, chemical and radiative transfer simulations of cloud collisions under both disc- and CMZ-like conditions, and investigate collision signatures in a number of commonly-observed molecular lines.  Under the Milky Way disc conditions  has the standard bridging feature; however, the other tracers, , ,  only emit in the intermediate-velocity bridge region, making the feature itself non-existent.  In the CMZ, the higher density and temperature make the bridging feature far more indistinct for , but the other tracers have morphologically similar bridging features to the  disc model, validating their use as tracers of cloud collisions under these conditions.


  






Cloud Collision Signatures in the Central Molecular Zone

    Felix D. Priestley^1
    July 2024
=========================================================





§ INTRODUCTION
 





Current theory suggests that collisions between molecular clouds are potential triggering mechanisms for star formation <cit.> and are expected to be fairly common occurrences in galactic discs <cit.>.  These cloud collisions have also been observed outside of the Milky Way's disk, in the Small and Large Magellanic Clouds <cit.> and are theorized to take place closer to the galactic center, as gas flows into the Central Molecular Zone (CMZ) <cit.>.

When searching for high velocity molecular cloud collisions in observational data, the most common method of identification is via  bridging features <cit.>.  This signature consists of two intensity peaks in position-velocity space connected by intermediate-velocity emission, corresponding to the material decelerated by the collision.  Cloud collision signatures, usually bridging features, were identified in more than 50 high-mass star formation regions of the Milky Way disc <cit.>.


In the Milky Way disc, these bridging features are identified with CO as a tracer. Recent studies of the CMZ have, in addition to  <cit.>, claimed to identify bridging features in lines of other species such as  <cit.> and SiO <cit.>.  , being a dense gas tracer, should not show any bridging features under the normal Milky Way conditions as the emission is concentrated in the density-enhanced intermediate velocity gas <cit.>.  In the Milky Way disc, SiO only traces shocked gas and as such should only present in the bridge region itself, rather than tracing the entire bridge feature <cit.>. Within the CMZ, however, the environment behaves entirely different from the normal Milky Way conditions of previous bridging feature studies.  As such, the common methods of identifying bridging features may not be appropriate for this environment.  Observational studies suggest that molecular clouds in the CMZ are denser, hotter, and more turbulent than the Milky Way disc <cit.>.  Furthermore, these regions of the CMZ have a higher ionization rate, which may have a significant impact on their chemistry <cit.>.

This paper seeks to examine observational signatures of cloud collisions under CMZ conditions via a combination of hydrodynamical, chemical, and radiative transfer models.  The distinct chemical properties of the CMZ <cit.> require that the molecular abundances are evolved self-consistently, as simplifications such as spatially and temporally invariant abundances are likely to produce erroneous results even under better-understood Milky Way disc conditions <cit.>.  Our synthetic observations will allow us to investigate the validity of extrapolating the well-known  bridging feature signature into a regime which has not previously been studied.





















 

§ METHOD




	
	
	
	
   Our simulation setup is similar to previous studies on this topic <cit.>, and consists of a head-on collision between two initially-spherical, differently-sized clouds. The larger cloud has an initial radius of 5, the smaller one a radius of 2.5, and the cloud centres are separated by 10 at the beginning of the simulation. Both clouds have an initially uniform density, with the smaller cloud being twice as dense as the larger one. Each cloud is initialised with a turbulent velocity field following <cit.>, and given a bulk motion of 10 towards each other. We perform simulations using the smoothed-particle hydrodynamics (SPH) code phantom <cit.> with 375,000 particles in the clouds, and a background medium with a density 100 times lower than the cloud material with the sound speed increased to ensure pressure balance, containing another ∼ 100,000 particles. Sink particles are introduced with a formation density of 10^-17 and an accretion radius of 0.01.

We perform two SPH simulations, representing conditions typical for the Galactic disc and the CMZ. The disc simulation has a large cloud mass of 10^4 and a small cloud mass of 2500, giving initial volume densities of 550 and 1100 respectively. The SPH particle mass is 0.03. The sound speed within the clouds is set to 0.19, appropriate for molecular gas at a temperature of 10, and the root-mean-squared velocity of the turbulent velocity field is set to five times this value. For the CMZ simulation, we increase the cloud masses to 10^5 and 2.5 × 10^4 and the sound speed to 0.42 (i.e. 50). We keep all other parameters fixed, so the turbulent velocity field has a higher average value but the same Mach number, the collision speed is unchanged, and the particle mass is now 0.3. The simulations are run until they have accreted a few percent of the cloud mass into sink particles, which occurs after 0.32 for the disc simulation and 0.18 for the CMZ one.





   
   
   
   
   
   





We select 10^5 SPH particles which end the simulation within 5 of the collision centre, and post-process their chemical evolution using uclchem <cit.>, a time-dependent gas-grain chemical code using the UMIST12 network <cit.>. We take elemental abundances from <cit.>, and assume an initially-atomic composition for all species except hydrogen, which is in the form of H_2. The background ultraviolet (UV) radiation field is taken to be 1.7 <cit.> units, and the cosmic ray ionisation rate (CRIR) is set to 1.3 × 10^-17  s^-1. Although these parameters do not enter into the SPH simulations, the increased gas temperature of clouds in the CMZ is likely to be caused by an enhanced CRIR in this region <cit.>, so we additionally investigate running the chemistry for the CMZ model with a CRIR increased by a factor of 100. To estimate shielding column densities to attenuate the UV field, we follow the approach in <cit.> and multiply the local volume density by the Jeans length, and convert to extinction via a factor of 6 × 10^-22  mag   cm^2 <cit.>.

Finally, we obtain position-position-velocity (PPV) cubes of the molecular line emission using the radiative transfer code radmc3d <cit.>. We use splash <cit.> to interpolate physical properties from the SPH simulation onto a cube with side length 10 and spatial resolution 0.05, and assign each cell the molecular abundances of the nearest tracer particle. Our output spectra cover a velocity range of ± 12 with a resolution of 0.12. We investigate the J=1-0 transitions of CO, HCO^+ and N_2H^+, and the J=2-1 transition of CS, using collisional data taken from the LAMDA database <cit.>. Dust properties are a mixture of <cit.> and <cit.> opacities, as described in <cit.>.




§ RESULTS


The left-most column of Fig. <ref> displays the Milky Way disc cloud collision model in position-velocity space.  In this environment,  is highly abundant at densities between 10^3-10^5 (Fig. <ref>), and so emits strongly in both the molecular clouds themselves and the bridging feature of the collision (Fig. <ref>).  , ,  on the other hand are far less abundant and have higher critical excitation densities <cit.>, so are only visible in emission in the compression region at the interface between the clouds (Fig. <ref>).  In position-velocity space (Fig. <ref>), the clouds themselves are either only weakly apparent or completely absent, making the identification of bridging features challenging, if not impossible.

In the CMZ, the increased temperature and density alter the emission properties of  such that the ambient cloud material becomes much brighter.  This serves to make  bright everywhere and reduces the contrast of the bridging feature (Fig. <ref>), thus limiting its viability as a tracer molecule in the CMZ environment.  On the other hand,  increases in abundance, and emits more readily due to the higher density and temperature throughout all densities (Fig. <ref>).  In the CMZ  shows the bridging feature and the cloud in greater detail than  (Fig. <ref>).  The abundance curves for  and  flatten in the CMZ, losing the peak around 10^4 cm^-3 in the Milky Way disc, and as such they no longer preferentially trace the dense region of the collision.

In the CMZ with a high ionization rate,  again has a low contrast between cloud and bridge regions.  , however, decreases in abundance back down to levels similar to the Milky Way Disc (Fig. <ref>).  The image of the bridging feature in the  in Fig. <ref> is less pronounced.  However, the high ionization rate causes the  abundance curve to mimic the abundance curve of  in the Milky Way Disc (Fig. <ref>).  As such, the position-velocity graph of  provides a readily apparent bridging feature in the highly ionized CMZ (Fig. <ref>).  Similarly,  provides a strong bridging feature, albeit with a greater emphasis on the the feature itself.  In the case of a high ionization rate,  and  may be more promising tracers of cloud collisions than  and .




§ DISCUSSION


Some recent studies into CMZ cloud collisions have used  as an alternative cloud collision tracer to   <cit.>.  Based on the results of this study, that choice appears to be a valid one for identifying cloud collisions in the CMZ, which would not be the case in the Milky Way disc.  Studies in the CMZ using  have encountered difficulties in identifying strong bridging features <cit.>, in agreement with our results.  The extreme environment of the CMZ appears to allow the use of other species which under normal conditions preferentially trace dense gas, in an analogous manner to  as signatures of cloud collisions.  Similarly, the presence of widespread supersonic turbulence in the CMZ <cit.> may make SiO, normally a shock tracer, more suited to tracing the bulk of the cloud material, as in <cit.>.

The widespread  emission seen in the high-CRIR CMZ model is in good agreement with the observed behaviour of this molecule <cit.>, and in start contrast to its role as a tracer of high-density gas in the Milky Way disc <cit.>.  To our knowledge, this is the first time this behaviour has been reproduced using a self-consistent treatment of the dynamics and chemistry; <cit.> use a fixed  abundance estimated from CMZ observations, while <cit.> include an increased CRIR in their chemical model, but do not investigate the higher densities and temperatures present in the CMZ.  In addition to its role as a tracer of dense gas, the altered chemical behaviour in the CMZ is likely to affect the relationship between the  emission and the star formation rate proposed by <cit.> under Milky Way disc conditions.  Simulations with more realistic thermodynamics than the isothermal equation of state adopted here <cit.> will be required to investigate this point in more detail.



§ CONCLUSION


We have examined the simulated behavior of molecular line emission in the Milky Way Disc, and the CMZ with a normal and enhanced cosmic ray ionization rate.  We investigate the utility of these lines for investigating the presence of cloud-cloud collisions in  different environments.  We have concluded the following:

    
  * , while a good tracer molecule for Milky Way Disc collisions, fails to provide adequate contrast in the CMZ to properly identify bridging features.
    
  *  emits more strongly under CMZ conditions than in the Milky Way disc, as such it provides a much more pronounced bridging feature.
    
  * For CMZ simulations with an enhanced ionization rate, the visibility of the bridging feature in both  and  is reduced, but  and  both provide very strong collisions signatures due to their enhanced chemical abundances and the higher gas densities and temperatures found in the CMZ.





§ ACKNOWLEDGEMENTS

FDP acknowledges the support of a consolidated grant (ST/W000830/1) from the UK Science and Technology Facilities Council (STFC).


mnras




 Paper Title: Do all the quasars and high-excitation radio galaxies (HERGs) in the 3CRR catalog contain a magnetically arrested disk (MAD)?.





0000-0002-7299-4513]Shuang-Liang Li
Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, People's Republic of China

0000-0002-4521-6281]Wenwen Zuo
Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, People's Republic of China

0000-0002-2355-3498]Xinwu Cao
Institute for Astronomy, School of Physics, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, People's Republic of China

Shuang-Liang Li,Wenwen Zuo, Xinwu Cao
lisl@shao.ac.cn, wenwenzuo@shao.ac.cn, xwcao@zju.edu.cn



§ ABSTRACT 
Based on the magnetization, an accretion disk with large-scale magnetic field can be separated into either standard and normal evolution (SANE) or magnetically arrested disk (MAD), which are difficult to identify from observations. It is still unclear whether all the radio-loud active galactic nuclei (RLAGNs) with a thin disk and strong radio emissions contain a MAD. We investigate this issue by utilizing the 3CRR catalog. We compile a sample of 35 quasars and 14 high-excitation radio galaxies powered by a thin accretion disk. In order to consistently compare with the MAD sample given by <cit.>, the optical-UV emissions of our sample are all detected by the Hubble Space Telescope (HST). It is found that the average X-ray luminosity (L_ X) of our sample is about 5.0 times higher than that of radio-quiet AGNs (RQAGNs) with matching optical-UV luminosity (L_ UV), in general accord with the factor of 4.5 times in MAD sample within the uncertainty. The relationship between radio (5 GHz) and X-ray (2 keV) luminosities in the 3CRR sources is also found to be consistent with the MAD sample. Furthermore, the jet efficiencies of 3CRR sources are consistent with those from the GRMHD simulations of MAD. Therefore, we suggest that probably all the quasars and at least a fraction of high-excitation radio galaxies in the 3CRR catalog, and perhaps all the RLAGNs with strong radio emissions contain a MAD.















§ INTRODUCTION




<cit.> suggested that with the accumulation of magnetic flux, the magnetic pressure in the inner accretion disk will be comparable or even higher than the gas pressure, leading to the destruction of symmetry in the inner parts of the accretion disk. This kind of disk is called MAD (magnetically arrested disk), where the magneto-rotational instability (MRI) is suppressed and the magnetic Rayleigh–Taylor (RT) instability will be responsible for the accretion of gas (e.g., ). In the general relativistic magnetohydrodynamic (GRMHD) simulations, an advection-domintated accretion flow (ADAF) can be divided into two classes, i.e., the so-called standard and normal evolution (SANE) and MAD according to the magnetization of ADAF (e.g., ). However, it is very difficult to discriminate between MAD and SANE scenarios from observations. Although the jet power produced in MAD is generally larger than that produced in SANE, we cannot distinguish MAD and SANE based on the jet power alone, because it depends not only on the strength of magnetic field but also on the black hole spin and mass accretion rate <cit.>. Additionally, <cit.> suggested that the spectral energy distributions (SED) of SANE and MAD in an ADAF are quite similar, though with a higher radiative efficiency for MAD. Fortunately, the Faraday effect caused by the magnetic field along the direction of light propagation can help to identify MAD from SANE when the polarization information is available. By comparing the rotation measure of jets from observations and simulations of MAD, <cit.> suggested that the accretion flow of M87 should be a MAD. Unfortunately, this method cannot be extensively applied to other low-luminosity active galactic nuclei (AGNs) because their polarization is usually weak (see  for details). The more direct evidence for the presence of MAD was discovered recently in black hole X-ray binary MAXI J1820+070, where the radio fluxes are delayed about 8 days compared with the X-ray flux <cit.>. In this process, the outburst of X-ray flux is produced by the expanding corona, resulting in the amplification of magnetic field and the formation of MAD around the time of the radio peak (8 days later).

Except for the MAD in an ADAF, it is also possible to generate a MAD in an optically thick and geometrically thin accretion disk (e.g., ). By compiling a sample of radio-loud active galaxies, <cit.> discovered a tight correlation between the jet magnetic flux and disk luminosity, which is consistent with the theoretical prediction of a MAD in MHD simulations. A similar relationship between the jet power and the disk luminosity supporting the MAD scenario is also reported in blazars <cit.>. However, the samples of these two works include both BL Lacertae objects and flat-spectrum radio quasars (FSRQs), which may correspond to either the MAD in an ADAF (BL Lac) or the MAD in a thin disk (FSRQs), respectively. Furthermore, their physical parameters adopted (e.g., jet power, magnetic flux and disk luminosity) are based on several approximations and assumptions. It is therefore difficult to separate MAD and SANE in a thin disk from these relationships.  

Another direct evidence for the MAD in a thin accretion disk comes from the obvious difference between the extreme ultraviolet (EUV) spectrum of radio-loud AGNs (RLAGNs) and the radio-quiet AGNs (RQAGNs, e.g., ), where the RLAGNs show a deficit in EUV band compared with the RQAGNs when the rest-frame wavelength is smaller than 1100 Å. This phenomenon may indicate a missing or suppressed energy dissipation in the innermost region of accretion flow and  can be qualitatively explained by the MAD model in a thin disk <cit.>. For a thin disk with MAD in the innermost region, the presence of large-scale magnetic flux therein will extract a fraction of gas energy to the jet as Poynting flux, resulting in the observed EUV deficit. Furthermore, this picture can also qualitatively explain the positive relationship between the jet power normalized with the bolometric luminosity and the EUV deficit normalized to the RQAGN value shown by HST data (see  for details).

Except for the EUV spectrum, a significant difference in X-ray emission is also found between the MAD and SANE <cit.>. The authors reported that the average X-ray flux of a MAD is 4.5 times higher than that of RQAGNs, while the average X-ray flux of RLAGNs without an EUV deficit is about 2–3 times larger than that of RQAGNs <cit.>. The X-ray excess in MAD sample may originate from the increase of radiative efficiency in a corona, similar with the process that a MAD can improve the radiative efficiency of an ADAF (see  and the last section for details). This result implies that not all the RLAGNs contain a MAD. 
Unfortunately, such a statistically several times higher X-ray flux is not enough to discriminate between SANE and MAD given their error bars. Additionally, the method of utilizing the EUV deficit cannot be employed for most RLAGNs, as the data for EUV emission are often absent. Therefore, we turn our eyes to the radio band and find that all the objects in the MAD sample have strong radio emission (the radio-loudness are all higher than 100, see table 1 in ). However, it is unclear whether all the RLAGNs with strong radio emission contain a MAD. In this work, we intend to investigate this issue by comparing the multiwavelength properties of the 3CRR sources, the most powerful radio galaxies in the universe, and the MAD sample of <cit.>.
 



§ SAMPLE




lllllllllllll


Sample.





1lName     1lz     1ltype     1lΓ      1llogL_X     1lRef.     1llogL_ UV      1lRef.     1lΔlog L_ X    
1llogL_ R     1llog R_ UV     1llogM_ bh/M_⊙     1lλ 





                    [erg s^-1          [erg s^-1          [erg s^-1     [erg s^-1                  

                    Hz^-1]          Hz^-1]          Hz^-1]     Hz^-1]                 

(1)      (2)      (3)      (4)    
 (5)      (6)     (7)      (8)      (9)      (10)      (11)      (12)      (13) 





3C9        2.012       Q       1.61^+0.12_-0.08       27.56^+0.16_-0.12       1        31.46      8      0.14       32.92       1.46     9.8     -0.70  

3C47        0.425       Q       1.87^+0.21_-0.22       27.31^+0.25_-0.17       1        30.00      8      1.01       32.60       2.61     9.2     -1.56  

3C48        0.367       Q       2.32^+0.16_-0.01       27.16^+0.02_-0.02       1        30.81      8      0.24       33.55       2.74     9.2     -0.75  

3C68.1        1.238       Q       1.9       27.21^+0.10_-0.10       1        30.43      8      0.57       31.81       1.38     9.9     -1.83  

3C138        0.759       Q       1.46^+0.24_-0.11       27.57^+0.10_-0.10       1        30.29      8      1.04       33.27       2.98     8.9     -0.97  

3C147        0.545       Q       1.85^+0.24_-0.22       26.91^+0.24_-0.15       1        30.33      8      0.35       34.38       4.05     9.1     -1.13  

3C175        0.768       Q       1.52^+0.40_-0.07       27.52^+0.08_-0.07       1        31.03      8      0.42       32.68       1.65     9.9     -1.22  

3C181        1.382       Q       1.72^+0.17_-0.10       27.56^+0.10_-0.08       1        30.84      8      0.61       32.66       1.82     9.6     -1.12  

3C186        1.063       Q       1.88^+0.05_-0.03       27.29^+0.03_-0.03       1        30.89      8      0.30       32.80       1.91     9.5     -0.96  

3C190        1.197       Q       1.61^+0.06_-0.05       27.22^+0.04_-0.04       1        30.51      8      0.53       33.60       3.09     8.7     -0.55  

3C191        1.952       Q       1.68^+0.11_-0.10       27.64^+0.09_-0.07       1        30.75      8      0.76       33.82       3.07     9.7     -1.31  

3C196        0.871       Q       1.67^+0.40_-0.38       27.23^+0.49_-0.25       1        30.48      8      0.56       32.28       1.80     9.6     -1.48  

3C204        1.112       Q       2.15^+0.14_-0.22       27.75^+0.16_-0.14       1        31.07      8      0.63       33.10       2.03     9.5     -0.79  

3C205        1.534       Q       1.83^+0.06_-0.17       27.93^+0.05_-0.07       1        31.38      8      0.57       33.28       1.90     9.6     -0.58  

3C207        0.684       Q       1.59^+0.08_-0.23       27.39^+0.19_-0.15       1        30.22      8      0.91       33.91       3.69     8.5     -0.64  

3C208        1.109       Q       1.63^+0.18_-0.14       27.44^+0.10_-0.08       1        30.99      8      0.38       33.37       2.39     9.4     -0.77  

3C212        1.049       Q       1.85^+0.03_-0.08       27.85^+0.01_-0.01       1        30.02      8      1.52       33.79       3.77     9.2     -1.54  

3C215       0.411       Q       1.88^+0.09_-0.08       27.16^+0.07_-0.05       1        29.65      8      1.12       31.92       2.27     8.3     -1.01  

3C216       0.668       Q       1.72^+0.26_-0.20       27.15^+0.08_-0.09       1        29.85      8      0.96       34.20       4.35     8.6     -1.11  

3C245       1.029       Q       1.57^+0.10_-0.05       27.63^+0.04_-0.03       1        30.19      8      1.17       34.55       4.37     9.4     -1.57  

3C249.1       0.311       Q       1.92^+0.13_-0.04       26.85^+0.08_-0.08       1        30.25      8      0.35       32.29       2.04     9.3     -1.40  

3C254       0.734       Q       1.93^+0.10_-0.07       27.36^+0.02_-0.02       1        30.70      8      0.52       32.55       1.84     9.3     -0.95  

3C263       0.652       Q       1.83^+0.09_-0.05       27.27^+0.01_-0.01       1        30.88      8      0.30       33.35       2.47     9.1     -0.58  

3C268.4       1.400       Q       1.45^+0.17_-0.12       27.62^+0.11_-0.09       1        31.20      8      0.40       33.59       2.39     9.8     -0.96  

3C270.1       1.519       Q       1.57^+0.07_-0.07       27.29^+0.03_-0.03       1        30.87      8      0.83       34.25       3.38     9.0     -0.49  

3C275.1       0.557       Q       1.79^+0.11_-0.10       27.02^+0.06_-0.06       1        29.77      8      0.89       33.11       3.35     8.3     -0.89  

3C286       0.849       Q       2.12^+0.51_-0.26       27.09^+0.12_-0.10       1        30.75      8      0.22       35.15       4.41     8.5     -0.11  

3C287       1.055       Q       1.86^+0.04_-0.04       27.39^+0.03_-0.03       1        30.59      8      0.64       35.10       4.51     9.6     -1.37  

3C309.1       0.904       Q       1.57^+0.05_-0.03       27.74^+0.05_-0.03       1        30.81      8      0.82       34.84       4.03     9.1     -0.65  

3C325       0.860       Q       1.45^+0.07_-0.02       26.54^+0.02_-0.01       1        29.84      8      0.36       31.80       1.96     9.6     -2.12  

3C334       0.555       Q       1.85^+0.18_-0.11       27.12^+0.04_-0.04       1        30.56      8      0.39       33.04       2.48     9.7     -1.50  

3C336       0.927       Q       1.93^+0.24_-0.28       27.49^+0.14_-0.11       1        30.58      8      0.74       32.80       2.22      9.2     -0.98 

3C345       0.594       Q       1.69^+0.09_-0.02       27.66^+0.02_-0.02       1        30.22      8      1.18       35.00       4.78     9.3     -1.44  

3C351       0.371       Q       1.90^+0.20_-0.13       27.02^+0.17_-0.09       1        30.52      8      0.32      31.42       0.90     9.5     -1.33  

4C16.49       1.296       Q       1.83^+0.20_-0.12       27.49^+0.10_-0.09       1        30.59      8      0.74      33.02       2.43     9.8     -1.57  

3C20      0.174       R       1.65^+ 0.21_-0.19       25.99± 0.10       2        27.24       5       1.78       30.27       3.03     8.7     -2.44  

3C33.1      0.181       R       0.89^+ 0.33_-0.37       26.01± 0.13       2        28.37       6       0.94       30.98       2.61     8.6     -1.58  

3C61.1        0.188       R       1.70       25.90± 0.13       2        26.81       5       2.02        30.31       3.50     8.1     -0.91   

3C79        0.256       R       1.77^+ 0.69_-0.61       25.78± 0.58       3        28.87       7       0.33       30.82       1.96     9.0     -1.42   

3C171       0.24       R       1.67^+ 0.20_-0.23       25.67 
± 0.11       2        26.79       5       1.80       30.13       3.34     8.7     -1.09    

3C184.1     0.118       R       0.57^+ 0.30_-0.34       25.39± 0.16       2        28.50       6       0.23       30.28       1.78      8.5     -1.55  

3C192       0.0597       R       1.70       24.89 ± 0.19       3        27.33       5        0.61        29.80       2.47     8.7     -2.64   

3C219       0.175       R       1.90^+ 0.19_-0.18       26.03± 0.07       3        28.51       6       0.86       31.57       3.06      9.2     -2.71 

3C223       0.137       R       0.71^+ 0.77_-0.61       25.21± 0.60       3        27.67       6       0.67       30.59       2.92      8.7     -1.81   

3C234       0.185       R       1.39^+ 0.10_-0.16       26.21± 0.09       2        29.48       6       0.30       31.87       2.40       9.3     -1.47  

3C285       0.0794      R       1.70       25.30± 0.10       3        26.82       6       1.41       29.93       3.11     8.6     -3.33   

3C300       0.270       R       1.78± 0.06       25.39± 0.02       2        28.04       6       0.57       31.23       3.19     8.8     -2.07   

3C303       0.141       R       1.60± 0.21       25.84± 0.08       3        28.77       6       0.46       31.84       3.07     9.0     -2.54   

3C321       0.0965      R       1.70       24.06± 1.32       4        27.28       6       -0.18      30.80       3.52     9.1     -3.47   

13p18cm Notes: Col. (1): Source name. Col. (2): Redshift. Col. (3): AGN type. Q: quasar; R: radio galaxy. Col. (4): X-ray photon index.
Col.(5): X-ray intrinsic luminosity at 2 keV. Col. (6): References for L_X. Col. (7): optical-UV luminosity at 2500 Å. 
Col. (8): References  for L_UV. Col. (9): Excess of X-ray luminosity in 3CRR sources to that in RQAGNs. 
Col. (10): Radio spectral luminosity at 5 GHz. Col. (11): Radio loudness defined as R_UV=L_R/L_UV.
Col. (12): black hole mass. Col. (13): Eddington ratio. 

13p18cmReferences. 1, <cit.>; 2, <cit.>; 3, <cit.>; 4, <cit.>; 5, <cit.>; 6, <cit.>; 7, <cit.>; 8, this work. 











The RLAGNs with EUV deficit are suggested to contain a thin accretion disk with MAD in the inner region <cit.>. In order to compare consistently with the MAD sample, the accretion mode of 3CRR sources is also required to be a thin disk. Therefore, we adopt the quasars and the high-excitation radio galaxies (HERGs) in 3CRR catalog in this work. For one thing, the accretion flow of quasar is widely accepted to be a radiatively efficient thin disk due to the big-blue-bump in optical-UV band, which is thought to originate from an optically thick, geometrically thin disk. For another, <cit.> suggested that a radio galaxy with excitation index (EI = log[O_ III]/H_β-1/3(log[N_ II]/H_α+ log[S_ II]/H_α + log[O_ I]/H_α)) higher than 0.95 is a HERG, whose Eddington ratio is found to be higher than 0.01 and is suggested to comprise a thin accretion disk around the black hole (e.g., ). 

3CRR catalog contains 43 quasars and 130 radio galaxies. Firstly, we pick up all the quasars and HERGs with detected EI larger than 0.95 in 3CRR catalog, where the values of EI are given by <cit.> and <cit.>. A sample of 43 quasars and 17 radio galaxies are obtained. To avoid uncertainty from different telescopes, only sources observed by Hubble Space Telescope (HST) are chosen, since the optical-UV emission of MAD sample is detected by HST <cit.>. The optical-UV data of 3CRR catalog observed with HST has been extensively explored in many previous works (e.g.,). 

In order to obtain their properties in a consistent way, we analyze the HST images of all the 43 quasars ourselves using the Python package photulis <cit.>. First, we estimate the background level and its standard deviation σ, and sigma clip the background data with a threshold of 2σ. 

Following this, we use the task detect_sources to detect sources and generate a segmentation map, providing information of sources including their centroid, semi-major and semi-minor axis, as well as position angle (PA), etc. Using this information, we can derive the surface brightness profile of the target with the task ellipse. By maintaining the ellipticity and PA obtained initially, we refit the isophotes in linear steps to sample the target's surface brightness profile. Finally, we determine the aperture size by the isophote at the surface brightness level of 25 mag arcsec^-2, and perform the force aperture photometry to estimate the flux and uncertainty of the target. By visually checking the fitting results and analyzing the ratio of the obtained flux to the corresponding uncertainty (SNR), we have adopted the results of 35 quasars with SNR larger than 10. The flux at different optical-UV wavelengths (eg. 6060 Åof F606W filter, 4750 Åof F475W filter) are obtained from photometry analysis of the HST images, and then de-reddened for Galactic extinction using the <cit.> Milky Way reddening law and E(B-V) derived from the <cit.> dust map. The fluxes at 2500 Å are then calculated by extrapolating the HST optical-UV flux and assuming a spectral index α_o = -0.5 (f_ν∼ν^α_o, e.g.,  ). We fit only the quasars because it is difficult to detect the weak emission lines needed to calculate EI for middle and high redshift HERGs. Additionally, it is challenging to achieve a high SNR in middle and high redshift (z > 0.5) HERG observations due to their faint flux compared to background noise.




Lastly, we get a 3CRR sample composed of 35 quasars and 14 HERGs (see table 1), where all objects have been observed with Chandra and/or XMM-Newton telescope, so the 2 keV X-ray flux is avaible. The photon index Γ in Col. (4) and the intrinsic X-ray luminosity at 2 keV of quasars (L_ X, obtained from X-ray spectral
modeling) in Col. (5) are all taken from <cit.>, while the L_ X of HERGs are from NED[ http://ned.ipac.caltech.edu/] (see Col. 6 for references). All the L_ X have been corrected for both intrinsic and Milky Way N_ H and K-corrected. We can find that, except for three radio galaxies (3C79, 3C223 and 3C321), the uncertainty of X-ray luminosity in other sources are all quite small. 
The spectral luminosity at 2500 Å(L_ UV) of HERGs in Col. (7) are also from NED (see Col. (8) for detailed references), which is derived from the data at nearby frequency assuming a spectral index α_ o=-0.5 (). The Δ log L_ X in Col. (9) indicates the excess of X-ray luminosity above the RQAGN value, calculated from the L_ UV-L_ X relationship of <cit.> (for further details see Section <ref>). The core radio luminosity at 5 GHz in Col. (10) is taken from the online 3CRR catalog[https://3crr.extragalactic.info/]. Except for 3C216, 3C325, and 3C345, the black hole mass of quasars and radio galaxies in Col. (12) are all taken from <cit.> and <cit.>, respectively. The black hole mass in 3C216, 3C325, and 3C345 are obtained from  <cit.>, <cit.>, and <cit.>, respectively. In quasars, the broad line width of Hβ, C4, and Mg2 is separately adopted to calculate the black hole mass (see  for details), while the host galaxy bulge H band luminosity is used in radio galaxies (see  for details). These two methods give consistent BH mass estimates (see Fig. 1 in ). The Eddington ratio of quasars and radio galaxies in Col. (13) are also estimated by different methods. We use the bolometric correction factor provided by <cit.> to calculate the bolometric luminosity of quasars, while the calculation of radio galaxy bolometric luminosity is based on the [OIII]λ5007 luminosity  <cit.>, as the correction factor for radio galaxies is not available. Indeed, [OIII] luminosity may not be as a reliable proxy for bolometric luminosity for the HERGs as it is for the quasars. This is because the [OIII] emitting region extends to sufficiently small radius (i.e., sufficiently close to the supermassive black hole) to be partly obscured by the dusty torus when the active nucleus is viewed edge-on (see, e.g., ).





§ RESULTS











L_ X-L_ UV relationship is extensively adopted to investigate the accretion physics in quasars. <cit.> presented a tight relationship between L_ X and L_ UV, i.e., log L_ X=(0.76± 0.02) log L_ UV +3.51± 0.64 by compiling a type-1 RQAGN sample. This relationship can be qualitatively fitted with the disk-corona model <cit.>, where the X-ray emission comes from the inverse Compton scattering
of optical-UV photons from a thin disk by the hot corona. However, though the average X-ray luminosity of MAD sample is found to be roughly 4.5 times larger than that in RQAGNs, matched in L_ UV, their slopes are very similar (the slope is 0.75, see  for details), which may also indicate a disk-corona origin of the L_ X-L_ UV relationship in MAD objects. 

Not all the RLAGNs contain a MAD since the average X-ray luminosity is only 2-3 times higher than that in RQAGNs <cit.>. Therefore, in order to check whether all the 3CRR sources with a thin disk and strong radio emissions contain a MAD, we firstly compare their  L_ X-L_ UV relationship with the MAD sample given by <cit.> in Fig. <ref>, where the blue line represents our best-fitting result. The red and green lines are the best-fitting results for MAD sample <cit.> and RQAGNs <cit.>, respectively. It is found that the average X-ray flux of 3CRR sources is about 5.0 times higher than that of RQAGNs, which is consistent with the 4.5 times given in MAD sample within uncertainty. We adopt the ordinary least squares (OLS) method to fit all the relationships for both the 3CRR and the MAD samples <cit.>. The correlation between L_ X and L_ UV reads

    log L_ X=(0.68± 0.06) log L_ UV +6.51± 2.02,

where the confidence level based on a Pearson test is larger than 99.9%. The slope 0.68± 0.06 of L_ X-L_ UV relationship is shallower but consistent within errors with that in MAD sample (0.75± 0.25). However, it is known that the ratio of X-ray luminosity to the UV luminosity will increase with the decreasing Eddington ratio (see e.g., ). Therefore, we check the distribution of Eddington ratio in our sample and find it is equally distributed (Fig. <ref>). Our best-fitting result (the blue line) is several times higher than that from RQAGNs in <cit.> (the green line), and the confidence level of the relationship

is 99.3%. We note that many HERGs have  λ < 0.01 in our sample, which marks the division between a thin disk and a radiatively inefficient accretion flow <cit.>. However, similar values for HERGs had been reported by other works with larger samples (see e.g., Fig. 11 in  and Fig. 6 in ). The reasons for this may stem from the significant uncertainties associated with calculating both the black hole mass using bulge H-band luminosity and the bolometric luminosity using [OIII] luminosity.

The traditional relationship between radio (5GHz, L_ R) and X-ray (2 keV, L_ X) luminosities in AGNs is also investigated in Fig. <ref>, where the blue line is the best-fitting result, which can be given as 

    log L_ R=(1.35± 0.11) log L_ X -3.47± 3.11,

where the confidence level based on a Pearson test is larger than 99.9%. Though the MAD sample is located on the upper right corner of 3CRR objects due to the higher luminosity, they follow the L_ R-L_ X relationship (the blue line) in 3CRR objects quite well. The results of Fig. <ref> and <ref> indicate that all the quasars and many HERGs in the 3CRR catalog may contain a MAD. 



In addition, the GRMHD simulations suggested that the jet efficiency (η= L_ BZ/Ṁc^2) in a MAD could be very large, where L_ BZ and Ṁ are the jet power produce by the BZ mechanism <cit.> and the mass accretion rate, respectively. The jet efficiency η can be larger than 1 in MAD around a black hole with high spin (e.g., ), where the extra energy is suggested to be extracted from the rotating black hole. In Fig. <ref>, we investigate the relationship between the jet power L_ jet and the bolometric luminosity L_ bol for both the 3CRR sample and MAD sample. Here L_ jet (=0.81 log L_ R + 11.9) is the kinetic jet power calculated with the radio core luminosity at 5 GHz <cit.>. The black solid line represents the maximum jet efficiency η=140% in a MAD with black hole spin a=0.99 and the dotted line is for η=1.4%, which roughly corresponds to a=0.1 since L_ BZ∝ a^2 <cit.>. It is found that most of the 3CRR sources and MAD sample lie between the solid and dotted lines. Therefore, the jet efficiencies of 3CRR sources are consistent with the GRMHD simulations of MAD.          




§ DISCUSSION
 


In theory, the formation of MAD depends on the accumulation of large-scale magnetic fields in the inner disk region. For a standard thin disk, however, it is difficult to amplify the large-scale magnetic field due to its low radial velocity, resulting in the relatively faster diffusion of magnetic field compared with advection (e.g., ). However, this problem may be resolved by taking the magnetically driven outflow into account, which can help to increase the radial velocity of gas by transferring the angular momentum of disk <cit.>.  Furthermore, the outflow takes away not only the angular momentum, but also the energy of gas, resulting in a far smaller radiative efficiency. The radiative efficiency given by theoretical model can be several order of magnitudes smaller than 10% in extreme cases (see e.g.,  ). This result can explain the phenomenon that the jet efficiency of some objects in Fig. <ref> are even several times higher than 140%. The detailed physics of a disk-corona system with MAD is still unclear, though the MHD simulations do suggest a higher jet power and smaller bolometric luminosity <cit.>. However, for an ADAF, the presence of MAD can increase its radiative efficiency <cit.>. If the properties of corona is similar with ADAF as suggested by some works <cit.>, we can anticipate that the X-ray flux will also increase several times for a MAD in thin disk. 


Recent works suggest that the magnetically elevated accretion disks (e.g., ) can also lead to a MAD. In this scenario, the authors suggested that it is the strong toroidal magnetic field making an accretion disk MAD, though weak poloidal field is still necessary to trigger the dynamo process. However, the jet power in a magnetically elevated accretion disk should be much weaker compared with the standard MAD scenario, since the poloidal field responsible for the jet power is weak (L_ BZ∝ B_ p^2, see e.g., ). 

The 3CRR catalog contains objects with the strongest radio emissions at 178 MHz in the sky, so the black hole spins in these objects are possibly high, leading to high jet efficiencies. Although the jet in the objects around the dotted line in Fig. <ref> can be launched by a SANE with high black hole spin, other objects around the solid line should contain a MAD judging by their high jet efficiency. Furthermore, the EUV deficit in the MAD sample is difficult to explain with the SANE scenario. The origin of the X-ray luminosity excess remains debatable. In principle, both the jet core and the corona, influenced by the large-scale magnetic field, can contribute to this excess. However, if this excess were attributed to the jet core, two specific conditions must be met to maintain a similar L_ X-L_ UV slope between MAD and RQAGNs: 1) the jet core must depend strongly on L_ UV; and 2) the slope of this dependence must be consistent with the L_ X-L_ UV slope in RQAGNs (see  for details). Therefore, it is more natural to assume a coronal origin for the X-ray emissions. However, the jet core and corona may be indistinguishable in spatial resolution. In this context, one could also argue that the X-ray luminosity excess originates from the jet. This slope is also consistent with that observed in radio-loud quasars (see e.g., ).



§ SUMMARY
 

We investigate whether all RLAGNs with strong radio emission harbor a MAD by compiling a sample of quasars and HERGs from 3CRR catalog in this work. By comparing the multi-band data with the MAD sample given in <cit.>, it is found that the average X-ray luminosity of 3CRR objects is higher by the same factor as the MAD objects when compared with the RQAGNs matched in L_ UV from <cit.> (Fig. <ref>). The  L_ X-L_ UV slope of the 3CRR sample is also consistent with that of the MAD sample. Furthermore, the 3CRR sample has a larger range of L_ X (4 dex) than the MAD sample (1 dex), so the L_ X-L_ UV relation and slope are much better determined than those from the MAD sample. We find a positive relationship between the radio (5 GHz) luminosity L_ R and the 2 keV X-ray luminosity L_ X for the 3CRR sample (Fig. <ref>). The MAD sample is found to follow the L_ R-L_ X relationship quite well, which further support the same physical mechanism for MAD sample and 3CRR sources. Lastly, the jet efficiencies of the 3CRR sources (Fig. <ref>) are also found to be qualitatively consistent with GRMHD simulations of MAD. These results indicate that all the quasars and a fraction of HERGs (at least for z<0.3) in 3CRR catalog should contain a MAD.




§ ACKNOWLEDGEMENTS

We thank the reviewer for very valuable and detailed comments, which have greatly improved the quality of this manuscript. This work is supported by the NSFC (grants 12273089, 12073023, 12233007, 12361131579, 12347103), the science research grants from the China Manned Space Project with No. CMSCSST-2021-A06, and the Fundamental Research Fund for Chinese Central Universities. This work has made extensive use of the NASA/IPAC Extragalactic Database (NED) and the 3CRR catalog <cit.>. NED is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). This research has also made extensive use of data obtained from the Chandra Data Archive and the observations made with the NASA/ESA Hubble Space Telescope, obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESAC/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA).


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