The HI reservoir in central spiral galaxies and the implied star formation process
Jing Dou Yingjie Peng Qiusheng Gu Alvio Renzini Luis C. Ho Filippo Mannucci Emanuele Daddi Chengpeng Zhang Jiaxuan Li Yong Shi Tao Wang Dingyi Zhao Cheqiu Lyu Di Li Feng Yuan Roberto Maiolino Yulong Gao






Jing Dou, Yingjie Peng, Qiusheng Gu
doujing@nju.edu.cn, yjpeng@pku.edu.cn, qsgu@nju.edu.cn


0000-0002-6961-6378]Jing Dou*
School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China


Department of Astronomy, School of Physics, Peking University, 5 Yiheyuan Road, Beijing 100871, China
Kavli Institute for Astronomy and Astrophysics, Peking University, 5 Yiheyuan Road, Beijing 100871, China


0000-0002-3890-3729]Qiusheng Gu*
School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China


0000-0002-7093-7355]Alvio Renzini
INAF - Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, I-35122 Padova, Italy


0000-0001-6947-5846]Luis C. Ho
Kavli Institute for Astronomy and Astrophysics, Peking University, 5 Yiheyuan Road, Beijing 100871, China
Department of Astronomy, School of Physics, Peking University, 5 Yiheyuan Road, Beijing 100871, China


0000-0002-4803-2381]Filippo Mannucci
Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy


0000-0002-3331-9590]Emanuele Daddi
AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France


0000-0001-6469-1582]Chengpeng Zhang
George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA
Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA


0000-0001-9592-4190]Jiaxuan Li
Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton, NJ 08544, USA


0000-0002-8614-6275]Yong Shi
School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China


0000-0002-2504-2421]Tao Wang
School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China



Department of Astronomy, School of Physics, Peking University, 5 Yiheyuan Road, Beijing 100871, China
Kavli Institute for Astronomy and Astrophysics, Peking University, 5 Yiheyuan Road, Beijing 100871, China


0009-0000-7307-6362]Cheqiu Lyu
Department of Astronomy, School of Physics, Peking University, 5 Yiheyuan Road, Beijing 100871, China
Kavli Institute for Astronomy and Astrophysics, Peking University, 5 Yiheyuan Road, Beijing 100871, China


0000-0003-3010-7661]Di Li
CAS Key Laboratory of FAST, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China


0000-0003-3564-6437]Feng Yuan
Center for Astronomy and Astrophysics and Department of Physics, Fudan University, Shanghai 200438, People’s Republic of China


0000-0002-4985-3819]Roberto Maiolino
Cavendish Laboratory, University of Cambridge, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, UK
Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK


0000-0002-5973-694X]Yulong Gao
School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China







§ ABSTRACT 


The cold interstellar medium (ISM) as the raw material for star formation is critical to understanding galaxy evolution. It is generally understood that galaxies stop making stars when, in one way or another, they run out of gas. However, here we provide evidence that central spiral galaxies remain rich in atomic gas even if their star formation rate and molecular gas fraction have dropped significantly compared to “normal" star-forming galaxies of the same mass. Since  is sensitive to external processes, here we investigate central spiral galaxies using a combined sample from SDSS, ALFALFA, and xGASS surveys. After proper incompleteness corrections, we find that the key  scaling relations for central spirals show significant but regular systematic dependence on stellar mass. At any given stellar mass, the  gas mass fraction is about constant with changing specific star formation rate (sSFR), which suggests that  reservoir is ubiquitous in central spirals with any star formation status down to M_* ∼ 10^9. Together with the tight correlation between the molecular gas mass fraction and sSFR for galaxies across a wide range of different properties, it suggests that the decline of SFR of all central spirals in the local universe is due to the halt of  supply, though there is plenty of  gas around. These hence provide critical observations of the dramatically different behavior of the cold multi-phase ISM, and a key to understand the star formation process and quenching mechanism.


















§ INTRODUCTION
  

The cold interstellar medium (ISM) plays a vital role in driving galaxy formation and evolution. As galaxies evolve, ISM is replenished by gas cooling and accretion from the circumgalactic medium; consumed by star formation; and enriched by stellar winds and feedback <cit.>. The global star formation rates (SFRs) of galaxies are determined by their cold gas content (M_ gas) and star formation efficiency (SFE, defined as SFR/M_ gas) or the depletion timescale (the inverse of SFE, defined as M_ gas/SFR). The SFE is a key galaxy parameter that reflects the efficiency with which a galaxy can convert cold gas into stars. Furthermore, SFE is closely tied to a galaxy’s dynamical time, which represents the time it takes for some fraction of gas to be transformed into stars per galactic orbital time, influenced by the gravitational instability of the cold gas in the galactic disk. This fraction is dependent on the detailed feedback physics <cit.>.

Observation evidence strongly supports the well-established Kennicutt-Schmidt (KS) type star formation law, asserting a tight correlation between star formation rate (SFR) and total gas content, including atomic and molecular gas <cit.>. This relationship is more pronounced with molecular gas, especially dense molecular gas <cit.>, as stars are commonly believed to originate from cold, dense molecular clouds. Numerous studies have corroborated the molecular gas KS law on both global and spatially resolved scales <cit.>, leading to the proposal of additional scaling relations for molecular gas. These include the SFE of molecular gas (SFE_ H_2 = SFR/M_ H_2) and the molecular gas mass fraction (μ_ H_2 = M_ H_2/M_*), both have been found to tightly depend on the specific star formation rate (sSFR = SFR/M_*) <cit.>, for both AGNs and non-AGNs <cit.>. The molecular gas mass has also been shown to correlate with stellar mass, a relationship often referred to as the molecular gas main sequence <cit.>. Although the underlying physical mechanisms of these scaling relations remain debated and somewhat elusive, they are extensively utilized to estimate cold gas masses and to put constraints in theoretical models and simulations.

In <cit.>, utilizing the xCOLD GASS survey <cit.>, we proposed the Fundamental Formation Relation (FFR), a tight relation between sSFR, SFE_ H_2, and μ_ H_2. Other scaling relations, including the integrated KS law, star-forming main sequence (SFMS), and the molecular gas main sequence can all be derived from this fundamental cube. The molecular gas FFR demonstrates that star formation levels in galaxies are determined by the combined effects of galactic dynamical timescales (related to the gas depletion timescale, 1/SFE) and gas instability (associated with μ_ H_2). The molecular gas FFR governs the star formation and quenching processes with small scatters. Galaxies with different stellar masses, sizes, structures, metallicities, and in different environments all evolve on the same single scaling relation of μ_ H_2-SFE_ H_2-sSFR. These unique features and simplicities make the molecular FFR an ideal framework to study galaxy formation and evolution, for instance, to accurately derive the  gas cycles in galaxy populations with different stellar masses, from star-forming galaxies to the galaxies in the process of being quenched <cit.>.

Another critical component of the ISM in galaxies is atomic gas ().  generally distributes more extended and loosely bounded comparing to , and reacts sensitively to external environmental influences like ram pressure stripping and galaxy interactions <cit.>. Using xGASS survey <cit.>, <cit.> explored whether  follows a similar FFR as , and found that
the relation between SFE_ HI (defined as SFR/M_ HI) and sSFR for all galaxies shows significant scatter and strong systematic dependence on the key galaxy properties that have been investigated, revealing that  does not follow a similar FFR as . The dramatic difference between  and  indicates that different physical processes, such as environmental effects, notably impact the  gas, while  relations remain insusceptible.

Given that  serves as the precursor for , it play a critical role in star formation. To accurately assess the intrinsic properties of  and its actual role in star formation, we must exclude any external environmental factors to which  is particularly sensitive. Central galaxies are the most massive galaxies within a dark matter halo and usually locate at the center of a galaxy cluster or group. They are typically distinguished from satellite galaxies, which orbit around the central galaxy. Since external environmental effect mainly operates on satellite galaxies <cit.>, in this work, only central galaxies are selected to minimize the environmental effects, which allows us to focus on star formation and quenching processes due to internal mechanisms. 

Different galaxy types can follow very different evolutionary paths. We only focus on spiral galaxies for the following reasons. Firstly, many ellipticals nowadays are already quenched at higher redshift <cit.>. Including them can introduce severe progenitor bias. Secondly, ellipticals in the local universe are mostly transformed from the spiral galaxies via mergers rather than internal secular evolution <cit.>. Internal quenching mechanisms, such as AGN feedback alone, cannot directly transform spirals to ellipticals. And also, the formation mechanisms for irregulars and S0 galaxies are still not fully understood and may involve recent mergers or strong interactions as well <cit.>.

Central spiral galaxies are ideal candidates for studying the overall properties and behavior of  gas and star formation, significantly contributing to our understanding of galaxy formation and evolution. In combination with the molecular FFR, we aim to provide a comprehensive understanding of the cold multi-phase ISM, star formation process and (internally-driven) quenching mechanisms in local galaxies. Throughout this work, we adopt the cosmological parameters: Ω_m=0.3,  Ω_Λ=0.7,  H_0=70 km s^-1 Mpc^-1. 













§ SAMPLE
 







 §.§ The ALFALFA-SDSS matched sample
 

The main  sample used in this work is Arecibo Legacy Fast ALFA (ALFALFA) survey <cit.>, which is a blind -selected survey out to z ∼ 0.06. The survey utilized the seven-horn Arecibo L-band Feed Array (ALFA) to map ∼ 7000 deg^2 of the high Galactic latitude sky in drift-scan mode <cit.>. Conducted between 2005 and 2011, ALFALFA covered a frequency range from 1335 to 1435 MHz, corresponding to heliocentric velocities from -2000 km/s to 18000 km/s, and detected ∼31,500 extragalactic  21cm line sources. 


The ALFALFA survey contains sources of quality code 1 and quality code 2. Code 1 refers to the  sources with the highest quality, evaluated using several criteria: (1) a good signal consistence between the two independent polarizations observed by ALFALFA, (2) a spatial extent consistent with or larger than the telescope beam, (3) the spectral profile is free from radio-frequency interference (RFI), (4) an approximate minimum signal-to-noise ratio (S/N) threshold of 6.5. Code 2 refers to the sources with low S/N (≲ 6.5) but have been matched with optical counterparts with known optical redshifts coincident with those measured in . They are also included in the ALFALFA catalog as they are highly likely to be real. Both Code 1 and Code 2 sources are considered  detections in our analysis.


The parent SDSS Data Release 7 (DR7) <cit.> sample was retrieved from the SDSS CasJobs site, covering ∼9,500 deg^2 of the sky. The SDSS spectroscopic survey covers a wavelength range of 3,800 to 9,200Å, utilizing fibers with a diameter of 3 arcseconds on the sky. Following the criteria by <cit.>, galaxies with clean photometry and Petrosian r magnitudes in the range of 10.0 - 18.0 after correction for Milky-Way galactic extinction are selected. The bright limit of 10 magnitudes is set to exclude extremely bright, large nearby galaxies, while the faint limit of 18 magnitudes ensures the completeness of the SDSS Spectroscopic Survey. After removing duplicates, the parent photometric sample contains 1,579,314 objects, of which 72,697 have reliable spectroscopic redshift measurements in the redshift range 0.02 < z < 0.05. This narrow and low redshift range is used to match the depth of the ALFALFA survey. The physical scales within this redshift range vary from 1.2kpc to 2.9kpc.



There are 43,448 SDSS galaxies with reliable spectroscopic redshift measurements in the SDSS and ALFALFA overlapped region within the redshift range of z = 0.02 - 0.05. The ALFALFA  detections are then cross-matched with the parent SDSS sample in this narrow redshift range. Briefly, the spatial separation between the most probable optical counterpart of each  detection and SDSS galaxy is less than 5”. Also, the velocity difference between the  source and SDSS galaxy is less than 300 km/s. For most galaxies, the line-of-sight velocity difference is generally less than 100 km/s, and using 300 km/s can encompass more than 99% of galaxies. Slightly adjusting the matching conditions will not significantly affect the matched sample. It should be noted that the angular resolution is ∼ 3.5 arcmin in ALFALFA. Close companions may contaminate the measured  spectra within the large Arecibo beam. We hence exclude galaxies that have multiple SDSS counterparts within the ALFALFA beam size (∼ 3.5 arcmin) and within a velocity difference of three times the  line width (W_50), where W_50 is defined as the difference between the velocities corresponding to the fitted polynomial at a level of 50% of the maximum value of the flux on each horn. The threshold of three times the W_50 is an empirically standard that has been found effective and employed in many studies because it balances the need for accurate matches without missing potentially relevant sources <cit.>. Also, galaxies that are in dense regions or have close companions are more vulnerable to environmental effect. Since our goal of this work is to investigate in-situ star formation process and mass-quenching (i.e. the internal quenching) mechanism, we try to exclude any environmental effect. About 12% of ALFALFA galaxies were excluded to avoid contaminations from the interlopers. This subset of  detections with clean optical counterparts is referred to as the ALFALFA-SDSS matched sample, consisting 9571 galaxies. 

The aperture is also an important issue. The  spatial scale is, on average, much larger than the optical and  scales. Before the Square Kilometre Array <cit.>, it is difficult to have a large sample with deep and resolved  measurements. Nevertheless, with the well-established  mass-size relation based on resolved deeper  observation of nearby spiral galaxies <cit.>, we can roughly estimate the  spatial scales of our galaxies. The massive star-forming galaxies (which are also about the most -rich galaxies, in terms of the absolute  gas mass) on average have a  gas mass of ∼ 10^10, which corresponds to a  diameter of about 50 kpc. The ∼ 3.5 arcmin’s beam of the Arecibo telescope corresponds to an angular size of approximately 85 kpc at a redshift of z = 0.02 and 200 kpc at a redshift of z = 0.05, which are larger than the  diameter. Hence, this should not cause a significant bias. The most relevant bias might be the interlopers into the large beam, as discussed above.









 §.§ Incompleteness corrections
 


As detailed in Appendix <ref> and illustrated in Figure <ref>, both SDSS and ALFALFA are flux-limited samples, resulting in significant selection biases in both stellar mass and  gas mass, even within the narrow redshift range of z = 0.02 - 0.05. Therefore, when conducting statistical studies using the ALFALFA-SDSS matched sample, it is essential to apply a joint incompleteness correction to account for these biases.

Following the method introduced in <cit.>, we have used a joint V_ max correction to account for the volume incompleteness within the given redshift range. For the ALFALFA-SDSS matched sample, we calculated for each individual galaxy the maximum redshift to which the galaxy can still be observed according to the ALFALFA and SDSS detection limits. This maximum redshift was then used to calculate the maximum observable comoving volume (V_ max) for each galaxy. By assuming that the spatial distribution of our sample is homogeneous and there is no evolution in the comoving volume (within a narrow redshift range), we weight each galaxy using the value of V_ total/V_ max to account for the galaxies missed in the surveys, where V_ total is the total comoving volume that our sample spans. The corrections of the SDSS and ALFALFA sample are performed independently and they are combined together to correct the ALFALFA-SDSS matched sample, i.e., we have simultaneously corrected the strong sample selection effects shown in both panels in Figure <ref>.


One of the advantages of this method is that the weighting factor has been calculated for each individual galaxy in our sample. This allows us to perform statistical analysis conveniently for a subsample, e.g., central spirals, ellipticals and uncertains. As we discussed and emphasized in Figure <ref> and Appendix <ref>, galaxies with different visual morphology (i.e., spiral, uncertain and elliptical) have intrinsically distinct  properties, and should be treated and studied separately, for instance, in a stacking analysis. 








 §.§ XGASS


To test our incompleteness correction on the large but shallow ALFALFA-SDSS sample and verify the results, we have included in our analysis the  observations from a much deeper  target survey, the extended GALEX Arecibo SDSS Survey <cit.>. It provides the  gas measurements for 1179 galaxies in the nearby universe. These galaxies are selected only by redshift (0.01 < z < 0.05) and stellar mass (10^9< M_* <10^11.5) from the overlapped area of the SDSS DR7 spectroscopic survey, the GALEX Medium Imaging Survey <cit.> and projected ALFALFA footprints <cit.>. Those galaxies with reliable  detections already available from the 40% ALFALFA catalog or the Cornell  digital archive <cit.> were not reobserved in xGASS to optimize the efficiency. The rest galaxies were observed with the Arecibo telescope until the  line was detected, or a limit of a few percent in M_ HI/M_* was reached. This limit of M_ HI/M_* is 2% for galaxies with log M_*/ > 9.7, and a constant gas mass limit of log M_ HI/= 8 for galaxies with lower stellar masses. Each galaxy is weighted by a correction factor to account for selection effects in stellar mass, described in <cit.>. 

 






 §.§ The selection of central spiral galaxies
 


It is well known that  is sensitive to external environmental effects <cit.>. Therefore, if we want to focus on the star formation and quenching processes due to internal mechanisms, only central galaxies are selected to minimize the environmental effects that are strongly operating on satellites <cit.>.

The galaxies are classified into central and satellite galaxies using the SDSS DR7 group catalogue from <cit.>. The central galaxies are defined as the most massive and most luminous ones in the r-band within a given group. “Centrals with satellites" and “isolated centrals/singletons" are both included as “centrals" in our analysis. Among the 4470 central spiral  detections in ALFALFA, 87% of them are singletons in <cit.> group catalog, i.e., groups with the richness N = 1. The remaining 13% are centrals with N > 1 (i.e., with at least one satellite). This is expected since the majority of low-mass centrals (much more abundant than the massive ones) are singletons just above the detection limit, and their fainter satellites are not observed for a flux-limited survey. We have also checked the  detection fraction and  scaling relations for “Centrals with satellites" and “isolated centrals/singletons". The results show little difference for these two cases and our conclusions remain robust. 


As mentioned in the introduction, our aim is to better understand the processes of in-situ star formation and internal-origin quenching. Environmental effects can strongly impact  gas, hence our analysis focuses exclusively on central spiral galaxies. In practice, spiral galaxies can be classified based on various criteria, such as visual morphology, structural parameters, or kinematics. Each classification method results in significantly different samples, as illustrated in Appendix <ref> and Figure <ref>. Visually-classified “spiral/disk" is the most effective parameter to distinguish -rich galaxies and -poor galaxies. This is because  gas disk (extending to much outer regions than the stellar disk) is most sensitive to external interaction or perturbation, and then followed by the visual morphology of the disk, and the least sensitive parameters are the structural parameters (such as bulge-to-total ratio (B/T), concentration index (R_90/R_50) and Sérsic index. Hence, we focus only on central galaxies that are visually defined as spiral galaxies. 

Galaxies are classified into different morphologies using data from the Galaxy Zoo (GZ) project <cit.>. In this project, hundreds of thousands of volunteers are assisted to view each SDSS image and classify the galaxy morphology. A clean sample has been defined by requiring at least 80 % of the corrected vote to be in a particular category. A morphology flag (“spiral", “elliptical" or “uncertain") is assigned to each galaxy after performing a careful debiasing process. The contamination of lenticular or S0s into the GZ clean spiral sample is small, about 3% <cit.>. Most S0 galaxies with smooth and rounded profiles are classified in GZ as “elliptical” or “uncertain”. It should be noted that in GZ, “spiral" includes disky galaxies with spiral arms and also those without clear spiral arms. In this work, we categorize them both as “spirals". 

Since galaxy mergers can have a complicated effect on the star formation of galaxies by enhancing or suppressing star formation, depending on the gas content of the merging galaxies and also the phase of the merger, we exclude the merger systems in our sample if the vote fractions of a merger are greater than 30%. As we will show later in Figure <ref> and <ref>, central spiral galaxies defined by visual morphology classified by the GZ project achieve a very high  detection fraction, which is essential for obtaining unbiased intrinsic  scaling relations. In contrast, central spiral galaxies defined by structural parameters show a significantly lower average  detection fraction.










 §.§ Stellar mass and SFR measurements
 


The stellar masses (M_*) of the galaxies are estimated from the k-correction program <cit.> with <cit.> stellar population synthesis model and a <cit.> initial mass function (IMF), which show a small scatter of ∼ 0.1 dex compared with the published stellar masses of <cit.>. 

The star formation rates (SFRs) are taken from the value-added MPA-JHU catalog <cit.>, which are based on the  emission line luminosities. These luminosities are corrected for extinction using the Hα/Hβ ratio. To correct for the aperture effects, the SFRs outside the SDSS 3” fiber were obtained by performing the spectral energy distribution fitting to the ugriz photometry outside the fiber, using the models and methods described in <cit.>. The  emission for AGN and composite galaxies can be contaminated by central nuclear activities. Their SFRs are derived based on the strength of 4000 break, calibrated with Hα for non-AGN, pure star-forming galaxies <cit.>. These SFRs are computed for a Kroupa IMF and we convert them to a Chabrier IMF using log SFR (Chabrier) = log SFR (Kroupa) - 0.04. Different SFR estimators may produce different results. The results using different SFR estimators are shown and discussed in the Appendix <ref>.















§ RESULTS







 §.§ HI detection fraction














ALFALFA is a blind, relatively shallow, flux-limited  survey over a significant volume. As discussed in Section <ref> and shown in Figure <ref>, even within the narrow redshift range of z = 0.02 - 0.05, both ALFALFA and SDSS are highly biased samples, with strong selections in  gas mass,  line width and redshift for ALFALFA, and in stellar mass, color and redshift for SDSS. Hence, when combining ALFALFA and SDSS (i.e., the ALFALFA-SDSS matched sample), a joint incompleteness correction is necessary, as discussed in Section <ref>. The corrected ALFALFA-SDSS matched sample contains 9571 reliable  detections, and 4470 of them are central spirals classified by visual morphology.


In Figure <ref>, we show the  detection fraction (DF) on the SFR-M_* plane for different samples with or without the incompleteness correction. The  DF is defined as the ratio between the number of galaxies with  detections and the number of all galaxies in the parent SDSS sample, obtained by using a moving box of size 0.5 dex in SFR and 0.5 dex in M_*. 


The upper left panel of Figure <ref> shows the raw  DF for all galaxies in the ALFALFA-SDSS matched sample without the incompleteness correction. The overall  DF is evidently low, even for galaxies on the SFMS. The lower left panel shows the raw  DF for central spirals (defined by the visual morphology as in the Galaxy Zoo project; see Section <ref> for details). Compared to all galaxies, the DF increases significantly, particularly for those with low SFRs.

The middle panels are similar to the left panels but have done incompleteness corrections. In both panels, the corrected DFs are significantly elevated compared to the raw DFs shown in the left two panels. For the case of all galaxies (upper middle panel), the corrected average  DF for galaxies on and above the SFMS (above the lower dotted lines) is significantly higher than that below the SFMS (below the lower dotted lines), indicating that quenching or quenched galaxies are indeed cold gas-poor, on average. Remarkably, in the case of central spiral galaxies (lower middle panel), the corrected  DF is further enhanced. Although it should be noted that below the SFMS, the DF is slightly lower in both ALFALFA and xGASS samples. The average  DF for central spiral galaxies, including low-mass galaxies with M_* > 10^9 and galaxies below the SFMS, is ∼ 95%, i.e., there is a ubiquitous  reservoir in the vast majority of central spirals. 

To test our incompleteness correction to the ALFALFA-SDSS sample and the robustness of our results, we show the results obtained from a much deeper  target survey xGASS in the right two panels. There are 662 reliable  detections (i.e., the  line is detected and not confused by close companions) in the xGASS sample, and 273 of them are central spirals (classified by visual morphology). The  DFs for all galaxies and central spiral galaxies in the xGASS sample (right two panels) look distinct from the left two panels (which have not done incompleteness corrections) but similar to the middle two panels (which have done proper incompleteness corrections). In particular, the xGASS central spirals consistently show a nearly 100%  DF across a wide range of stellar mass and SFR. The overall raw  DF is ∼ 96%, and ∼ 98% with the statistical weights given by <cit.>, and hence strongly supports the ubiquitous  gas content in central spiral galaxies. There are some “green holes” representing a lower DF in both the ALFALFA central spirals and xGASS central spirals panels. They do not seem to follow a systematic trend, and they do not occupy a similar region on the SFR-M_* plane. These could be caused by small number statistics (for the small but deep xGASS) or imperfect incompleteness corrections (for the large but shallow ALFALFA). Future larger and deeper surveys will verify these results. 


As shown in Figure <ref>, at a given stellar mass, a significant amount of visually-defined central “spirals" have large values of R_90/R_50, B/T and Sérsic index, and will be classified as “elliptical" if the definition is in accordance with their structural parameters. As shown in <cit.>, these central spirals with a massive bulge have lower sSFR, but are -rich. On the other hand, as shown in Figure <ref>,  many visually-defined “uncertain" galaxies have small values of R_90/R_50, B/T and Sérsic index, and will be classified as “spiral" according to their structural parameters. These “uncertain" galaxies, on average, are -poor as shown in the lower left panel in Figure <ref>, in particular for those below the SFMS, which are almost all  non-detections. Therefore, using “spiral" defined by quantitative structural parameters produces a lower  DF towards low sSFR (by including many -poor “uncertain"). In the upper panels of Figure <ref>, we show that for central galaxies with B/T < 0.3 and B/T < 0.5, the  DFs drop significantly towards low sSFR in both cases, consistent with the results of <cit.>; and also the overall  DF is ∼ 64% for both B/T cuts, much lower than that of the central spirals defined by visual morphology (∼ 95%). 


To complete, we also show the  DFs for the central “elliptical" galaxies defined from the Galaxy Zoo project in the lower right panel in Figure <ref>. The overall  DF is only ∼ 13.4%, consistent with the fact that ellipticals, on average, are cold gas-poor systems. These results show that galaxies with different visual morphology (i.e., spiral, uncertain and elliptical) have intrinsically distinct  properties, and should be treated and studies separately, for instance, in stacking analysis. 








 §.§ HI scaling relations








The high overall  DF of ∼ 95% for the central spiral galaxies makes it possible to derive the unbiased  scaling relations for this particular population. The left panels of Figure <ref> show the distributions of the central spirals in the ALFALFA-SDSS matched sample on the SFE_ HI-sSFR plane (upper left panel, where  star formation efficiency SFE_ HI = SFR/M_ HI) and μ_ HI-sSFR plane (lower left panel, where  gas fraction μ_ HI = M_ HI / M_*). The SFE_ HI is the inverse of the  gas depletion timescale, describing how efficiently the galaxy can convert the available cold  gas into stars, or how long the  gas reservoir would be depleted by current star formation activities. Although SFR and M_ HI happen at very different spatial scales, SFE_ HI can be interpreted as the product of the star formation efficiency of  and the molecular-to-atomic gas mass ratio M_ H_2/M_ HI (SFE_ HI = SFE_ H_2× M_ H_2/M_ HI). The size of each dot represents the weight used for incompleteness correction. The weighting factor for most galaxies ranges from 1 to 10, with the median value is about 1.34 and the mean value is about 2.73, while the maximum value is around 42. Different studies may use different sSFR cuts to define star-forming, green valley, and passive galaxies. Typically, star-forming galaxies are defined as log sSFR (Gyr^-1) > - 1.5, fully quenched galaxies are defined as log sSFR (Gyr^-1) < -2.5, with green valley galaxies occupying the range in between. It is evident that even for star-forming galaxies with high sSFR, many of them have a large dot size, i.e., a large weighting factor, suggesting that the sample there is highly incomplete. Therefore, the incompleteness correction is necessary for both star-forming and passive galaxies. On average, both SFE_ HI and μ_ HI increase with increasing sSFR, but with significant scatters. 

The thick grey line in each panel in Figure <ref> shows the fundamental formation relation (FFR) for  as found in <cit.>. As discussed in <cit.>, for , both SFE_ H_2-sSFR relation and μ_ H_2-sSFR relation are very tight, independent of other key galaxy parameters, and their scatters can be entirely explained by measurement errors. However, the  relations for all galaxies does not follow a similar tight FFR as  <cit.>. Here we further show that even for the central spiral galaxies, their  relations still exhibit significant scatters as shown in Figure <ref>. It is well known that SFR does not correlate well with  content while it does so with <cit.>. In a sense, here we demonstrate that this lack of correlation is due to central spirals, which have  even when their SFR is low.


The middle panels in Figure <ref> use the common 1-dimensional analysis to show the median SFE_ HI and μ_ HI as a function of sSFR for different stellar mass bins, calculated with a sliding window of 0.5 dex in sSFR, which is chosen to match the typical observational uncertainty in measuring sSFR and also to include a sufficient number of data points, ensuring statistical robustness. Error bars on each line indicate the 5% and 95% percentiles of the distribution. The right panels use the 2-dimensional analysis to show the average M_* on the SFE_ HI-sSFR plane and μ_ HI-sSFR plane, calculated with a moving box of 0.5 dex in sSFR, SFE_ HI and μ_ HI, and the contour lines mark the equal stellar mass distribution. The overall trends shown in the corresponding panels are similar, but with notable differences in the low stellar mass regions. As discussed in detail in Figure <ref>, the widely used 1-dimensional analysis (which considers only the variation of y at a fixed x) can be heavily affected by the shape of the sample distribution, in particular for the low stellar mass bin; while the 2-dimensional analysis (which takes the variation of both the x- and y-axes into account) is more robust. Therefore, the results shown in the right panels in Figure <ref> are more objective and less biased representations of the true underlying trends.

The contour lines in the upper right panel in Figure <ref> are almost all parallel to the constant μ_ HI, which is consistent with those shown in Figure <ref>, where the distribution of the galaxies (indicated by the ridge of the contour lines) is around the constant μ_ HI and the slope of the distribution (indicated by the red line) is about unity at a given stellar mass. Consistent results are also shown in the lower right panel of Figure <ref>, where the contour lines are about horizontal. It is expected, since by definition, sSFR = μ_ HI× SFE_ HI; hence the μ_ HI-sSFR relation is closely related to the SFE_ HI-sSFR relation. Both panels indicate that for central spirals, at a given stellar mass, star-forming galaxies, green valley galaxies and passive galaxies all host a similar amount of  gas. The  gas fraction primarily depends on stellar mass and weakly depends on sSFR. We also investigate the SFE_ HI-sSFR and the μ_ HI-sSFR relation for central spirals in the xGASS sample, which exhibit consistent general trends but with considerable scatter compared to ALFALFA due to their much smaller sample size. 

We also tested the SFE_ HI-sSFR and the μ_ HI-sSFR relation for central spirals defined by other spiral definitions, such as concentration, B/T, sersic index and probability of a galaxy to be late-type disk galaxy with T-type > 0 as shown in Figure <ref> in the Appendix <ref>. Interestingly, these different definitions do not significantly affect these scaling relations. This is because ALFALFA is a relatively shallow survey and these relations are derived using only galaxies with  detections. However, as demonstrated in Figure <ref> and <ref>, different definitions of spiral galaxies strongly affect the detection fraction of ALFALFA-SDSS sample. Central spiral galaxies, defined by visual morphology classified by Galaxy Zoo project, achieve a very high  detection fraction, which is essential for obtaining unbiased intrinsic  scaling relations. Other definitions result in lower detection fractions. 

As mentioned before, there is a single tight  FFR for all galaxies (grey thick line), while both the SFE_ HI-sSFR and μ_ HI-sSFR relation are systematically dependent on stellar mass for central spiral galaxies, but both relations show a similar slope for different stellar mass bins (i.e., the contour lines in the right two panels of Figure <ref> are nicely parallel to each other). As above, the two relations are closely related. It is important to notice that the  FFR has a non-zero slope (∼ 0.5), while the slope of the SFE_ HI-sSFR relation is about unity and that of the μ_ HI-sSFR relation is about zero for all stellar masses. This indicates that for central spirals, at any stellar mass, when sSFR decreases, both  gas mass and SFE_ H_2 decrease.  gas fraction remains almost constant and SFE_ HI decreases. The M_ H_2/M_ HI ratio also decreases. Previous studies found that there do exist some -rich galaxies with low SFRs <cit.>. Here we show that for a significant population of central spirals,  reservoir is ubiquitous, down to M_* ∼ 10^9.  












§ SUMMARY AND DISCUSSION


Since  gas usually extends much further than stars, external environmental effects such as interactions and mergers can strongly impact the  gas. To better understand the processes of in-situ star formation and internal-origin quenching, this study aims to focus exclusively on central galaxies to minimize the strong environmental effects that can significantly influence satellite galaxies. Additionally, a galaxy's visual morphology is more sensitive to external interactions or mergers than structural parameters like the bulge-to-total ratio (B/T), concentration index (R_90/R_50), and Sersic index. Therefore, in this work, we focus only on central galaxies those are visually defined as spiral galaxies.


Because both SDSS and ALFALFA are flux-limited surveys, they exhibit strong selection biases in stellar mass and   gas mass, respectively. Consequently, a joint incompleteness correction is necessary for the SDSS-ALFALFA matched sample. After performing proper incompleteness correction, the average  detection fraction in the ALFALFA-SDSS matched sample is significantly increased. For the central spiral galaxies (defined by visual morphology), the  detection fraction is, on average, larger than 90%, even for many low-mass and low-SFR systems. These are in good consistency with the results from the deeper xGASS survey, hence supporting our incompleteness correction method. It is important to note that if the “spiral/disk” are defined by their structural parameters (e.g., bulge-to-total ratio, B/T < 0.3), the average  detection fraction (∼ 64%) is significantly lower than that of spiral galaxies defined by visual morphology, especially for galaxies below the SFMS. This is likely because the structure of a galaxy is generally expected to be less sensitive to external environmental effects compared to its visual morphology, which more readily reveals features such as tidal disturbances, mergers, and asymmetries.

The high overall  detection fraction for the central spiral galaxies (defined by visual morphology) allows for the derivation of the unbiased  scaling relations for this particular population. We find that the SFE_ HI-sSFR and μ_ HI-sSFR scaling relations for central spirals show strong systematic dependence on stellar mass. At any given stellar mass, the  gas mass fraction remains roughly constant with varying sSFR, suggesting that  reservoir is present in central spirals regardless of their star formation status, down to M_* ∼ 10^9. 
Along with the tight correlation between the molecular gas mass fraction and sSFR for galaxies across a wide range of different properties, these results indicate that a cessation of  supply drives the decline of SFR of central spirals in the local universe, despite the abundance of  gas. Our findings hence provide key observational evidence of the dramatically different behavior of their multi-phase ISM. 

In regular undisturbed spiral galaxies, the atomic gas usually distributes towards a larger radius than the stellar and molecular gas disk <cit.>. Gas inflow carrying excess angular momentum can accumulate in a stable outer  ring, persisting over extended periods in the absence of perturbations <cit.>. This would deplete the material available in the inner disk for new star formation, providing a straightforward explanation for our observations, a phenomenon also supported by simulations <cit.>.

Moreover, the surface density of gas at larger radii is often below the critical threshold needed to convert  into , necessary for initiating star formation <cit.>. Coupled with the tight correlation between molecular gas mass fraction and sSFR across diverse galaxy types, our results indicate that the reduction in SFR in central spirals predominantly results from a cessation in  supply and a concomitant decline in  star formation efficiency, despite there is plenty of  gas around. 

Alternatively, the disruption in  supply could result from feedback mechanisms. In this scenario, our findings indicate that such feedback should have minimal impact on the  located in the outer disk regions, thereby imposing significant constraints on the strength and nature of feedback in theoretical models <cit.>.

Future high spatial resolution 21 cm observations (e.g., the SKA) for a sample of central spiral galaxies with different star formation levels and feedback status will be necessary to obtain their resolved  gas properties, including  surface density, kinematics, and disk instability. Such future 21 cm observations will help determine whether  in quenched central spirals is confined beyond the optical disk, as proposed in the scenario by <cit.>, or whether the  lies within the disk itself but does not convert to  for some reason. These observations will be crucial in testing these hypotheses and advancing our knowledge of the complex interplay between gas dynamics, star formation, and feedback processes in galaxies. Dark matter halo may also play an important role in regulating gas cycling and star formation, and will be explored in our following work.  

















§ ACKNOWLEDGMENTS


This work is supported by the National Natural Science Foundation of China (No. 12303010, 12125301, 12192220, 12192222, 12121003, 12192223), and the science research grants from the China Manned Space Project with No. CMS-CSST-2021-A07.
















§ SELECTION BIASES IN SDSS AND ALFALFA SAMPLES
 







Due to the SDSS spectroscopic selection of r < 17.77, the sample is flux-limited. As shown in the left panel of Figure <ref>, even within the narrow redshift range of 0.02 <z< 0.05, this selection produces a strong bias towards massive and star-forming galaxies, and faint sources are progressively missed at higher redshifts. 

Similar to SDSS, ALFALFA is also a flux-limited sample and the effective integration time is typically 48 seconds for each source, leading to a strong selection in  gas mass. As shown in <cit.>, the completeness limits for Code I and Code II sources in ALFALFA are both functions of W_50, with a break at W_50 = 300km/s. At the same integrated line flux, ALFALFA sources with narrower  profiles (i.e., smaller W_50) host larger S/N, hence are easier to be detected than broader ones. The selection effects of ALFALFA within the narrow redshift range of 0.02 <z< 0.05 are clearly shown in the right panel of Figure <ref>. At a given (low)  gas mass, the number of  non-detections increases significantly with both redshift and W_50 due to sample incompleteness, which must be properly accounted for in any statistical analysis. 











§ COMPARISON BETWEEN DIFFERENT CLASSIFICATIONS OF SPIRAL GALAXIES
 






Spiral galaxies can be defined by their visual morphology, structure or kinematics. To demonstrate the impact of different methods to define “spiral" galaxies, in Figure <ref>, we show the distribution function of concentration index R_90/R_50 (upper left panel), bulge-to-total ratios B/T (upper right panel), and Sérsic index (lower left panel) for central galaxies in a narrow stellar mass range of 10^10 - 10^10.3 in the SDSS parent sample within the redshift range 0.02 < z < 0.05. We retrieved the r band Sérsic index, Petrosian half-light radii R_50 and R_90 from the New York University Value-Added Catalog <cit.>. The mass-weighted bulge-to-total ratios (B/T) are taken from <cit.> and <cit.>, with a fitting model using a pure exponential disk and a de Vaucouleurs bulge. Galaxies are split into “spirals" (blue histograms, 3166 galaxies), “ellipticals" (red histograms, 537 galaxies) and “uncertains" (grey histograms, 2918 galaxies) as classified by Galaxy Zoo (visual classifications). Figure <ref> clearly shows that morphology is not a one-to-one correspondence with structure. Visually-defined spirals/ellipticals/uncertains span a wide range of R_90/R_50, B/T, and Sérsic index. The results for other stellar mass bins also show similar results that at a given structural parameter, there are significant overlaps between the three populations. Hence, different definitions (i.e., defined by visual morphology or structural parameters) can produce significantly different galaxy samples.


It should be noted that the machine learning (ML) method trained on visually classified morphology (e.g., Galaxy Zoo) has also been used widely to classify galaxies. For instance, using an ML-based morphology catalog from <cit.>, disk galaxies can be selected with T-type > 0 and P_ disk > 0.5, where T-type describes the galaxy morphology type and galaxies with T-type > 0 correspond to late-type morphologies in the Hubble sequence, and P_ disk is the probability for a galaxy to be a disk. The lower right panel of Figure <ref>  clearly shows that for the centrals with T-type > 0 and P_ disk > 0.5, there are significant numbers of “uncertains” as classified in Galaxy Zoo. Therefore, although the ML-based morphology classification works very well in general for all galaxy populations in SDSS, at least for this particular case, it badly failed to recover the human eyeball classified results. As discussed before, many disk-like “uncertains" share similar structure parameters (e.g., B/T, sersic index) as “spirals", but their visual morphology features look different from “spirals". These differences maybe related to external environmental effects such as perturbation and interaction, which are difficult to be catched by some of the ML method. These external environmental effects tend to produce -poor systems. 











§ BIAS INTRODUCED BY 1-DIMENSIONAL STATISTICAL ANALYSIS
  






Figure <ref> shows the SFE_ HI-sSFR relation of central spirals in the ALFALFA-SDSS matched sample in three stellar mass bins. Blue dots in the upper panels are individual galaxies. Level contours for the number density of the galaxies at given stellar mass bins are shown in the lower three panels, with colors ranging from blue to red as a function of number density, applied with sample incompleteness corrections. The red lines are the best fits to the data using the orthogonal distance regression (ODR) fitting method, which calculates the sum of the orthogonal distances from the data points to the fitted line. The blue lines show the average SFE_ HI (at a given sSFR) as a function of sSFR, calculated with a moving average of 0.5 dex in sSFR. 


In the lower panels, the contour lines of the 2-dimensional density distributions clearly indicate the underlying trends. Evidently, the ODR fitting (red line) better traces the ridge of the contour lines than the blue line, and hence represents a more accurate fit to the data, in particular for the case of low mass bin where the scatter is larger. This is expected since ODR fitting takes the variation in both x- and y-axes into account. The slope of the best ODR fits is around unity in all three stellar mass bins, indicating that galaxies distribute along with the constant gas-to-mass ratio, i.e., when sSFR decreases, the  gas-to-mass ratio remains constant. 

While the commonly used 1-dimensional scaling relation (e.g., the blue lines), which considers only the variation in the y-axis at a given x, agrees with the ridge line and ODR fitting for the massive galaxies (lower right panel), due to the relatively narrow data distribution, i.e., the variation is small in both x- and y-axes. However, in the low-mass bin (lower left panel), the blue line significantly deviates from the ridge line and the red line, due to the larger scatter and the shape of the data distribution. Also, the blue line has, on average, a shallower slope than unity, indicating that when sSFR decreases, the  gas-to-mass ratio also decreases, i.e., galaxies become more -poor. 

The results shown in Figure <ref> demonstrate that using 1-dimensional scaling relations (e.g., the blue lines in the lower panels in Figure <ref> and the lines in the middle panels in Figure <ref> to describe the trend can be biased, due to the shape of the data distribution. For instance, in the upper middle panel in Figure <ref>, the fact that the blue line (lowest stellar mass bin) is flattened out at high sSFR is due to the effect described in Figure <ref>. Clearly, the corresponding contour lines in the upper left panel are all well parallel to the diagonal constant  gas-to-mass ratio line. 













§ ALTERNATIVE SFR INDICATORS
  






As discussed in the main text, with proper sample incompleteness corrections, for central spirals, the overall  detection DF reaches ∼ 95% for the ALFALFA-SDSS matched sample, and ∼ 98% for the xGASS sample. Hence, our main conclusion that there is a ubiquitous  reservoir in the vast majority of central spirals (defined by visual morphology) is largely independent of any particular SFR indicator. Here we further test the detailed  scaling relations shown in Figure <ref> with alternative SFR indicators. 

We repeat the analyses using SED SFRs derived from UV, optical and mid-IR fluxes <cit.>. The results are shown in Figure <ref>. As discussed in the previous Section and Figure <ref>, the trends derived from the 1-dimensional method (the middle two panels of Figure <ref>) can be significantly biased. Using 2-dimensional analysis and ODR fitting produces more accurate representations of the true underlying trends. Therefore, comparing the right two panels of Figure <ref> with those in Figure <ref>, although the range of the galaxy distribution in sSFR is narrower (due to the use of different SFR indicators), the general trends are similar. Both SFR indicators reveal that the SFE_ HI-sSFR relation and μ_ HI-sSFR relation strongly correlate with stellar mass, and that at a given stellar mass, μ_ HI is largely constant across sSFR. 

It should be noted that although there are few fully quenched central spirals with log sSFR < -2 Gyr^-1 based on the SED-based SFRs, our main conclusions that there is a ubiquitous  reservoir in the vast majority of central spirals remain robust, and that at a given stellar mass, μ_ HI is largely constant across sSFR. The exact name of the galaxies with the lowest sSFR, i.e., fully quenched or green valley, is therefore less critical. 

In addition, in the right two panels in Figure <ref>, we also show the  FFR derived from the SED-based SFRs, which has a steeper slope than the one in Figure <ref>. It is important to note that though the amount of the decrease in sSFR is smaller for the SED-based SFRs (due to the narrower range of sSFR), the corresponded amount of decrease in the  gas mass is similar to those shown in Figure <ref>. The ∼10 times less  gas accompanied by the suppressed star formation efficiency in the central spirals with the lowest sSFRs indicates that they are indeed in the process of being quenched, while their  gas mass fraction remains about constant.














natexlab#1#1




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