We present a new constraint on the Galactic SUP12SUPCSUP13SUPC gradient with sensitive HCOSUPSUP absorption observations against strong continuum sources. The new measurements suffer less from beam dilution optical depths and chemical fractionation allowing us to derive the isotopic ratios precisely. The measured SUP12SUPCSUP13SUPC ratio in the solar neighborhood 665 is consistent with those obtained from CHSUPSUP. Two measurements toward the GC are 42.21.7 and 37.56.5. Though the values are a factor of two to three higher than those derived from dense gas tracers e.g. HSUB2SUBCO complex organic molecules toward Sagittarius Sgr B2 regions our results are consistent with the absorption measurements from cCSUB3SUBHSUB2SUB toward Sgr B2 40 and those from CHSUPSUP toward Sgr A and Sgr B2N gt30. We have calculated a new Galactic SUP12SUPCSUP13SUPC gradient of 6.41.9RSUBGCSUBkpc25.910.5 and found an increasing trend of the SUP12SUPCSUP13SUPC gradient obtained from highdensity to lowdensity gas tracers suggesting that opacity effects and chemical fractionation may have a strong impact on the isotopic ratios observed in highdensity regions.
['astrochemistry', 'ISM: abundances', 'ISM: clouds', 'ISM: molecules', 'galaxy: evolution', 'Astrophysics - Astrophysics of Galaxies']
A new measurement of the Galactic SUP12SUPCSUP13SUPC gradient from sensitive HCOSUPSUP absorption observations
{'A new measurement of the Galactic 12 C/ 13 C gradient from sensitive HCO + absorption observations': "Gan Luo 1 , Laura Colzi 2 , Tie Liu 3 , Thomas G. Bisbas 4 , Di Li 5 , 6 , Yichen Sun 7 , and Ningyu Tang 8  \n- 1 Institut de Radioastronomie Millimetrique, 300 rue de la Piscine, 38400, Saint-Martin d'Hères, France e-mail: luo@iram.fr\n- 2 Centro de Astrobiología (CAB), CSIC-INTA, Ctra. de Ajalvir Km. 4, 28850 Torrejón de Ardoz, Madrid, Spain\n- 3 Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n- 4 Research Center for Astronomical Computing, Zhejiang Laboratory, Hangzhou 311100, China\n- 5 Department of Astronomy, Tsinghua University, Beijing 100084, China\n- 6 CAS Key Laboratory of FAST, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China\n- 7 School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China\n- 8 Department of Physics, Anhui Normal University, Wuhu, Anhui 241002, China  \nReceived xx; accepted xx", 'ABSTRACT': 'We present a new constraint on the Galactic 12 C / 13 C gradient with sensitive HCO + absorption observations against strong continuum sources. The new measurements su ff er less from beam dilution, optical depths, and chemical fractionation, allowing us to derive the isotopic ratios precisely. The measured 12 C / 13 C ratio in the solar neighborhood (66 ± 5) is consistent with those obtained from CH + . Two measurements toward the GC are 42.2 ± 1.7 and 37.5 ± 6.5. Though the values are a factor of two to three higher than those derived from dense gas tracers (e.g., H2CO, complex organic molecules) toward Sagittarius (Sgr) B2 regions, our results are consistent with the absorption measurements from c-C3H2 toward Sgr B2 ( ∼ 40) and those from CH + toward Sgr A ∗ and Sgr B2(N) ( > 30). We have calculated a new Galactic 12 C / 13 C gradient of (6.4 ± 1.9) R GC / kpc + (25.9 ± 10.5) and found an increasing trend of the 12 C / 13 C gradient obtained from high-density to low-density gas tracers, suggesting that opacity e ff ects and chemical fractionation may have a strong impact on the isotopic ratios observed in high-density regions.  \nKey words. astrochemistry - ISM: abundances - ISM: molecules - ISM: clouds - Galaxy: evolution', '1. Introduction': 'The measurements of isotopic ratios in the interstellar medium (ISM) are important for understanding Galactic chemical evolution (GCE) due to di ff erent stellar yields with di ff erent masses (Guesten & Mezger 1982; Maeder 1983; Iben & Renzini 1983; Clayton 2003; Kobayashi et al. 2011; Romano et al. 2017; Kobayashi et al. 2020). One of the few isotopic ratios that can be easily measured is 12 C / 13 C . Notably, 12 C is mainly produced through He-burning as the primary element (e.g., core-collapse supernovae and He-burning shells in low-mass stars), while 13 C is an intermediate product of CNO cycling in intermediate-mass asymptotic giant branch (AGB) stars (Kobayashi et al. 2011; Romano et al. 2017). Since the timescale in which massive stars release the elements into the ISM is much shorter than for low-tointermediate mass stars, the 12 C / 13 C ratios predicted from GCE models would decrease as a function of time with a given initial mass function (IMF). In the Milky Way, a radial gradient in the 12 C / 13 C ratio inferred from 12 C 18 O and 13 C 18 O rises from approximately 24 at a galactocentric distance ( R GC) of ∼ 0.5 kiloparsec (kpc) to roughly 70 at R GC ∼ 12 kpc (Langer & Penzias 1990, 1993).  \nWhile various methodologies and tracers have been employed in recent years to constrain the Galactic 12 C / 13 C gradient (Halfen et al. 2017; Yan et al. 2019; Jacob et al. 2020; Sun et al. 2024), the di ff erent methods have yielded inconsistent results, especially for the Galactic center (GC) regions. Measur-  \ning the 12 C / 13 C isotopic ratio with molecular lines faces challenges from both observational factors (e.g., opacity, beam dilution) and chemical e ff ects (e.g., selective photodissociation and fractionation). The most abundant carbon-bearing isotopologs (e.g., 12 CO, H 12 CO + , H 12 CN) can easily become optically thick in dense clouds, making precise estimation of column densities di ffi cult. In di ff use and translucent clouds, the main isotopologs may not pose challenges for optical depths, but the rare isotopologs are often di ffi cult to detect due to their low abundance and sub-thermally excitation of even the ground state transition (Godard et al. 2010; Luo et al. 2020). Additionally, distant clouds have smaller beam-filling factors, which reduces the reliability of the measurements observed with a single dish.  \nIsotope-selective photodissociation and isotopic exchange reactions can strongly alter the 12 C / 13 C isotopic ratios in molecules from the original element ratios. For abundant species such as CO, the self-shielding of 12 CO is significantly stronger than less abundant isotopologs (e.g., 13 CO and C 18 O). Thus, the 12 C / 13 C ratio in CO would be higher under the existence of external UV radiation (Bally & Langer 1982; Chu & Watson 1983; Liszt 2007). Additionally, due to the di ff erences in zero-point energy between di ff erent isotopologs, isotopic exchange reactions can further alter 12 C / 13 C ratios in various molecules. For instance, the isotopic exchange reaction between 13 C + and CO is exothermic, leading to an enrichment of 13 C in CO and other molecules primarily formed through CO in cold environments  \n(Watson et al. 1976; Langer et al. 1984; Roue ff et al. 2015; Colzi et al. 2020; Sipilä et al. 2023).  \nAbsorption lines against strong continuum sources can overcome such di ffi culties. The advantage of using absorption lines is to measure the optical depth as well as the column density precisely even if the transition is sub-thermally excited. Such a methodology has been widely used to quantify the physical properties of low-density gas (Lucas & Liszt 1996, 1998; Luo et al. 2020, 2023b; Rybarczyk et al. 2022b; Liszt & Gerin 2023; Gerin et al. 2024). Lucas & Liszt (1998) is one of the first works that measured the isotopic ratios in the solar neighborhood through millimeter molecular absorption lines. Liszt & Gerin (2018) measured the H 12 CO + / H 13 CO + ratios in four directions toward the Galactic bulge, and they inferred a much higher value ( ∼ 60) than the other tracers ( ∼ 20). Inspired by these pioneering works, systematic measurements at di ff erent R GC with such a methodology could be useful to constrain the 12 C / 13 C gradient.  \nIn this work, we present a new measurement of the Galactic 12 C / 13 C gradient by using absorption lines of H 12 CO + and H 13 CO + with high-angular observations of the Atacama Large Millimeter / submillimeter Array (ALMA) and the Northern Extended Millimeter Array (NOEMA). We emphasize that such a methodology to constrain the isotopic gradient of the Milky Way with a large sample, especially for future searches in the anti-center direction (though rare and challenging), could provide valuable constraints for GCE models.', '2.1. Quasar sight lines': "We carried out H 12 CO + and H 13 CO + J = 1-0 observations toward six quasars (Fig. 1). Five were observed with ALMA (2022.1.01438.S, PI: Thomas G. Bisbas) during March 20-30, 2023, and one source (3C 111) was observed with NOEMA (W20BB, PI: Gan Luo) in December 2020 and January 2021. The angular resolution of ALMA is ∼ 0.6 '' at 89 GHz. The spectral resolution of ALMA is 122 kHz, corresponding to a velocity resolution of ∼ 0.4 km s -1 at 89 GHz. The raw data was calibrated using the standard pipeline with the Common Astronomy Software Applications (CASA, version 6.4.1; CASA Team et al. 2022). The imaging of the calibrated visibilities was performed using the tclean algorithm with Briggs weighting (robust = 0.5). The NOEMA observations have an angular resolution of ∼ 2.1 '' at 89 GHz and a velocity resolution of ∼ 0.21 km s -1 . The PolyFiX backend of NOEMA covers H 12 CN, H 13 CN, HN 12 C, and HN 13 C J = 1-0 transitions simultaneously. The calibration of the raw data was performed using clic software in the gildas . 1 The typical optical depth noise levels are 3 ∼ 7 × 10 -3 per 0.4 km s -1 velocity channel for ALMA observations and 2 × 10 -3 per 0.21 kms -1 velocity channel for NOEMA observations.", '2.2. UCH ii sight lines': "The ALMA observations toward ten UCH ii regions (red crosses in Fig. 1), which were selected from the ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS) survey (2019.1.00685.S, PI: Tie Liu), were observed from September to November 2019 with both 12-m and 7-m arrays at band 3. The baselines of ATOMS range from 15 to 783.5 m, corresponding to an angular resolution of ∼ 1.2 '' at 89 GHz. The spectral resolution of H 12 CO + and H 13 CO + J = 1-  \nFig. 1. Distribution of the observed quasar sight lines (yellow lines) and ultra-compact H ii region (red crosses) projected onto a topdown schematic view of the Milky Way (artist's concept, R. Hurt: NASA / JPLCaltech / SSC).  \n<!-- image -->  \n0 transitions are 0.2 km s -1 and 0.422 km s -1 , respectively. The raw data were calibrated using CASA version 5.6, and the combination and imaging of 12-m and 7-m data were performed with CASA version 6.4.1. The sensitivity of the resultant spectra depends on the properties of each source, a detailed description of observations can be found in Liu et al. (2020).", '3.1. Absorption spectra and integrated optical depth': 'The absorption spectra of HCO + (hereafter, HCO + refers to H 12 CO + ) and H 13 CO + 2 were extracted from the continuum peak of each source. Figure 2 shows an example of normalized spectra of HCO + and H 13 CO + toward J1851 + 0035. Spectra toward all other sources can be found in Appendix A.  \nSince most of the sources are located in the Galactic plane ( | b | < 2 · ), the foreground absorption components are mixed, and it is di ffi cult to decompose individual Gaussian components (except for the high-latitude source 3C111; see Appendix B). To obtain the column density ratios, we integrated the optical depths ( R τν d υ ) of HCO + and H 13 CO + in the same velocity range (shadowed region in Fig. 2 and A.1). We set four criteria when identifying the integrated range: 1) H 13 CO + absorption should not be contaminated with absorption features of other molecules (e.g., -25 km s -1 component of H 13 CO + in Fig. 2); 2) each of the integrated ranges of H 13 CO + should be distinguished from the others (no overlap); 3) the absorption profile of HCO + should not be saturated ( e -τ > rms); and 4) absorption spectra toward UCH ii regions should not be contaminated with emission features from the compact foreground envelopes. The uncertainty of R τν d υ  \n( σ I) through an error propagation formula is thus defined by  \nσ I = d υ 2 v u t N -1 X i = 1 ( σ 2 τ i + σ 2 τ i + 1 ) , (1)  \nwhere d υ is the channel width, N is the length of the data array in the velocity range over which the opacity profile is integrated, and στ i = RMS / e -τ i is the uncertainty of τ at the i th channel. The integrated optical depths of HCO + and H 13 CO + toward all sources are listed in Table C.1.  \nThe molecular column density can be written as a function of R τν d υ (Mangum & Shirley 2015):  \nN tot = 3 h 8 π 3 | µ lu | 2 Q rot g u e E u kT ex e h ν kT ex -1 Z τν d υ, (2)  \nwhere h is the Planck constant, k is the Boltzman constant, | µ lu | 2 is the dipole matrix element, Q rot is the rotational partition function, g u is the degeneracy of the upper energy level, E u is the upper energy level, and T ex is the excitation temperature. For each transition, | µ lu | 2 , E u, and the rest frequency ν were taken from the Cologne Database for Molecular Spectroscopy (CDMS; Müller et al. 2001, 2005), and they are listed in Table D.1. For linear molecules, the simplified partition function is given by McDowell (1987)  \nQ tot = kT hB 0 e hB 0 3 kT , (3)  \nwhere B 0 is the rigid rotor rotation constant.  \nThe excitation temperature of HCO + in di ff use molecular clouds is usually close to the cosmic microwave background temperature ( T CMB = 2.73 K) (Godard et al. 2010; Luo et al. 2020). If we fill in all the constants in Eq. 2 and take T ex = 2 . 73 K for both HCO + and H 13 CO + , the column density ratios can be simplified as  \nN HCO + N H 13 CO + = 0 . 974 R τ HCO + d υ R τ H 13 CO + d υ . (4)  \nThough T ex of HCO + can rise above 2.73 K when the gas density is higher than 300 cm -3 (Rybarczyk et al. 2022a), a variance of T ex from 2.73 to 5 K only results in a variance of the column density ratio of less than 1%. The calculated ratios in our samples range from 12.7 ± 0.2 3 to 139.4 ± 38.0 (Table B.1).', '3.2. The 12 C/ 13 C gradient': 'Obtaining an accurate distance of a distant molecular cloud is di ffi cult, especially without parallax measurements from maser emissions. The most common estimation of such a distance is based on kinematic distance. We calculated the R GC for each velocity component with the Monte Carlo kinematic distance method, using the latest rotational curve and updated solar motion parameters (Wenger et al. 2018). This model is obtained through the trigonometric parallax results from the high-mass star-forming regions (HMSFRs) in the BeSSeL Survey (Reid et al. 2014, 2019). This method samples the local standard of rest velocity ( V lsr) and Galactic rotational curve parameters for HMSFRs and derives the probability density distribution (PDF) of kinematic distance, resulting in a median uncertainty of 13%  \nJ1851+0035  \nFig. 2. Normalized absorption spectra of HCO + (black curve) and H 13 CO + (blue curve) toward J1851 + 0035. The spectrum of H 13 CO + has been scaled by a factor of five and shifted upward by 0.5 for better display. The gray shaded regions denote the velocity ranges used to calculate the column density ratios. The red vertical lines represent HCO absorption, where the -25kms -1 component of H 13 CO + absorption is contaminated with HCO J = 1 / 2-1 / 2, F = 1-1. Thus, these components were discarded since they can only obtain lower limits of 12 C / 13 C.  \n<!-- image -->  \nto the parallax distances. A detailed description of this method can be found in Wenger et al. (2018).  \nThe optical depth-weighted V lsr in our samples is calculated by  \nV lsr = R υτ HCO + d υ R τ HCO + d υ . (5)  \nThe calculated V lsr and R GC as well as the uncertainties are listed in Table B.1. We note that such an estimation with pure circular motions may fail to predict the R GC near the GC (e.g., the highly negative V lsr toward J1720-3552), in which non-circular motions should be taken into account (Liszt & Gerin 2018). Therefore, we used the tilted-disk model presented by Burton & Liszt (1978) to estimate the velocity components of V lsr < -140 kms -1 toward J1720-3552, resulting in an R GC between 1.24 to 1.5 kpc. Thus, we adopted a value of 1.37 ± 0.04 kpc for this component.  \nFigure 3 shows the measured HCO + / H 13 CO + ratios as a function of R GC. The weighted-mean 12 C / 13 C ratios increase from 42 ± 1 toward the GC to 66 ± 5 in the solar neighborhood. To avoid an underestimation of the HCO + optical depth when τ is large, we set stricter constraints ( τ < 3) when fitting a gradient. We used the Markov chain Monte Carlo (MCMC) method within the emcee code (Foreman-Mackey et al. 2013) to sample the free parameters and the posterior probability distribution. The maximum likelihood fit of the data is shown with a red solid curve in Fig. 3, which gives a H 12 CO + / H 13 CO + gradient as a function of R GC:  \nH 12 CO + H 13 CO + = (6 . 4 ± 1 . 9) R GC kpc + (25 . 9 ± 10 . 5) . (6)  \nFig. 3. Measurements of H 12 CO + / H 13 CO + as a function of R GC and comparison of the derived gradients between di ff erent works. Blue dots represent τ HCO + < 3, and black dots represent τ HCO + > 3. The two lower limits are shifted to R GC = 0 . 5 kpc for better visualization. The red curve denotes the maximum likelihood fit of the blue points only; orange curves denote the 3 σ deviation from the MCMC sampling.  \n<!-- image -->', '4.1. The 12 C/ 13 C ratios in the solar neighborhood': 'While the 12 C / 13 C ratios in the nearby molecular clouds have been derived extensively with various molecules, the most reliable tracer thought to represent the true element 12 C / 13 C ratios is CH + (Ritchey et al. 2011). The measured 12 C / 13 ratios from our HCO + samples range from 62.0 ± 4.4 to 139.4 ± 38.0 within 500 pc of the solar circle (7 . 6 ≤ R GC ≤ 8 . 6 kpc), with a weighted mean value of 66 ± 5. This value is in good agreement with the mean value obtained through optical 12 CH + / 13 CH + measurements toward di ff use sight lines (74.4 ± 7.6, Ritchey et al. 2011) and the -0 . 9 kms -1 component of 3C 111 (Appendix B).', '4.2. The 12 C/ 13 C ratios in the Galactic center': 'The measurements of the 12 C / 13 C ratio within ∼ 2 kpc of the GC are rare. This is mainly due to the high gas column density (e.g., N H2 ≳ 10 24 cm -2 ), which makes the molecular transitions optically thick, even for the rare isotopologs (e.g., C 18 O). Halfen et al. (2017) measured the isotopic ratios using complex organic molecules (COMs) toward Sgr B2(N) and found an average value of 24 ± 7, which is similar to the value obtained from dense gas tracers (e.g., C 34 S, Humire et al. 2020). The measurements from absorption lines of CH toward Sgr B2(M) and H2CO toward Sgr B2 result in 12 C / 13 C ratios of 15.8 ± 2.4 (Jacob et al. 2020) and 11.48 ± 0.03 (Yan et al. 2019), respectively.  \nPrevious absorption observations toward the Galactic bulge have revealed a significantly high 12 C / 13 C ratio ( ∼ 60, Liszt & Gerin 2018). However, since these observations integrated the full velocity range, which has HCO + absorptions (the H 13 CO + absorptions are much narrower), the absorption of HCO + could be contaminated with foreground di ff use gas, leading to a high value. Since the HCO + absorptions toward the dense regions (e.g., Sgr B2(N)) are completely saturated, the measured values at R GC < 2 kpc in our work are in fact the di ff use molecular components (a few hundred cm -3 , Gerin & Liszt 2017; Liszt & Gerin 2018).  \nThe two measurements at R GC < 2 kpc from our observations have 12 C / 13 C ratios of 42.2 ± 1.7 and 37.5 ± 6.5, values which are consistent with absorption measurements of c-C3H2 ( ∼ 40 at R GC < 1 kpc, Corby et al. 2018) but still larger than the other tracers in high-density ( n H2 > 10 5 cm -3 ) regions. Furthermore, the two lower limits of 12 C / 13 C at -181 and -162 kms -1 of J1720-3552 are > 19 and > 31. These results are consistent with previous observations of CH + toward Sgr A ∗ and Sgr B2(N) (e.g., 12 CH / 13 CH > 30 at -168 ∼ -150 km s -1 of Sgr A ∗ , Godard et al. 2012), which is again distinct from the previously reported low values toward Sgr B2 but supports our results. Thus, either opacity e ff ects or fractionation may have an impact on the measured isotopic ratios in the high-density tracers (e.g., CN, and COMs), while our measurements at low density are less influenced.', '4.3. The 12 C/ 13 C gradient and comparison with GCE models': 'Di ff erent tracers have been used to calculate the Galactic 12 C / 13 C gradient. This gradient is mostly constrained by results from 12 C 18 O / 13 C 18 O (e.g., Langer & Penzias 1990, 1993; Wouterloot & Brand 1996; Giannetti et al. 2014); 12 CN / 13 CN (e.g., Savage et al. 2002; Milam et al. 2005; Sun et al. 2024); H 12 2 CO / H 13 2 CO (Henkel et al. 1982; Yan et al. 2019); C 34 S (Yan et al. 2023); and a combined analysis from various tracers (e.g., COMs, CH; Halfen et al. 2017; Jacob et al. 2020). The gradients from di ff erent methodologies are shown with di ff erent curves in Fig. 3. 4  \nBy comparing the gradients using di ff erent tracers, we found that the measurements in the low-density molecular clouds (HCO + , n H2 ∼ a few 10 2 cm -3 ) are higher than those from higher density environments ( n H2 ≥ a few 10 4 cm -3 ), such as C 18 O, H2CO, CS, and CN (Giannetti et al. 2014; Yan et al. 2019, 2023; Sun et al. 2024). The systematically increasing trend of the 12 C / 13 C gradient from high-density to low-density gas may again suggest that fractionation plays a crucial role in the measured 12 C / 13 Cratios in molecules. Predictions from the chemical models by Colzi et al. (2020) are in agreement with this observational trend, finding that 12 C / 13 C ratios of HCN, HNC, and HCO + tend to increase from the higher (10 6 cm -3 ) to the lower (10 3 cm -3 ) densities.  \nThe comparison between the derived 12 C / 13 C gradient and the GCE models presented in Colzi et al. (2022) is shown in Fig. 4, in which the models consider di ff erent mass ranges for white dwarf progenitors and average ejected masses of 13 C and 15 N per nova outburst (Romano et al. 2019, 2021). Our result is reasonably consistent with the GCE models with a mass range of white dwarf progenitors 1-8 M ⊙ and higher average ejected masses of 13 C (models 3 and 4). Given the limited range of R GC in the current samples, future observations at R GC > 10 kpc would be exceptionally useful to constrain GCE models.  \nHowever, one should always keep in mind that the formula of the isotopic gradient strongly depends on the accuracy of the R GC, which is mostly based on the kinematic distance estimation. For instance, the estimated R GC before and after the model by Reid et al. (2019) could di ff er by several kpc (Sun et al. 2024). The large scatter of 12 C / 13 C at R GC between 4 kpc to 8 kpc in both our work and the literature may suggest that our understanding of the Milky Way rotational model or inhomogeneous mixing of the elements may also contribute to the scatter.  \nFig. 4. Comparison between observations and GCE models, in which the models are taken from Table 2 in Colzi et al. (2022) with the same numbers.  \n<!-- image -->', '4.4. Chemical effects on the measured 12 C/ 13 C ratios': 'The isotopic exchange reactions could be one of the main processes that lead to di ff erent isotopic ratios in HCO + . In this section, we consider the isotopic exchange reaction that produces H 13 CO + (Langer et al. 1978; Roue ff et al. 2015; Colzi et al. 2020) 5 :  \n13 C + + CO ⇌ 13 CO + C , (R1)  \n13 CO + HCO + ⇌ H 13 CO + + CO . (R2)  \nWe considered the main formation pathways of H 13 CO + in lowto-intermediate density gas (van Dishoeck & Black 1988; Luo et al. 2023b):  \n13 CO + + H2 → H 13 CO + + H , (R3)  \n13 C + + H2O → H 13 CO + + H , (R4)  \n13 CH + O → H 13 CO + + e . (R5)  \nThe destruction of HCO + (and H 13 CO + ) is dominated by electrons:  \nHCO + + e -→ CO + H . (R6)  \nThus, the isotopic exchange reaction would influence the HCO + / H 13 CO + ratio only if the right side reaction R2 is comparable to reactions R3 ∼ R5. The reaction rate of the above reaction is 2 . 6 × 10 -10 × ( T / 300) -0 . 4 cm 3 s -1 (Roue ff et al. 2015). The typical abundance of CO + is 10 -10 ∼ 10 -9 (Stäuber & Bruderer 2009; Treviño-Morales et al. 2016), the abundance of HCO + is a few 10 -9 (Lucas & Liszt 1996; Gerin et al. 2019; Luo et al. 2020), and the abundance of CH is 3 × 10 -8 (Liszt & Lucas 2002; She ff er et al. 2008; Tang et al. 2021; Luo et al. 2023a). Even if we only consider reaction R3 (the reaction rate k = 7 . 5 × 10 -10 cm 3 s -1 ; McElroy et al. (2013)) and scale the above abundance with 12 C / 13 C = 70, the formation of H 13 CO + through reaction R3 would overwhelm reaction R2 by over four orders of magnitude at the typical gas temperature of ∼ 50 K (Snow & McCall 2006). Therefore, fractionation would have little impact on the measured HCO + / H 13 CO + ratios in low-density gas. This is  \nalso consistent with various chemical modelings of carbon fractionation, in which HCO + / H 13 CO + can overall best represent the original 12 C / 13 Celement ratio in low-to-intermediate density gas (Sz"ucs et al. 2014; Roue ff et al. 2015; Colzi et al. 2020; Sipilä et al. 2023).  \nIn dense regions, CO becomes the precursor of HCO + (Dalgarno 2006; Indriolo & McCall 2012; Bisbas et al. 2015):  \nCO + H + 3 → HCO + + H2 . (R7)  \nSince reaction R6 is still the dominant formation channel of CO even in high-density clouds (Luo et al. 2023a), the fractionation of CO in the dense cloud could greatly impact the isotopic ratio in HCO + only if reaction R7 is comparable to reaction R6. However, the gas density that will significantly alter the 12 C / 13 C ratio measured in HCO + would be above 10 4 cm -3 (Sipilä et al. 2023). The highest column density of HCO + in Table B.1 is ∼ 3 . 4 × 10 13 cm -2 , corresponding to an H2 column density of 10 22 cm -2 , assuming a constant HCO + abundance (3 × 10 -9 , Lucas & Liszt 1996; Liszt & Gerin 2016) 6 Therefore, most components are not expected to trace such a high-density regime and will be less influenced by the fractionation e ff ect. Nevertheless, both detailed chemical modeling (Colzi et al. in prep) and the constraints of gas volume density and temperature through multiple lines in the future are necessary to determine where and how fractionation impacts the isotopic ratios.', '5. Conclusion': "In this work, we have performed high sensitivity absorption line observations toward strong continuum sources (including quasars and UCH ii regions). We derived 12 C / 13 C ratios from HCO + absorption and R GC according to the latest parallax-based distance calculation. Our main conclusions are as follows:  \n- 1. The derived 12 C / 13 C gradient from HCO + absorption measurements is (6.4 ± 1.9) R GC / kpc + (25.9 ± 10.5), which is reasonably consistent with current GCE models.\n- 2. The derived weighted mean 12 C / 13 C ratio in the solar neighborhood is 66 ± 5, which is consistent with those measured from CH + (74.4 ± 7.6).\n- 3. Our measurements toward the GC are two to three times higher than those measured with dense gas tracers toward Sgr B2 (11 ∼ 24). Nevertheless, our results are supported by the CH + observations toward Sgr A ∗ and Sgr B2(N) ( > 30) as well as absorption measurements of c-C3H2 ( ∼ 40).\n- 4. The discrepancy between our method and those from dense gas tracers suggests that opacity e ff ects and fractionation may have a larger impact on the dense gas tracers in highdensity regions.  \nWe highlight the use of absorption lines to measure the isotopic ratios with interferometry observations, which are less affected by optical depth, beam dilution, and chemical fractionation. Future large samples toward the GC and the anti-center directions may provide more constraints on the Galactic 12 C / 13 C gradient as well as the GCE models.  \nAcknowledgements. We are grateful to the anonymous referee for the thoughtful comments and suggestions that greatly improved the clarity of our work, especially the suggestion of including the non-circular motion to estimate the distance near the GC. We thank Zhiyu Zhang, J'erˆome Pety, and Michel Gu'elin  \nfor their useful comments, Donatella Romano for providing the GCE models, and the sta ff s at IRAM for carrying out the NOEMA observations and reducing the data. L. C acknowledges support from the grant No. PID2022136814NB-I00 by the Spanish Ministry of Science, Innovation and Universities / State Agency of Research MICIU / AEI / 10.13039 / 501100011033 and by ERDF, UE. Tie Liu acknowledges the supports by the National Key R&D Program of China (No. 2022YFA1603100), National Natural Science Foundation of China (NSFC) through grants No.12073061 and No.12122307, and the Tianchi Talent Program of Xinjiang Uygur Autonomous Region. D. L. is a New Cornerstone investigator. N.-Y. Tang is sponsored by the University Annual Scientific Research Plan of Anhui Province (No. 2023AH030052, No. 2022AH010013), the China Manned Space Program through its Space Application System, Zhejiang Lab Open Research Project (No. K2022PE0AB01). This paper makes use of the following ALMA data: ADS / JAO.ALMA#2022.1.01438.S and ADS / JAO.ALMA#2019.1.00685.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. This work is based on observations carried out under project number W20BB with the IRAM NOEMA Interferometer. IRAM is supported by INSU / CNRS (France), MPG (Germany) and IGN (Spain).", 'References': 'Bally, J. & Langer, W. D. 1982, ApJ, 255, 143 Bisbas, T. G., Papadopoulos, P. P., & Viti, S. 2015, ApJ, 803, 37 Burton, W. B. & Liszt, H. 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Future high angular resolution and high sensitivity observations may help reconstruct both the emission and absorption profiles around UCH ii regions.', 'Appendix B: Gaussian decomposition of absorption profiles toward 3C 111': 'Absorption profiles and Gaussian decomposition of H 12 CN, H 13 CN, HN 12 C, and HN 13 C J = 1-0 transitions toward 3C 111 are shown in Fig. B.1, in which the spectra of H 12 CNand H 13 CNare hyperfine transitions. The Gaussian decomposition is performed with curve \\_ f it package in scipy using the Levenberg-Marquardt algorithm, and the resultant optical depths and linewidth ( ∆ V ) are shown in Table B.1. We set constraints when fitting hyperfine transitions that all hyperfine lines have 1) the same linewidth ( ∆ V ) and 2) the same velocity o ff set with respect to V lsr.  \nThere are two velocity components ( -0 . 9 kms -1 and -2 . 5 kms -1 ) in front of 3C 111, the 3D extinction indicates that the cloud is within 300 pc from the Sun (Lucas & Liszt 1998). The gas volume density at -0 . 9 km s -1 is n H2 = 398 ± 22 cm -3 (Luo et al. in prep), and n H2 is supposed to be much lower at -2 . 5 km s -1 than at -0 . 9 kms -1 (Lucas & Liszt 1998). However, the HCO + absorption profile is almost saturated toward 3C 111 and we cannot get a good Gaussian decomposition. Thus, we use HCN and HNC to derive the 12 C / 13 C ratio. The optical depth ratios of the H 12 CN hyperfine transitions are 1:2.3:3.5 and 1:2.9:4.6 at -0.9 kms -1 and -2.5 km s -1 , respectively. While the latter represents the intrinsic line ratio (1:3:5), the former deviates from it by 30%, indicating that the optical depths of the H 12 CN (F = 1-1 and 2-1) at -0.9 km s -1 are underestimated. As an alternative, we can fix the optical depth ratios at 1:3:5 instead of treating them as free parameters to obtain a more accurate value of the column density.  \nThe 12 C / 13 C ratio at -0 . 9 kms -1 derived from H 12 CN / H 13 CN is 74 ± 3, which is 30% higher than that previously obtained by Lucas & Liszt (1998). Measurement from HN 12 C / HN 13 C (62 ± 6) also show similar result. The 12 C / 13 C ratio at -2 . 5 kms -1 component derived from H 12 CN / H 13 CN is 138 ± 28, which is ∼ 2 times higher than that at -0 . 9 kms -1 . As suggested by Lucas & Liszt (1998), this could be a particular case, where the 13 CO has been enriched and fractionation leads to a deficit of 13 C in less abundant carbon carriers. Chemical models that consider the isotopic fractionation also predict a higher isotopic ratio of H 12 CN / H 13 CN than that from CO or HCO + (Roue ff et al. 2015; Colzi et al. 2020). Our detection of HN 13 C at -2 . 5 kms s -1 (S / N of R τ dv ∼ 4) is consistent with the hypothesis (HN 12 C / HN 13 C = 95 ± 39).', 'Appendix C: The source properties': 'The derived source properties from Sect. 3 are shown in Table C.1.', 'Appendix D: The Molecular transitions': 'The molecular transitions mentioned in this work are taken from the CDMS database (Müller et al. 2001, 2005), which are listed in Table D.1.', 'Appendix E: The unusual low H 12 CO + /H 13 CO + toward J1720-3552': 'The -22 kms -1 velocity component was recognized as an independent component in the H 13 CO + line profiles when we calculated the H 12 CO + / H 13 CO + ratios. The derived isotopic ratio is more than three times lower than the components toward the GC; however, the reason is still unclear. If this low value is caused by chemical fractionation, the gas component at -22 kms -1 must have a high density and compact size ( ≤ 0.01 pc at a distance of ∼ 3 kpc; otherwise, we would see emission lines around the continuum source). It should be surrounded by low-density envelopes since the H 12 CO + / H 13 CO + ratios toward the neighboring velocity components are much higher. Future highJ molecular line observations may help reveal the nature of this low value.  \nFig. A.1. Same as Fig. 2 but for other sources. Red vertical lines denote HCO absorption.  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \nFig. B.1. Gaussian decomposition of normalized absorption profiles of HCN, H 13 CN, HNC, and H 13 NCtoward 3C 111. Red dashed curves denote the fitting results, and green dotted lines denote each Gaussian component.  \n<!-- image -->  \nTable B.1. Optical depths and line widths toward 3C 111.  \nNotes. ( a ) Optical depth of J = 1-0, F = 0-1 transition.  \nTable C.1. Source name, velocity, galactocentric distance, integrated optical depths, isotopic ratios, and RMS of the absorption spectra.  \nNotes. ( a ) Estimation through tilted-disk model near the GC (see Sect. 3.2). ( b ) H 13 CO + is contaminated with HCO, thus, it is an upper limit.  \nTable D.1. Molecular transitions mentioned in this work.'}