First detection of 13CH in the interstellar medium

In recent years, a plethora of high spectral resolution observations of sub-mm and FIR transitions of methylidene (CH), have demonstrated this radical to be a valuable proxy for H2, that can be used for characterising molecular gas within the interstellar medium (ISM) on a Galactic scale, including the CO-dark component. Here we report the discovery of the 13CH isotopologue in the ISM using the upGREAT receiver on board SOFIA. We have detected the three hyperfine structure components of the 2THz frequency transition from its ground-state toward four high-mass star-forming regions and determine 13CH column densities. The ubiquity of molecules containing carbon in the ISM has turned the determination of the ratio between the abundances of carbon's two stable isotopes, 12C/13C, into a cornerstone for Galactic chemical evolution studies. Whilst displaying a rising gradient with Galactocentric distance, this ratio, when measured using observations of different molecules (CO, H2CO, and others) shows systematic variations depending on the tracer used. These observed inconsistencies may arise from optical depth effects, chemical fractionation or isotope-selective photo-dissociation. Formed from C+ either via UV-driven or turbulence-driven chemistry, CH reflects the fractionation of C+, and does not show any significant fractionation effects unlike other molecules previously used to determine the 12C/13C isotopic ratio which make it an ideal tracer for the 12C/13C ratio throughout the Galaxy. Therefore, by comparing the derived column densities of 13CH with previously obtained SOFIA data of the corresponding transitions of the main isotopologue 12CH, we derive 12C/13C isotopic ratios toward Sgr B2(M), G34.26+0.15, W49(N) and W51E. Adding our values derived from 12/13CH to previous calculations of the Galactic isotopic gradient we derive a revised value of 12C/13C = 5.85(0.50)R_GC + 15.03(3.40).


Introduction
The methylidene radical, CH has received widespread attention as a general probe of diffuse and translucent interstellar clouds and in particular as a surrogate for the H 2 column density determinations in such environments (e.g., Federman 1982;Sheffer et al. 2008, and references therein). CH has been observed in widely different wavelength regimes, from the radio at 9 cm (Rydbeck et al. 1973) over the sub-millimetre (submm) and far-infrared (FIR) ranges, at 560 µm (Gerin et al. 2010) and 150 µm (Stacey et al. 1987;Wiesemeyer et al. 2018) and the optical (4300.3 Å. e.g., Danks et al. 1984;Sheffer et al. 2008) into the far-ultraviolet (FUV) regimes (1369.13 Å, Watson 2001). In fact, the famous 4300.3 Å CH transition was one of the first three molecular lines that were detected in the interstellar medium (ISM) (Dunham 1937;Swings & Rosenfeld 1937). While an abundance of 12 CH data exists, very little is known about its rarer isotopologue 13 CH. Unlike its parent molecule, which is ubiquitously distributed in the ISM, the only known astronomical identification of 13 CH has been made in the solar spectrum by Richter & Tonner (1967). As to the ISM, Bottinelli et al. (2014) report the non-detection of the N, J = 1, 1/2 → 1, 3/2 and N, J = 1, 3/2 → 2, 5/2 transitions of 13 CH toward the well studied low-mass protostellar condensation IRAS 16293−2422.
The 12 C/ 13 C ratio has been widely studied toward molecular clouds in the Milky Way (e.g., Henkel et al. 1982;Steimle et al. 1986;Wilson & Rood 1994;Henkel et al. 1994) and, recently, also in the nuclear regions of nearby starburst galaxies (Tang et al. 2019). It is an important diagnostic tool for probing Galactic chemical evolution or simply the nucleosynthesis history of the Galaxy. 12 C is synthesised as the primary product of shell and core He-burning in intermediate-and highmass stars via the triple-α reaction, while 13 C is a secondary product of stellar nucleosynthesis and is produced over longer timescales. It is predominantly formed as a by-product of the carbon-nitrogen-oxygen (CNO) cycle in asymptotic giant branch (AGB) stars. Initiated by the proton capture of the 12 C nucleus produced from an older stellar population, the CNOcycle forms 13 N which then decays via positron emission to form the 13 C nucleus ( 12 C(p,γ) 13 N(β + ) 13 C) (Pagel 1997). The 13 C intermediate product is injected into the ISM via mass loss of the AGB stars, after the ashes of the helium burning shell of these objects have intermixed with their convective envelopes in the third "dredge-up" (Herwig 2005). This establishes the 12 C/ 13 C isotopic ratio as a measure of the degree of astration present in the Galaxy. Chemical evolution models of the Galaxy (Tosi 1982;Prantzos et al. 1996) have predicted the 12 C/ 13 C ratio to exhibit a positive gradient, increasing with Galactocentric distances and decreasing with time.
The predictions of these models have been confirmed by observational measurements of the 12 C/ 13 C isotopic ratio carried out by studying the rotational transitions of molecules like H 2 CO (Henkel et al. 1982), CO (Langer & Penzias 1990), and CN (Milam et al. 2005) and of their respective 13 C Article number, page 1 of 11 arXiv:2007.01190v1 [astro-ph.GA] 2 Jul 2020 A&A proofs: manuscript no. AA201937385 isotopologues, at cm and mm wavelengths 1 . While the average fit to the 12 C/ 13 C gradients derived independently using the three molecules mentioned above are in agreement within the quoted error bars, their individual trends display systematic variations amongst themselves. Reasons for these variations may be related to the observations of the different tracers and/or to isotopeselective chemical processes like gas-phase fractionation and selective photo-dissociation which do not impact every molecule in the same way. Chemical fractionation occurs as a result of ion-molecule exchange reactions that preferentially transfer and incorporate the heavier atomic isotope into molecules due to differences in zero-point energies between the different isotopes (see, e.g., Wilson 1999;Roueff et al. 2015). Isotopic fractionation does not impact all molecules in the same way as its degree greatly depends upon the formation pathway of the molecule and the environment in which it is formed and exists. In molecules that are susceptible to fractionation, like CO, the chemical fractionation enriches the 13 C isotope and lowers the 12 C/ 13 C ratio while it is increased by selective photodissociation of the rarer isotopic species containing 13 C, due to its weaker self-shielding in regions with a large UV flux (Bally & Langer 1982). Therefore, in such regions the 12 CO/ 13 CO ratio might be higher than the underlying 12 C/ 13 C ratio. In denser regions where carbon exists mostly in the form of CO, 13 C is locked up in CO and is depleted in other carbon-bearing molecules (Roueff et al. 2015). Precise measurements of the 12 C/ 13 C isotopic ratio have also been made using observations of the CH + A − X (0, 0) transition near 4232 Å (Ritchey et al. 2011) but their observations are limited to nearby stars (<7 kpc) that are bright (V <10 mag) in the visible wavelength range. The corresponding sub-mm transitions of CH + are often optically thick with saturated absorption profiles and can only yield lower limits on the carbon isotopic ratio (Falgarone et al. 2010). Hence, the high optical depths of many abundant 12 C bearing molecules, and effects of saturation and self absorption pose a problem when using the intensities of such lines, which in turn skews estimates of the 12 C/ 13 C ratio. In an attempt to provide additional constraints on the 12 C/ 13 C ratio, we here propose the use of a new tracer -CH. CH should be a good candidate for conducting isotopic ratio measures because it is an abundant species that is ubiquitously formed in the ISM and its spectral lines are predominantly optically thin. In particular, the hyperfine structure (hfs) components of the N, J = 1, 1/2 → 2, 3/2 transitions of CH near 2 THz have recently been observed in generally unsaturated absorption, ideal for column density determinations (Wiesemeyer et al. 2018;Jacob et al. 2019). Models and simulations by  for photo-dissociation regions (PDRs) show that the fractionation present in CH is dominated by the fractionation of its parental species. CH originates from C + and is formed via the dissociative recombination of CH + 3 : Hence, the degree of fractionation in CH is closely coupled with that of C + . At low visual extinctions, A V , the isotopic fractionation ratio of C +2 is comparable to the elemental abundance ratio, however, it increases with A V at low gas temperatures typically by a factor of at most ∼2. This is a consequence of the enrichment of 13 C in CO in these regions (favouring the forward reaction of the C + -CO ion-molecule exchange reaction (Langer & Penzias 1990)), which results in the depletion of 13 C + and all subsequent species like 13 CH that are formed from it. In addition, the abundance of CH is often enhanced through hydrogen abstraction reactions of CH + , which is formed endothermically (∆E/k B = 4620 K) (Hierl et al. 1997), in shocks or the dissipation of turbulence (Godard et al. 2014), followed by the dissociative recombination of CH + 2 : Being formed at high effective temperatures via non-thermal processes, CH + is not affected by fractionation and is believed to reflect the ambient C-isotopic ratio in the diffuse ISM. Hence, in low A V diffuse clouds, where turbulence driven reactions are favoured, CH, like its parent CH + , is not affected by fractionation. Therefore, the abundance ratio of the CH isotopologues does not deviate from the elemental ratio of the atomic carbon isotopes. As mentioned above, optical and UV absorption studies of CH require visually bright early type stars as background whose light is unhampered by interstellar extinction (Federman 1982;Sheffer et al. 2008). Owing to this, they can only probe the ISM in the solar neighbourhood out to a few kpc. In contrast, we observe supra-THz transitions of CH and 13 CH in absorption against the bright dust emission of far away star-forming regions (SFRs) out to the Galactic centre (GC) and beyond. Thus our absorption spectra not only probe the molecular envelopes of these sources, but also the diffuse and translucent interstellar clouds along their lines of sight over a wide range of Galactocentric radii. Due to the Galaxy's differential rotation, the absorption covers wide local standard of rest (LSR) velocity ranges. As a caveat, we mention that given, first, the expected 12 CH/ 13 CH ratios, which range from ≈20 in the GC to ≈90 at the Solar circle and even higher values beyond (Wilson & Rood 1994, and references therein) and, second, that even 12 CH lines are predominantly optically thin 3 we expect a detection of 13 CH absorption only toward the LSR velocities of the star forming regions studied, because these sources have far greater column densities than the intervening diffuse clouds along their lines of sight. In this paper, we present our search for 13 CH in the ISM along the line-of-sight (LOS) toward five high-mass SFRs in the Milky Way, Sgr B2(M), G34.26+0.15, W49(N), W51E and W3(OH) and discuss its use as an unbiased tool for benchmarking the 12 C/ 13 C Galactic gradient.

13 CH spectroscopy
Similar to CH, 13 CH conforms to Hund's case b coupling but differs in the nuclear spin, I, of the Carbon atom, I( 12 C)=0 and I( 13 C)=0.5. Due to the non-zero nuclear spin of the 13 C isotope, the total angular momentum J first couples with I 1 ( 13 C) to generate F 1 (= J + I 1 ) which further couples with the nuclear spin of the H atom, I 2 (H) = 0.5 to yield F (= F 1 + I 2 ). The energy level diagram of the 13 CH Λ-doublet transitions that are discussed in this study are displayed in Fig. 1. The hyperfine transitions of 13 CH that are presented in this study are highlighted using red and blue arrows. The proton hyperfine structure splittings are not included. Note that the level separations are not to scale. Table 1. Spectroscopic parameters for the N, J = 2, 3/2 → 1, 1/2 hyperfine structure transitions of 13 CH . Taken from Davidson et al. (2004).

Transition
Frequency effort has been expended in the laboratory to measure the rotational spectrum of 13 CH. The spectroscopic parameters of the rotational transitions of the 13 CH radical between the X 2 Π ground state have been measured using the technique of laser magnetic resonance (LMR) at FIR wavelengths by Davidson et al. (2004). The results of their experiments were combined with previously determined Λ-doublet intervals of the molecule by Steimle et al. (1986) to provide accurate predictions of the transition frequencies between the low-lying rotational levels and the ground state. The spectroscopic parameters of the observed N, J = 2, 3/2 → 1, 1/2 transitions are tabulated in Table 1. The Einstein A coefficients, A E,i j , were computed from the line strengths, S i j , using the relation: for spontaneous emission from an energy level i to j. Where ν i j is the corresponding frequency, F i is the total hyperfine quantum number, of level i and µ represents the electric dipole moment of 13 CH, µ( 13 CH) =1.46 Debye (Pickett et al. 1998).

Observations
Using the upGREAT instrument 4 (Risacher et al. 2016) on board SOFIA (Young et al. 2012), we observed the 2 Π 1/2 N, J = 2, 3/2 → 1, 1/2 Λ-doublet transitions of 13 CH over several flight series as a part of the observatory's cycle 7 campaign (under the open time project 07_0148 supplemented by guaranteed time observations). In this pilot study we carried out observations toward five well known SFRs Sgr B2(M), G34.26+0.15, W49(N), W51E, and W3(OH). Given that so far 13 CH has never been detected in the ISM before, the primary source selection criterion was the existence of a strong sub-mm and FIR background continuum. Secondly, we selected sources that are almost evenly spaced in Galactocentric distance between the GC and the Solar circle in order to obtain quantitative constraints on the Galactic 12 C/ 13 C abundance ratio gradient. Observational properties of the different sources are summarised in Tab. 2. The receiver configuration is comprised of the (7+7) pixel low frequency array (LFA) receiver module of upGREAT, in dual polarisation. Only data from the central pixels were used because the continuum targets are unresolved in our 13.5 FWHM beam 5 . The spectra were taken in the double-beam switch mode, chopping at a frequency of 2.5 Hz with a chop throw between 210 and 240 and a chop angle of 90 • (counter-clockwise against North), to account for both atmospheric fluctuations, as well as fluctuations that may arise from the instrument. The receiver was connected to an evolved version of the MPIfR Fast Fourier Transform Spectrometer described by Klein et al. (2012). This backend provides a 4 GHz bandwidth per pixel and a velocity resolution of 0.036 km s −1 (∼244.1 kHz) over 16384 channels. In this detection experiment, the double-sideband (DSB) receiver was tuned to 1997.4437 GHz (the strongest hfs transition of the 1997 GHz Λ-doublet) in the lower sideband. Three different intermediate-frequency (IF) settings were used in our observations in order to disentangle any contamination present in the bandpass, toward all sources except W3(OH) toward which we used only a single IF setting at 1.45 GHz in our pilot search. For G34.26+0.15, W49(N) and W51E the IF was tuned to 1.2, 1.4 and 1.6 GHz while for Sgr B2(M) the IF was tuned to 1.4, 1.6, and 1.8 GHz. The 13 CH spectra obtained along the LOSs to Sgr B2(M), G34.26+0.15, W51E and W49(N) taken with each of the three IF settings are displayed in Appendix. A. Using a forward efficiency of 0.97 the spectra were further calibrated using the KALIBRATE program (Guan et al. 2012). Fluctuations of the continuum level can either be due to telescope tracking problems, or due to gain drifts in the mixers. From a comparison between the continuum fluxes in the highfrequency array, operated in parallel at 4.7 THz and offering a 6 FWHM beam, we can rule out the former (which even if they occurred would not have an impact on the line-to-continuum ratio). Gain drifts that are faster than the calibration rate, however, affect the measurement of the atmospheric total power and therefore the applied transmission correction. Since they potentially distort the line-to-continuum ratio, a new calibration strategy was applied to analyse the gain fluctuations of the GREAT receiver, thanks to the larger amount of data now available. In a first step, the most stable off-centre pixels were identified by monitoring the line areas of a simultaneously  Notes. Columns are, left to right, source designation, equatorial coordinates, LSR velocity, signal band continuum brightness temperature derived by means of a DSB calibration, Galactocentric distance, heliocentric distance, flight id and flight leg duration. (a) The observing leg time (t obs ) refers to the total duration of time for which the source was observed. This includes the total (on+off) observing time as well as the overheads, which in total is typically a factor of two larger than the (on+off) time.
observed narrow telluric ozone line, which is largely insensitive to baseline uncertainties. Since the atmospheric emission arises in the near-field of all pixels, they must, therefore, all see the same ozone line flux. From this correlation analysis, only those pixel pairs whose line flux ratios were persistently close to unity were retained to determine the atmospheric transmission correction. The quality of the correlation analysis was ensured by forming closure products of the gain ratios, including those of the central pixel used (which for our case deviates from unity by at most 1.6%). In order to eliminate spectra in the central pixel affected by gain drifts, only data with closure products deviating from unity by at most 0.4% were retained to determine the continuum level. The DSB-continuum level is then determined by accounting for contributions from both the signal and image bands, which is added back to the spectra to obtain the correct line-to-continuum ratio. This calibration technique was applied not only to the 13 CH data presented in this work but also to the previously published 12 CH data (Wiesemeyer et al. 2018;Jacob et al. 2019), which thus were re-calibrated for use in our analysis, to avoid any inconsistencies. For the 12 CH spectra, we note that the continuum levels derived using the closure products are compatible with those derived using the standard calibration methods, except for W49(N). Using the closure product analysis we derive a continuum level of 14 K for the 12 CH spectrum toward W49(N) which agrees with the continuum level cited by Wiesemeyer et al. (2018) within a 20% uncertainty. It is to be noted that, in the analysis that follows, we adopt a value of 14 K as the continuum level of the 12 CH spectrum toward W49(N). Subsequently, the fully calibrated spectra obtained from both polarisations of the central pixel were converted to main-beam brightness temperature scale (using a main beam efficiency of 0.66) and analysed using the GILDAS-CLASS software 6 . The spectra were box-smoothed to ∼1.1 km s −1 wide velocity bins and the spectral baselines were corrected for by removing up to a second order polynomial. The resultant spectra obtained after carrying out a simple sideband deconvolution (discussed in Appendix A) are displayed in Figures 2 and 3. On average we achieved a noise level of ∼68 mK at a velocity resolution of 1.1 km s −1 after the sideband deconvolution. In the following paragraphs we briefly describe the LOS properties of the observed 13 CH spectra and compare them with previously obtained CH spectra.
Sgr B2(M): The unwavering nature of the absorption feature at υ∼64 km s −1 observed toward the envelope of Sgr B2(M) in each of the different IF frequency settings and the detection of its image band Λ-doublet counterpart near 2001 GHz with the absorption features displaying their expected relative intensities, solidifies our detection of 13 CH near 1997.44 GHz at this velocity. We compare the 13 CH spectrum with that of CH towards Sgr B2(M) published in Jacob et al. (2019). The CH spectrum has a true continuum of 15 K and is contaminated by C 3 absorption at 2004.833 GHz arising from the image band as indicated by the blue box in Fig. 2. The similarities between the CH and 13 CH spectra suggest the presence of weak blue-shifted sight-line absorption features in addition to the deep absorption seen near 64 km s −1 corresponding to the systemic LSR velocity of the molecular cloud. The shift of the atmospheric ozone feature at 2002.347 GHz in the image band toward the signal band features, by 60 km s −1 with each 0.2 GHz IF offset, leads to uncertainties while fitting polynomial baselines particularly for the weaker features. Hence, the true nature of the sight-line absorption features remains uncertain because of calibration and baseline uncertainties for the broad blended features. We will follow this up in future observations. G34.26+0.15: In order to avoid the blending of the atmospheric ozone feature from the image band with the signal band features, we used an IF setting of 1.2 GHz instead of 1.8 GHz. Similar to the 13 CH spectrum observed toward Sgr B2(M), we see absorption at the systemic velocity of the G34.26+0.15 molecular cloud at 58 km s −1 , in all three IF settings. However, we do not clearly detect 13 CH in foreground gas at velocities between 0 and 50 km s −1 .
W49(N): We used a setup similar to that used for our observations toward G34.26+0.15 for those toward W49(N). In addition to 13 CH absorption at the velocities corresponding to that of the molecular cloud, we see a weaker absorption feature close to 65 km s −1 , associated with the far-side crossing of the Sagittarius spiral arm. However, we do not include this feature in the analysis that follows because of its low signal-to-noise level.
W51E: By choosing the 1.4 GHz IF tuning as the nominal setting for carrying out the DSB deconvolution, we observe 13 CH absorption at the source intrinsic velocity of W51E near ∼62 km s −1 . Comparing this with the corresponding 12 CH spectrum which closely resembles that of the 2 Π 3/2 , J = 3/2 → 5/2 SH line at 1383.2 GHz, between 43-80 km s −1 (Neufeld et al. 2015), it is not clear whether 13 CH shows a second absorption component at 53 km s −1 at the given noise level. The weaker and narrower absorption seen at 26 km s −1 is merely a remnant feature from the image band.
Toward W3(OH) no 13 CH lines are detected above the noise (77 mK at a spectral resolution of 1.1 km s −1 ) in the spectrum at a continuum level of 5.3 K. The baseline-subtracted CH and 13 CH spectra toward W3(OH) are displayed in Appendix B.1. The corresponding CH spectrum is taken from Wiesemeyer et al. (2018) and has a continuum level at 5.4 K, prior to baseline removal.
Additionally we have checked whether the 12 C/ 13 C ratios derived by us are consistent with values derived using archival HIFI/Herschel data of the N, J = 1, 3/2 → 1, 1/2 transitions of CH and 13 CH near 532 GHz. While the 532 GHz CH line displays a deep absorption feature at the systemic velocity of the Sgr B2(M) molecular cloud with a peak temperature of 1.64 K (Qin et al. 2010), the corresponding 13 CH transition is not detected above a 3σ noise level of 0.33 K (at a spectral resolution of 0.5 km s −1 ) and yields a lower limit of 5 on the 12 C/ 13 C isotopic ratio. Similarly, we have analysed the 532 GHz CH spectra taken toward G34.26+0.15 discussed in Godard et al. (2012), W49(N), and W51E presented in Gerin et al. (2010) and W3(OH) from the Herschel archives 7 that also cover the corresponding 13 CH line frequencies. We find no signatures of 13 CH and, from the 3σ noise levels, are only able to derive lower limits to the 12 C/ 13 C ratio of 13, 32, 17, 68 for the above sources. We mention that, in contrast to the 2 THz lines, in the 532 GHz line, the molecular cores associated with these massive SFRs show complex line profiles with both emission and absorption components. In addition, the intensities and profiles of the 13 CH lines are quite uncertain as their HIFI spectra are affected by a standing wave and an unknown (and not yet assessed) level of potential line contamination. Thus the formal lower limits for the 12 C/ 13 C ratio derived from archival HIFI/Herschel data quoted above should be regarded with some caution.

Analysis and Discussion
High-resolution absorption line spectroscopy provides a powerful and straightforward to use tool for measuring column densities. The optical depth, τ, for a single absorption component can be calculated from the line to continuum ratio using where T l and T c represent the observed brightness temperatures of the line (prior to continuum subtraction) and the continuum, respectively. We have determined the optical depth profile, i.e., τ vs. υ LSR , using the Wiener filter fitting technique as described in Jacob et al. (2019). This fitting procedure first, fits the observed spectral profile by minimising the mean square error between the model and observations and then deconvolves the hyperfine structure from the observed spectrum using the hfs components' 7 See, http://archives.esac.esa.int/hsa/whsa/ relative weights. Other than the observed spectrum and the spectroscopic parameters of the line to be fit, the only other input parameter required by the Wiener filter technique is the spectral noise, which is assumed to be independent of the observed signal. The resulting deconvolved optical depth signature, τ decon , can then be converted into column density values per velocity channel, i using where the spectroscopic parameters g u (the upper level degeneracy), E u (the upper level energy) and A E (the Einstein A coefficient) remain constant for a given hyperfine transition. The partition function, Q is itself a function of the rotation temperature, T rot , which would be equal to the excitation temperature, T ex , under conditions of local thermodynamic equilibrium (LTE). Typically the rotational transitions of hydrides require large critical densities to be observable in emission. Since collisional rate coefficients are not presently available for 13 CH, we assume the critical density of this 13 CH line to be identical to the critical density of the corresponding CH transition, assuming a two-level system. Using hfs resolved collisional rate coefficients computed by Dagdigian (2018), we find the critical densities to be ∼2×10 9 cm −3 at 50-100 K. Within the diffuse and translucent interstellar clouds along the LOS (n = 10 − 500 cm −3 ) and the envelope of Sgr B2(M) (ranging from n∼10 3 -10 5 cm −3 ; (Schmiedeke et al. 2016)) the gas densities are much lower than the critical density, n crit , of these transitions making them sub-thermally excited. Hence we can assume the excitation temperature of such sub-thermally excited lines to be small and lower than the gas kinetic temperature. In our analysis we assume T rot to be equal to the temperature of the cosmic microwave background (CMB) radiation, T CMB = 2.728 K (Neill et al. 2014). Given this low rotation temperature and the inefficacy of purely collisional excitation, almost all of the CH molecules will reside in the molecule's ground state level. However, in the SFRs, radiative excitation by FIR dust radiation can affect the level populations (see, Neufeld et al. (1997) for the case of HF). Meaningful modelling of this is beyond the scope of the present study. In any case, given that the 12 CH and 13 CH lines under consideration here have, respectively, moderate and low optical depths, radiative excitation is expected to affect the observed transitions from both isotopologues in a similar way, leaving the 12 CH/ 13 CH intensity ratio unaltered. Given the knowledge of the frequency separation of the hfs transitions of 13 CH, we first deconvolve the hyperfine structure from the observed spectra using the Wiener filter formalism (briefly discussed above) and then derive column densities by adopting a T ex value equal to T CMB and integrating over the deconvolved velocity range of the line. We derive 13 CH column densities between ∼2 × 10 12 and 4.6 × 10 13 cm −2 toward the different sources. Given that the optical depths are computed directly from the line-to-continuum ratio, the uncertainties in the true continuum level give rise to systemic errors in the derived column densities. We assume a 10% error in the continuum level calibration based on the instrumental performance (Kester et al. 2017) and sideband dependence of the atmospheric transmission. The subsequently derived errors in the column densities (per velocity interval) are computed following the description presented in Jacob et al. (2019)   excitation temperature. We compare the 13 CH column densities derived here, over velocity intervals associated with the different molecular clouds, with those of their corresponding N, J = 2, 3/2 → 1, 1/2 hyperfine hfs transitions of CH near 2007 GHz discussed in Wiesemeyer et al. (2018) and Jacob et al. (2019). In Tab. 3, we present the derived 12 CH and 13 CH column densities, using the same excitation conditions by adapting Eq. 5, as well as the resulting 12 C/ 13 C isotopic ratio. For W3(OH), toward which the 13 CH line remains undetected, we derive a 2σ lower limit on the 12 CH/ 13 CH abundance ratio of > 58 over the velocity interval between (-55 --38) km s −1 . The 12 C/ 13 C isotopic abundance ratio has been determined towards the GC region using a wide variety of molecules ranging from simple species like CO, CN, H 2 CO and HCO + (Henkel et al. 1982;Langer & Penzias 1990;Savage et al. 2002) to more complex ones containing more than six atoms like CH 3 CH 2 CN, CH 3 CCH, CH 2 CHCN and NH 2 CHO (Belloche et al. 2016;Halfen et al. 2017) to name a few. The relatively lower values of the 12 C/ 13 C isotopic ratio towards the GC in comparison to the inner Galaxy, the local ISM and the solar system bears evidence to its advanced state of chemical evolution and reflects on its unique nucleosynthesis history. Moreover, the value of the GC strongly pivots the derived Galactic gradient. Therefore, as discussed by Halfen et al. (2017), it is essential to obtain more accurate measurements of the 12 C/ 13 C ratio towards the GC region since several of the derived molecular isotopic ratios can be hindered by effects of optical depth and saturation, chemical fractionation and selective photo-dissociation. The limits on the 12 C/ 13 C isotopic ratio derived using CH are consistent with those derived by Savage et al. (2002) using CN for our sample of sources except for G34.26+0.15. The latter difference could be due to difficulties in deriving the 12

>58 63±16
Notes. (a) Values taken from Milam et al. (2005) and references therein. (b) The column density for the non-detection was derived using the 2σ rms of level.
an underestimation of the column density) because, as the authors of the above study state, the observed relative line intensity ratios of the hfs components does not follow LTE. The comparable isotopic compositions of the two molecular species stems from their inter-linked formation routes 8 and suggests that CH similar to CN shows negligible amounts of fractionation.
Further, Halfen et al. (2017) estimated 12 C/ 13 C isotopic ratios between 19 and 33 using several different complex organic species and an average value of ∼24 ± 9 towards the 64 km s −1 component of the GC source Sgr B2(N). Within the errors, the average 12 C/ 13 C isotopic ratio derived by these authors is also consistent with the values derived from CH and CN. This presents solid evidence that the 13 C isotopic enrichment in more complex molecules must arise from progenitor molecules like CH and CN since the 13 C substitution of complex species via simple ion-molecule exchange reactions is not as straightforward as that of simple molecules.
In general, almost all the PDR models studied by  with varying physical parameters display a 12 CH/ 13 CH fractionation ratio that is enhanced at higher values of A v (≥ 1). The degree of fractionation is coupled with the FUV flux present in the models, the weaker the FUV flux, the greater is the fractionation ratio. The 12 C/ 13 C isotopic ratios we derive from CH show no indication of an enhanced value in comparison to those derived from for e.g., CN as shown in Tab. 3 and therefore no signature of fractionation. This is because toward the SFRs toward which we detect both 12 CH and 13 CH, the absorption from both isotopologues primarily traces these regions' extended envelopes, which are exposed to a significant UV field and whose densities have been estimated to be of the order of 10 3 cm −3 on parsec scales for Sgr B2(M) and other regions (Schmiedeke et al. 2016;Wyrowski et al. 2016), a value typical for a translucent molecular cloud. The gas-phase carbon reservoir in such regions is predominantly in either its atomic or ionised form and not locked up in CO, which means that there is enough 13 C and 13 C + present for ion-molecule exchange reactions to form 13 C-substituted CH.
The previously determined 12 C/ 13 C isotopic ratios suffer from large error bars that may either be due to opacity effects in the main isotopologue or other systematic effects. Therefore it is not clear whether the large dispersion in values between Galactocentric radii of 4 to 8 kpc, corresponding to regions with the most molecular mass content in the Milky Way (apart from the GC region), are due to actual cloud-cloud variations. If the spread is indeed due to opacity effects then the ground state rotational transitions of CH studied in this work which are free from such effects, should be well-suited to quantitatively constrain the 12 C/ 13 C ratio. By combining the 12 C/ 13 C ratio values derived using CH with those derived by Langer & Penzias (1990), Wouterloot & Brand (1996) 9 , Milam et al. (2005, Giannetti et al. (2014), Ritchey et al. (2011), andHalfen et al. (2017) and carrying out a weighted least squares fit, we derive a revised 12 C/ 13 C Galactic gradient of 12 C/ 13 C = 5.85(0.50) R GC + 15.03(3.40) 10 displayed in Fig. 4. The addition of our CH data points plus those from Wouterloot & Brand (1996), Ritchey et al. (2011), andGiannetti et al. (2014) results in values for the best fit slope and intercept that are, within the combined uncertainties, consistent with the values derived by Halfen et al. (2017). The small uncertainties of the CH data result in somewhat smaller formal uncertainties of the fitted values. 9 The authors of the cited article note that the discrepancy between the higher ratio derived form the J = 1−0 lines of 12 C 18 O and 13 C 18 O to the lower value from the J = 2 − 1 lines "is not yet explained, but may be due to the emission of the two transitions originating in different parts of the cloud with different excitation conditions." 10 The values in parentheses represent 1σ uncertainties.   4. Plot of 12 C/ 13 C isotope ratios as a function of Galactocentric distance, R GC (kpc). The filled red circles represent the 12 C/ 13 C ratio obtained using CH (this paper) while the unfilled black and purple triangles, grey pentagons, yellow circles, dark blue squares and green, and light blue diamonds are those obtained using isotopologues of C 18 O ( J = 1 − 0 and J = 2 − 1 transitions) (Wouterloot & Brand 1996;Giannetti et al. 2014), CN (Savage et al. 2002;Milam et al. 2005), CO (Langer & Penzias 1990), CH + (Ritchey et al. 2011), and complex organic molecules (Halfen et al. 2017), respectively. The black solid line represents the weighted fit to the data with the grey shaded region demarcating the 1σ interval of this fit. For comparison the fit obtained by Halfen et al. (2017) is displayed by the dashed blue line.

Conclusions
In this paper we report the first detections of 13 CH in the ISM, namely towards the Sgr B2(M), G34.26+0.15, W49(N), and W51E massive SFRs in the Milky Way. Hyperfine structure transitions connecting sub-levels of the 13 CH N, J = 2, 1/2 and 1, 1/2 Λ-doublet states with frequencies near 1997 GHz were observed in absorption using GREAT/SOFIA, which provides an avenue to observe frequency bands for which spectrally resolved observations were previously not possible with HIFI/Herschel or earlier missions. The detection of 13 CH along with observations of the main isotopologue CH towards the same sources opens a new, independent way for determinations of the 12 C/ 13 C isotopic abundance ratio across the Galaxy. We derive 12 C/ 13 C isotopic ratios for those of our target sources with a 13 CH detection and a lower limit for W3(OH) toward which we did not detect this isotopologue. Our values are in agreement with previous determinations made using varied chemical species and in particular CN. Our observations do not hint at a possible enhancement in the 12 C/ 13 C ratio derived from CH as it traces the more diffuse and translucent regions of the ISM in which CO is not the main reservoir of carbon. Furthermore, as its abundance peaks in regions of high UV radiation, CH is relatively unaffected by selective photo-dissociation and optical depth effects like saturation. Hence, measurements of the 12 C/ 13 C isotopic ratio based on the fundamental rotational lines of CH potentially reflect the actual 12 C/ 13 C ratio in the gas. In addition, knowledge of the 13 C substitution in CH will improve our understanding of interstellar chemistry because direct substitution of 13 C in more complex species is currently poorly understood and their observed 12/13 C isotopologue ratios are speculated to have their origin in simpler precursors like CH. Investigating a larger sample of SFRs at different Galactocentric radii for 13 CH will allow for a better constraint on the average 12 C/ 13 C abundance ratio value in the ISM and on the Galactic 12 C/ 13 C gradient, facilitating accurate Galactic chemical evolution models. However, the requirement of very high signal-to-noise ratios at high spectral resolutions that are required to detect the weak 13 CH absorption lines greatly restricts the selection of sources to those with strong continuum backgrounds for carrying out future, follow-up studies. Further, we hope that our study will encourage coordinated laboratory efforts resulting in refinements of the spectroscopic parameters of 13 CH, for which, e.g., several of the constants describing the fine structure of its transitions have not yet been well established (Halfen et al. 2008)..  which further validates our assumption of this line arising from H 2 S.
Despite pushing the 2001 GHz Λ-doublet transitions into the atmospheric ozone feature at 2002.347 GHz, the additional observing setup with an IF of 1.6 GHz was used to confirm the origin of the deeper absorption feature as being from the signal band. Using this setup it is clear that the deeper H 2 S absorption feature must arise from the signal band while further confirming our detection of 13 CH absorption toward the