ALMA view of the $^{12}$C/$^{13}$C isotopic ratio in starburst galaxies

We derive molecular-gas-phase $^{12}$C/$^{13}$C isotope ratios for the central few 100 pc of the three nearby starburst galaxies NGC 253, NGC 1068, and NGC 4945 making use of the $\lambda$ $\sim$ 3 mm $^{12}$CN and $^{13}$CN $N$ = 1--0 lines in the ALMA Band 3. The $^{12}$C/$^{13}$C isotopic ratios derived from the ratios of these lines range from 30 to 67 with an average of 41.6 $\pm$ 0.2 in NGC 253, from 24 to 62 with an average of 38.3 $\pm$ 0.4 in NGC 1068, and from 6 to 44 with an average of 16.9 $\pm$ 0.3 in NGC 4945. The highest $^{12}$C/$^{13}$C isotopic ratios are determined in some of the outskirts of the nuclear regions of the three starburst galaxies. The lowest ratios are associated with the northeastern and southwestern molecular peaks of NGC 253, the northeastern and southwestern edge of the mapped region in NGC 1068, and the very center of NGC 4945. In case of NGC 1068, the measured ratios suggest inflow from the outer part of NGC 1068 into the circum-nuclear disk through both the halo and the bar. Low $^{12}$C/$^{13}$C isotopic ratios in the central regions of these starburst galaxies indicate the presence of highly processed material.


Introduction
Even though interstellar carbon isotope ratios are locally understood (e.g., Wilson & Rood 1994;Henkel et al. 1994a;Wilson 1999), in extragalactic space beyond the Magellanic Clouds they are almost unexplored. We lack information on objects outside the Local Group of galaxies tracing environments that drastically differ from those in the Milky Way and the Large Magellanic Cloud (LMC). We do not know whether our Galaxy is typical for its class of objects or whether its isotopic properties are exceptional. What would the latter imply? Moreover, will we see strong variations in isotopic ratios when observing nearby galaxies with high angular resolution?
In the past, observational data have been mostly obtained for the Galaxy and the Magellanic Clouds (e.g., Wouterloot & Brand A copy of the reduced datacubes is available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/629/A6 1996; Wouterloot et al. 2008;Wang et al. 2009). A surprising result is that the metal-poor outer Galaxy is not merely providing a "bridge" between the solar neighborhood and the even more metal-poor LMC. This is explained by the different age of the bulk of the stellar populations of the outer Galaxy and the LMC and can be exemplified by the 12 C/ 13 C and 18 O/ 17 O ratios, which are both a measure of "primary" versus "secondary" nuclear processing. While 12 C and 18 O are produced on rapid timescales primarily via He burning in massive stars, 13 C and 17 O are predominantly synthesized via CNO processing of 12 C and 16 O seeds from earlier stellar generations. The latter occurs on a slower timescale during the red-giant phase in low-and intermediatemass stars or novae (e.g., Wilson & Rood 1994;Henkel et al. 1994a,b).
Molecular spectroscopy is fundamentally important to constrain stellar nucleosynthesis and the chemical evolution of galaxies. Atomic spectroscopy of stellar or interstellar gas does not allow us to discriminate between different isotopic species. However, isotopic abundances are readily obtained by spectroscopy of molecular isotopologs (Henkel et al. 1994a). Locally, emphasizing carbon, observational constraints show very high molecular-gas-phase 12 C/ 13 C ratios ( 12 C/ 13 C given here and elsewhere represent the molecular gas) from molecular spectroscopy in the outer Galaxy (>100), high ratios in the local interstellar medium (ISM; ∼70), lower ones in the inner galactic disk and LMC (∼50), and a smaller value (∼20-25) in the galactic center region (e.g., Güsten et al. 1985;Wilson & Rood 1994;Henkel et al. 1994a;Wouterloot & Brand 1996;Wilson 1999;Wang et al. 2009). The solar system ratio (∼89; Wilson & Rood 1994;Henkel et al. 1994a) can be interpreted to represent conditions at a time when the local disk was 4.6 × 10 9 yr younger than today. Within the framework of "biased infall" (e.g., Chiappini et al. 2001) the galactic disk is slowly formed from the inside out, causing gradients in the abundances across the disk. The stellar 13 C ejecta, reaching the ISM with a time delay, are less dominant in the young stellar disk of the outer Galaxy than in the inner Galaxy and in the older stellar body of the LMC (for the LMC, see Hodge 1989). The solar-system ratio, referring to a younger disk with less 13 C, is consequently higher than that measured in the present local ISM.
While the 13 C-bearing molecular species can be safely assumed to be optically thin (with the possible exception of 13 CO), a basic problem is the optical depth of the 12 C bearing species (e.g., HCN, HCO + ; Nguyen et al. 1992;Wild et al. 1992;Gao & Solomon 2004;Jiang et al. 2011;Wang et al. 2014;Davis 2014;Jiménez-Donaire et al. 2017). Beam filling factors, τ( 12 CX), are in most cases unknown when it comes to extragalactic sources. With this in mind, a useful tracer should possess the following properties: -The tracer must be abundant, showing strong lines, to allow us to also detect the rare species, but not be so strong (i.e., opacity ∼1) as to cause optical thickness problems. -A useful check of the opacity should be provided by transitions exhibiting fine and hyperfine structure (fs and hfs, respectively). In such cases the splitting should be wide enough for the different components to be separated for a line emission with a width of several hundred kilometers per second, commonly encountered in external galaxies. -The components should show, in the optically thin limit, relative intensities as predicted by local thermodynamical equilibrium (LTE). Line ratios deviating from these values can then be used for optical depth estimates. -The tracer must be well understood theoretically and observationally; the former in terms of its physical and chemical properties related to photodissociation and fractionation, the latter by a systematic survey of 12 C/ 13 C ratios in galactic starforming regions. -Finally, there should be no blend with any other potential strong line of another species. Presently, there is only one molecule matching all these conditions, the cyanide radical (CN). The molecule C 2 H may come close but a systematic galactic survey based on this molecule has not yet been conducted. Previous observations show that CN is widespread in galactic molecular clouds (e.g., Rodríguez-Franco et al. 1998;Han et al. 2015;Gratier et al. 2017;Watanabe et al. 2017;Yamagishi et al. 2018) and a variety of other objects, including the circumstellar envelopes of evolved stars (e.g., Bachiller et al. 1997;Savage et al. 2002;Milam et al. 2005Milam et al. , 2009Hily-Blant et al. 2008;Adande & Ziurys 2012). It was detected for the first time in extragalactic sources by Henkel et al. (1988), and exhibits strong lines, allowing it to be easily detected outside the Galaxy. (e.g., Henkel et al. 1988Henkel et al. , 1990Henkel et al. , 1991Henkel et al. , 1994bHenkel et al. , 1998Henkel et al. , 2014Aalto et al. 2002Aalto et al. , 2007Wang et al. 2004Wang et al. , 2009Fuente et al. 2005;Pérez-Beaupuits et al. 2007García-Burillo et al. 2010;Chung et al. 2011;Martín et al. 2011;Aladro et al. 2013Aladro et al. , 2015Meier et al. 2014Meier et al. , 2015Sakamoto et al. 2014;Watanabe et al. 2014;Ginard et al. 2015;Nakajima et al. 2015Nakajima et al. , 2018Saito et al. 2015;König et al. 2016;Qiu et al. 2018;Wilson 2018).
Cyanide spectra are complex. Each CN rotational energy level with N > 0 is split into a doublet by spin-rotation interaction. Because of the spin of the nitrogen nucleus (I 1 = 1), each of these components is further split into a triplet of states. The 13 CN spectrum is further complicated by the spin of the 13 C nucleus (I 2 = 1/2). All this results in a very complex hfs splitting of the rotational lines. Numerically, it has been shown that carbon ratios resulting from CN measurements should not be affected by isotope selective photodissociation or chemical fractionation (Langer et al. 1984;Roueff et al. 2015). Observationally, this has been confirmed by Savage et al. (2002) and Milam et al. (2005).
Previous observations of CN in the Milky Way indicate a 12 C/ 13 C isotope ratio gradient with galactocentric distance (Savage et al. 2002;Milam et al. 2005), which agrees rather well with the gradient derived from measurements of CO and H 2 CO (e.g., Henkel et al. 1980Henkel et al. , 1982Henkel et al. , 1983Henkel et al. , 1985Henkel et al. , 1994aLanger & Penzias 1990Wilson & Rood 1994;Giannetti et al. 2014;Yan et al. 2019). This suggests that the 12 C/ 13 C isotope ratios obtained from CN are an excellent indicator of galactic chemical evolution (Milam et al. 2005). This is even more true for extragalactic targets, since CO and the millimeter-wave lines of H 2 CO do not allow for direct determinations of optical depths of the main species, while the centimeter-wave lines of H 13 2 CO are extremely weak.
So far, few 12 C/ 13 C isotope ratio determinations of extragalactic targets have been performed. In this study, we therefore carried out observations of three nearby starburst galaxies, NGC 253, NGC 1068, and NGC 4945. In Sects. 2 and 3, we introduce our targets, observations of CN, data reduction, and describe the main results. The resulting carbon isotope ratio derived from CN is then discussed in Sect. 4. Our main conclusions are summarized in Sect. 5.

Targets
The three objects we selected, namely NGC 253, NGC 1068, and NGC 4945, are prominent nearby starburst galaxies, exhibiting particularly strong molecular lines (e.g., Martín et al. 2006;Chou et al. 2007;García-Burillo et al. 2010, 2014Aladro et al. 2013;Meier et al. 2015;Henkel et al. 2018). The choice of the galaxies was made to have three of the strongest extragalactic line emitters and to cover a certain range of starbursts, that is, the transition from "moderate starbursts" (NGC 253 and NGC 4945) to more luminous infrared galaxies (LIRGs; NGC 1068). Single-dish spectral line surveys have been performed for all our selected starburst galaxies in the 3 mm band (e.g., Henkel et al. 1990Henkel et al. , 1994bWang et al. 2004;Aladro et al. 2013Aladro et al. , 2015Nakajima et al. 2018). The 12 C/ 13 C isotope ratio is ∼40 estimated from CN and CS Henkel et al. , 2014, but >81 obtained from C 2 H , in the starburst galaxy NGC 253. Interferometric measurements of 12 C 18 O/ 13 C 18 O in NGC 253 indicate a low value of ∼21 (Martín et al. 2019). This same ratio is ∼50 obtained from CN in NGC 1068 (Aladro et al. 2013) and a value of 40-50 was reported in NGC 4945 Henkel et al. 1994b;Wang et al. 2004). Toward M 82 and IC 342, Henkel et al. (1998) found 12 C/ 13 C > 40 and >30 from CN. For Arp 220 and Mrk 231, it appears to be 100 from CO and OH (González-Alfonso et al. 2012;Henkel et al. 2014), and for the Cloverleaf QSO it may be >100 from CO (Henkel et al. 2010). These determined values indicate a trend matching qualitative expectations of decreasing 12 C/ 13 C values with time and metallicity (Henkel et al. 2014). However, all classes of sources targeted so far only encompass one or two objects. Below follows a brief description of the selected targets. NGC 253, the Sculptor galaxy, an almost edge-on barred spiral (Pence 1981;Puche et al. 1991), is one of the most prolific infrared and molecular lighthouses of the entire extragalactic sky. At a distance of ∼3.9 Mpc (e.g., Mouhcine et al. 2005;Rekola et al. 2005), it is a prime example of a galaxy with a nuclear starburst devoid of an active galactic nucleus (AGN; e.g., Ulvestad & Antonucci 1997;Henkel et al. 2004). Because of the exceptional strength of its molecular lines, NGC 253 was selected as the target of choice for the first unbiased molecular line survey of an extragalactic source (Martín et al. 2006). It is therefore a highly suitable target for this study.
NGC 1068, a local LIRG and a prototypical Seyfert 2 galaxy with a starburst at a distance of ∼14.4 Mpc (Bland-Hawthorn et al. 1997), is one of the best extragalactic targets for studying the physical and chemical properties of the ISM in the vicinity of an AGN. Numerous molecular line observations have targeted the circumnuclear molecular ring of NGC 1068 and the effect of nuclear activity on its ISM (e.g., Schinnerer et al. 2000;Usero et al. 2004;García-Burillo et al. 2010, 2014Krips et al. 2011;Aladro et al. 2013;Viti et al. 2014;Wang et al. 2014;Qiu et al. 2018). Water maser emission has been observed forming an edge-on disk in the circumnuclear environment of NGC 1068 (e.g., Greenhill et al. 1996;Gallimore et al. 1996Gallimore et al. , 1997Gallimore et al. , 2001. NGC 4945, at a distance of ∼3.8 Mpc (e.g., Karachentsev et al. 2007;Mould & Sakai 2008), has an active Seyfert 2 nucleus and is, like NGC 253, an almost edge-on spiral galaxy. Its central region is known to show a rich molecular spectrum hosting not only a nuclear starburst but also an AGN (e.g., Marconi et al. 2000;Yaqoob 2012). Past molecular single-dish and interferometric observational studies exist for CO, CS, CN, HCN, HNC, HCO + , CH 3 OH, and H 2 CO (e.g., Henkel et al. 1990Henkel et al. , 1994bHenkel et al. , 2018Dahlem et al. 1993;Mauersberger et al. 1996;Curran et al. 2001;Wang et al. 2004;Chou et al. 2007;Hitschfeld et al. 2008;Green et al. 2016;McCarthy et al. 2018). Water megamaser emission has been observed in the nucleus of NGC 4945 (Greenhill et al. 1997).

Observations
Our observations were carried out from 2014 December to 2015 January with the Atacama Large Millimeter/submillimeter Array (ALMA) in Band 3 (Project: 2013.1.01151.S). During the observations, 36-40 12 m antennas were employed in a compact configuration with baselines ranging from 15 to 349 m. For each source, the observations took about 30 min and 1 h for 12 CN and 13 CN, respectively. The CN N = 1-0 transition consists of nine hyperfine components blended into two groups, with the stronger group representing the J = 3/2-1/2 transitions and the weaker group the J = 1/2-1/2 transitions. The 12 CN N = 1-0 (J = 1/2-1/2 and 3/2-1/2) and 13 CN N = 1-0 (J = 1/2-1/2 and 3/2-1/2) transitions have intensity weighted rest frequencies of 113.191, 113.491, 108.658, and 108.780 GHz, respectively, when LTE line ratios and optically thin emission are adopted. On each, the 12 CN and the 13 CN line, a spectral window was centered, with a bandwidth of 1875 MHz and a frequency resolution of 7812.5 kHz, corresponding to a channel width of ∼21 km s −1 . Basic observational parameters as well as phase center coordinates are listed in Table 1. The 12 CN data of NGC 253 were not part of our project. Instead, Meier et al. (2015) observed NGC 253 in 12 CN N = 1-0 with ALMA Band 3 (Project: 2011.0.00172.S). Quality and in particular beam sizes of these data match our ALMA observations well. 12 CN N = 1-0 data of NGC 253 are therefore taken from Meier et al. (2015) in this work. The observed spectra toward the central positions of NGC 253, NGC 1068, and NGC 4945 are shown in Fig. 1.
Due to spatial filtering, the missing flux, that is flux of large-scale structures not sampled by the interferometer, may affect 12 CN/ 13 CN line ratios. To evaluate the missing flux we reconstruct our ALMA data with beams of ∼22 (IRAM 30 m; Henkel et al. 2014;Aladro et al. 2015), ∼15 (NRO 45 m; Nakajima et al. 2018), and ∼44 (SEST 15 m; Wang et al. 2004) for NGC 253, NGC 1068, and NGC 4945, respectively. We find that ∼89% and ∼86% of the 12 CN and 13 CN integrated flux observed by single-dish telescopes is recovered for NGC 253 by our ALMA data, respectively. Only ∼30% and ∼53% of the 12 CN and 13 CN single-dish integrated flux of NGC 1068 is recovered, respectively. However, as mentioned above, the 13 CN N = 1-0 features observed with the 45 m NRO telescope (Nakajima et al. 2018) are weak and show large uncertainties. For NGC 4945, ∼63% of the 12 CN single-dish integrated flux is recovered. We do not evaluate the missing flux of 13 CN in NGC 4945 because (as already mentioned) the 13 CN N = 1-0 transition was not detected with the 15 m SEST (Wang et al. 2004). In their Table 2, Wang et al. (2004) provide an upper limit (3 sigma) to the 13 CN N = 1-0 line intensity, so at least ∼40% is recovered by our ALMA data. Based on similar missing flux of our 12 CN and 13 CN data in NGC 253 and NGC 1068, we note that 13 CN N = 1-0 is likely showing a less extended morphology (see Sect. 3.1) only because it is more rapidly reaching intensities below the detection threshold outside the line peaks. Therefore, our 13 CN data may cover a single-dish integrated flux fraction which is similar to that of 12 CN in NGC 4945. With similar missing flux levels related to our 12 CN and 13 CN data in NGC 253 and NGC 1068, which is based on a comparison of our interferometric measurements with previously published singledish observations, missing flux appears to affect 12 CN/ 13 CN line ratios in NGC 253, NGC 1068, and NGC 4945 only weakly.
There may be line blending with the CH 3 OH (0 0 -1 −1 E) transition at 108.894 GHz, 114 MHz (∼300 km s −1 ) away from the group of 13 CN (N = 1-0; J = 3/2-1/2) lines centered at 108.780 GHz (see Sect. 2 and Fig. 1). However, CH 3 OH can be clearly identified in most locations of NGC 253 and NGC 4945, which indicates that the I( 12 CN)/I( 13 CN) ratios are at most only weakly affected by CH 3 OH in these two galaxies. For NGC 1068, the typical line widths of 13 CN are broader (∼170 km s −1 ) and CH 3 OH cannot be identified in most locations. This could indicate that the I( 12 CN)/I( 13 CN) ratio may be underestimated from our ALMA data in NGC 1068. The slightly less extended 13 CN distributions also addressed in Sect. 3.1 when compared to 12 CN may merely indicate that the minimum detectable molecular H 2 column density is higher than in the case of 12 CN with its higher fractional abundance (see also Sect. 3.3).
A6, page 4 of 10 . The contour levels are from 20% to 100% with steps of 10% for 12 CN and 13 CN of the peak intensity. The 12 CN peak intensities are 71.9, 35.8, and 26.4 Jy beam −1 km s −1 , and the 13 CN peak intensities are 3.0, 1.1, and 3.2 Jy beam −1 km s −1 in NGC 253, NGC 1068, and NGC 4945, respectively. For the 12 CN map of NGC 253, see also Meier et al. (2015). The pixel size of each image is 0.3 × 0.3 . The synthesized beam of each image is shown in the lower left corner.

Distribution of 12 CN and 13 CN
The integrated intensity distributions of 12 CN and 13 CN in NGC 253, NGC 1068, and NGC 4945 are shown in Fig. 2. In all three galaxies 12 CN shows extended distributions, in agreement with previous observations of 12 CN in galaxies (e.g., Henkel et al. 1988;García-Burillo et al. 2010;Meier et al. 2014;Sakamoto et al. 2014;Ginard et al. 2015;Nakajima et al. 2015;Saito et al. 2015;Wilson 2018). This is also consistent with previous observational results for other gas tracers such as for example 13 CO, C 18 O, CS, HCN, or HCO + toward our sources (e.g., Krips et al. 2011;Sakamoto et al. 2011;García-Burillo et al. 2014;Viti et al. 2014;Meier et al. 2015;Henkel et al. 2018;Tan et al. 2018;Martín et al. 2019). Weak 12 CN emission is detected in the spiral arms of NGC 1068 (see Fig. 2). 13 CN is only detected in the central regions of NGC 253, NGC 1068, and NGC 4945, and shows slightly less extended distributions than 12 CN (see also the end of Sect. 2.4).
3.2. 12 CN/ 13 CN line ratios 12 CN/ 13 CN line ratio maps of NGC 253, NGC 1068, and NGC 4945 are shown in Fig. 3. The line ratios are calculated using velocity-integrated intensities where the 13 CN lines are detected with S /N 5σ. The I( 12 CN)/I( 13 CN) ratios range from 19 to 53 with an average of 30.0 ± 0.2 (errors given here and elsewhere are standard deviations of the mean) in NGC 253, from 20 to 47 with an average of 31.4 ± 0.3 in NGC 1068, and from 6 to 25 with an average of 11.5 ± 0.1 in NGC 4945. High ratios (>30) are obtained in the outskirts of the region analyzed by us in NGC 253. This shows that low ratios (<30) associate with 13 CN peak emission in NGC 253. Gradients are seen from the center to the northeastern and to the southwestern region of NGC 1068. Two locations in the northeast and southwest (see Table 2 and Sect. 4.2) have a low ratio (<25). For NGC 4945, low ratios (<15) associate with 13 CN peak emission and the northeastern region and high ratios (>15) are located in the outskirts and the southwestern region. One should note that the 13 CN emission is weak and shows low S/Ns on the edges of our three targets. This may lead to large uncertainties of I( 12 CN)/I( 13 CN) ratios in these locations.
We averaged all pixels in NGC 253, NGC 1068, and NGC 4945 for which the 13 CN line is detected with S /N 5σ. The line-integrated intensity ratios of the two 12 CN N = 1-0  features are 1.58 ± 0.11, 1.70 ± 0.02, and 1.68 ± 0.25 in NGC 253, NGC 1068, and NGC 4945, respectively, which is slightly lower than that for LTE and optically thin emission. Following the method applied by Wang et al. (2004), the optical depth of the 12 CN N = 1-0 lines can be obtained from the integrated intensity ratio of 12 CN (3/2-1/2)/(1/2-1/2) as where τ 1 and τ 2 are the optical depths of 12 CN J = 3/2-1/2 and 1/2-1/2, respectively, and τ 1 = 2τ 2 (see Skatrud et al. 1983 for relative LTE intensities under optically thin conditions). From the above average integrated intensity ratios of the two 12 CN N = 1-0 features the derived optical depths of 12 CN J = 3/2-1/2 are 1.1, 0.7, and 0.8 in NGC 253, NGC 1068, and NGC 4945, respectively. Opacities of 12 CN at 13 CN peaks and outskirts are also calculated in Table 2. These suggest that the opacity of 12 CN N = 1-0 slightly affects the line intensity ratios of 12 CN/ 13 CN in our three selected starburst galaxies. For 13 CN N = 1-0, the corresponding average line integrated intensity ratios are 1.04 ± 0.08, 1.03 ± 0.14, and 1.25 ± 0.01, which is consistent with LTE and optically thin emission considering the uncertainties of our interferometric measurements. In this work we assume that the 13 CN N = 1-0 line is optically thin in all of our three studied objects.
(2) range from 30 to 67 with an average of 41.6 ± 0.2 in NGC 253, from 24 to 62 with an average of 38.3 ± 0.4 in NGC 1068, and from 6 to 44 with an average of 16.9 ± 0.3 in NGC 4945 (see Table 3). The uncertainty of these 12 C/ 13 C isotope ratios is ∼10%, which is mainly caused by the absolute flux calibration error of ∼5%.

Comparison to previous 12 C/ 13 C isotopic ratio measurements
As deduced in Sect. 3.4, with ALMA we find average 12 C/ 13 C isotope ratios of 41.6 ± 0.2, 38.3 ± 0.4, and 16.9 ± 0.3 in the nuclear disks of NGC 253, NGC 1068, and NGC 4945, respectively (see Table 3). We compare our ALMA-measured 12 C/ 13 C isotope ratios with previous results obtained from single-dish observations in Table 3. For NGC 253 and NGC 1068, our average measured 12 C/ 13 C isotope ratios agree well with those obtained from the single-dish observations Henkel et al. , 2014Nakajima et al. 2018). However, our ALMA-measured 12 C/ 13 C isotope ratio is significantly lower than that obtained from the single-dish observations in NGC 4945 Henkel et al. 1994b;Wang et al. 2004). This may be caused by several factors. Previous singledish observations may include a lot of material from outside the nuclear disk, that is, from the bar extending from galactocentric radii of 100-300 pc and from the spiral arms even farther out (see the sketch in Henkel et al. 2018). Our ALMA data cover a smaller region with galactocentric radii out to ∼175 pc. The 12 CN distribution appears to be complex in NGC 4945 (see Sect. 3.1). The typical line widths of 12 CN are ∼50 km s −1 at a velocity of ∼700 km s −1 and ∼150 km s −1 at a velocity of ∼450 km s −1 in the northeastern and southwestern regions of its highly inclined (i ∼ 75 • ) nuclear disk (see our Fig. 1 or Figs. 5, 11, and 13 in Henkel et al. 2018). Perhaps, the starburst is still young and the gas moving outwards through the nuclear disk is a remnant of formerly quiescent gas highly enriched in 13 C by AGB stars through the CNO cycle (like in our galactic center), while 12 C enrichment from young massive stars has not yet taken over in a substantial way.
Considering the above-mentioned uncertainties of our interferometric and previous single-dish observations in the 12 CN and 13 CN N = 1-0 transitions, our averaged 12 C/ 13 C isotope ratios in NGC 253 (∼400 pc) and NGC 1068 (∼500 pc) confirm previous results from single-dish observations. We conclude that the averaged 12 C/ 13 C isotope ratios are ∼40-50 in NGC 253 and NGC 1068 and ∼20-50 in NGC 4945. The apparent discrepancy between the single-dish and our interferometric results in NGC 4945 will be further discussed in Sect. 4.3. For NGC 4945 (∼350 pc), our ALMA data offer a first value for the ∼200 pcsized nuclear disk, while the bar, the inner spirals, and the nuclear ∼50 pc are still waiting for a dedicated measurement. Further observations combining our 12 m ALMA with 7 m ACA and Total Power (TP) data of CN and eventually also other molecules and their isotopologs could therefore provide further progress in the determination of accurate 12 C/ 13 C isotope ratios for the various distinct morphological components.
Presently, high-resolution (∼3 ) observations of C 18 O with ALMA toward NGC 253 suggest a low 12 C/ 13 C isotope ratio of ∼21±6 (Martín et al. 2019), which is a factor of approximately two lower than our results obtained from CN. We compare our ALMA measured 12 CN/ 13 CN ratio map with their results from 12 C 18 O/ 13 C 18 O ratios in NGC 253 (see Fig. 3 in Martín et al. 2019). This comparison shows that the lowest 12 C 18 O/ 13 C 18 O ratios are associated with the northeastern hotspot which agrees with our results derived from 12 CN/ 13 CN ratios, but the distributions of 12 CN/ 13 CN and 12 C 18 O/ 13 C 18 O ratios are slightly different in other locations. The cause(s) of these discrepancies may be different beam sizes or different molecular distributions due to chemistry or critical densities, and could be settled by the combination of 12-m, 7-m, and TP measurements, making use of all the instruments available at the ALMA site.

Variation of the 12 C/ 13 C isotopic ratio
In our Galaxy, previous observations of H 2 CO, CO, and CN indicate the presence of a 12 C/ 13 C isotope ratio gradient and further suggest a significant dispersion at a given galactocentric radius (e.g., Henkel et al. 1980Henkel et al. , 1982Henkel et al. , 1983Henkel et al. , 1985Henkel et al. , 1994aLanger & Penzias 1990Wilson & Rood 1994;Savage et al. 2002;Milam et al. 2005;Giannetti et al. 2014). This is expected in an inside-out formation scenario for our Galaxy and in view of radial gas streaming and potential cloud-to-cloud variations due to local supernovae or ejecta from late-type stars (e.g., Milam et al. 2005;Henkel et al. 2014). However, even in the galactic center region isotope ratios are not everywhere the same as recently discovered by Riquelme et al. (2010) and Zhang et al. (2015). The data of the former authors indicate that gas from the halo is accreted to the disk and from the outskirts of the disk to regions closer to the galactic center (Riquelme et al. 2010).
In analogy to the galactic center region, our extragalactic ALMA data also reveal spatial variations of the 12 C/ 13 C isotopic ratio within the inner ∼400, ∼500, and ∼350 pc-sized regions of NGC 253, NGC 1068, and NGC 4945, respectively. As mentioned in Sect. 3.4, higher line ratios of 12 CN/ 13 CN indicate higher 12 C/ 13 C isotopic ratios. Therefore, the ratio maps can be used as a proxy for the relative 12 C/ 13 C isotopic ratio. 12 CN/ 13 CN line ratio maps and histograms of NGC 253, NGC 1068, and NGC 4945 are shown in Figs. 3 and 4, respectively. Variations of the 12 CN/ 13 CN line ratio as mentioned in Sect. 3.2 indicate that the highest 12 C/ 13 C isotopic ratios are located in some of the outskirts of the three starburst galaxies while the lowest ratios associate with galactic central regions and/or 13 CN peak emission. The velocity components in the southwest of NGC 253 and NGC 4945 (Henkel et al. 2014(Henkel et al. , 2018 suggest higher 12 C/ 13 C isotopic ratios than in the northeast. The 12 C/ 13 C isotopic ratio  varies by factors of approximately two to three in NGC 253 and NGC 1068 and even about seven in NGC 4945 (see Fig. 4 and Table 3). While these extreme differences may in part be due to low 13 CN S/Ns, the differences are too large to be entirely a consequence of this effect (see Table 2).
For NGC 253, integrated intensities of 13 CN are highest in two hotspots, located symmetrically with respect to the nucleus, one in the northeast and the other one in the southwest. The lowest 12 C/ 13 C isotopic ratios are associated with these two hotspots (see Fig. 3) corresponding to centimeter and millimeter continuum peak emission (e.g., Turner & Ho 1985;Ulvestad & Antonucci 1997;Sakamoto et al. 2011;Krips et al. 2016;Mangum et al. 2019). The gas at these locations may be CNO-processed by intermediate-mass stars in the more distant past. Two locations with low 12 C/ 13 C isotopic ratios in the northeast (3.3 , 1.8 ; offsets relative to our reference position; see Table 1) and southwest (-3.6 , -0.3 ) of NGC 1068 (see Figs. 3 and 5, and Table 2) associate with two outflow knots OUT-III and II , respectively, meaning that the highly processed gas has moved away from the center, while less processed gas may be infalling from the outer part of NGC 1068 into (at least the outer part of) the circum-nuclear disk (CND) through both the halo and the bar, and the CND is dominated by the outflowing motion. The decline of the 12 C/ 13 C isotopic ratio in these locations may be influenced by the outflow from the AGN and/or by processed material near the AGN. One should note that the two outflow knots OUT-II and III are identified with ∼1 resolution C 2 H data by García-Burillo et al. (2017), which corresponds to a ∼4.5 times higher resolution (with respect to beam area) than the CN data presented here. Beam dilution effects may not be negligible. Low 12 C/ 13 C isotopic ratios in the northeast of NGC 4945 show similar values to those in the nuclear region (see Fig. 3), which indicates that it may be strongly affected by highly processed outflowing material from the nuclear region (for this, see Henkel et al. 2018) having undergone substantial star formation in the past.
4.3. The 12 C/ 13 C isotopic ratio evolution in starburst galaxies The 12 C/ 13 C isotope ratio is a useful probe of the chemical evolution of galaxies (e.g., Milam et al. 2005;Martín et al. 2010;Henkel et al. 2014). It is believed to be a direct measure of primary to secondary nuclear processing (Wilson & Rood 1994).
The 12 C/ 13 C isotope ratio is expected to decline with time (e.g., Prantzos et al. 1996;Hughes et al. 2008;Martín et al. 2010;Henkel et al. 2014;Romano et al. 2017). This leads to the very low ratios in our galactic center region. However, in case of a starburst, triggered by a bar or by a merger, gas from outside with higher ratios is flowing into the central region of a galaxy, enhancing the 12 C/ 13 C isotope ratio. A few million years after the start of a starburst, this effect will be strengthened by the ejecta from massive stars. A top-heavy stellar initial mass function could make this effect even more pronounced (e.g., Romano et al. 2017;Zhang et al. 2018).
The inflow scenario discussed for starbursts may even lead to higher 12 C/ 13 C ratios for ultraluminous infrared galaxies (ULIRGs) since such objects have more powerful inflows (e.g., Toyouchi & Chiba 2015;Yabe et al. 2015;Falstad et al. 2017). Indeed, ULIRGs have not only a higher 12 C/ 13 C ratio, but are also deviating from the canonical mass-metallicity relation in the sense of having a lower metallicity for their mass or a higher mass for their metallicity (Pereira-Santaella et al. 2017). More moderate starburst galaxies have experienced less inflow, which may suggest lower 12 C/ 13 C isotope ratios. In comparison, our Galaxy shows only weak signs of inflow (e.g., Morris & Serabyn 1996;Riquelme et al. 2010), which is reflected in the lower 12 C/ 13 C isotope ratios measured in its central molecular zone. The CN data presented here indicate that the averaged 12 C/ 13 C isotope ratios in the nuclear regions of NGC 253 and NGC 1068 are higher than in our galactic center region. Nevertheless, the averaged 12 C/ 13 C isotope ratios in our selected nearby starburst galaxies are lower than previous observational results in the well-studied ULIRGs Arp 220 and Mrk 231 (∼100; González-Alfonso et al. 2012;Henkel et al. 2014), and also in the high-z Cloverleaf ULIRG/QSO ( 100; Henkel et al. 2010). This confirms the trend of declining 12 C/ 13 C values with time and metallicity proposed by Henkel et al. (2014).
Measurements of the 12 C/ 13 C isotope ratio based on CN lines have the potential to reveal the degree of gas processing in the nuclear regions of starburst galaxies. More galaxies are needed to study nucleosynthesis, to constrain galaxy dynamics, and to discriminate between different evolutionary stages to more closely follow the secular decline of 12 C/ 13 C ratios that is occasionally interrupted by inflow and starburst activity. With ALMA it is possible to extend such studies to objects at greater distances.

Summary
We measured the 12 C/ 13 C isotopic ratio in the nuclear regions of three nearby starburst galaxies NGC 253, NGC 1068, and NGC 4945 making use of the 12 CN and 13 CN N = 1-0 lines in the ALMA Band 3 at frequencies near 110 GHz. The main results can be summarized as follows. 1. The 12 C/ 13 C isotopic ratios derived from the 12 CN and 13 CN line ratios range from 30 to 67 with an average of 41.6 ± 0.2 in NGC 253, from 24 to 62 with an average of 38.3 ± 0.4 in NGC 1068, and from 6 to 44 with an average of 16.9 ± 0.3 in NGC 4945. The 12 C/ 13 C isotopic ratios vary by factors of approximately two to three in NGC 253 (∼400 pc) and NGC 1068 (∼500 pc) and about seven in NGC 4945 (∼350 pc). The large scatter of values, particularly in NGC 4945, is certainly in part a consequence of the limited sensitivity of our data. Nevertheless, the variations are too large to be only caused by this effect, suggesting the pres-ence of real variations, as recently found in our galactic center region. 2. The highest 12 C/ 13 C isotopic ratios are located in the outskirts of the nuclear regions of the three starburst galaxies. The lowest ratios are associated with the northeastern and southwestern molecular peaks of NGC 253, the northeastern and southwestern edge of the mapped region in NGC 1068, and the very center of NGC 4945. 3. The measured 12 C/ 13 C isotopic ratios in NGC 1068 indicate that the highly processed gas has moved away from the center and less processed gas may be infalling from the outer part of NGC 1068 into the CND through both the halo and the bar. 4. Low 12 C/ 13 C isotopic ratios in the central regions of these starburst galaxies indicate the presence of highly processed material. 5. Our results agree with the scenario of 12 C/ 13 C ratios slowly decreasing in galaxies with time.