Direct measurements of carbon and sulfur isotope ratios in the Milky Way

With the IRAM 30-m telescope, we performed observations of the $J$ = 2-1 transitions of CS, C$^{33}$S, C$^{34}$S, C$^{36}$S, $^{13}$CS, $^{13}$C$^{33}$S, and $^{13}$C$^{34}$S as well as the $J$ = 3-2 transitions of C$^{33}$S, C$^{34}$S, C$^{36}$S, and $^{13}$CS toward a large sample of 110 HMSFRs. We measured the $^{12}$C/$^{13}$C, $^{32}$S/$^{34}$S, $^{32}$S/$^{33}$S, $^{32}$S/$^{36}$S, $^{34}$S/$^{33}$S, $^{34}$S/$^{36}$S, and $^{33}$S/$^{36}$S abundance ratios with rare isotopologues of CS, thus avoiding significant saturation effects. With accurate distances obtained from parallax data, we confirm previously identified $^{12}$C/$^{13}$C and $^{32}$S/$^{34}$S gradients as a function of galactocentric distance (RGC). In the CMZ $^{12}$C/$^{13}$C ratios are higher than suggested by a linear fit to the disk values as a function of RGC. While $^{32}$S/$^{34}$S ratios near the Galactic center and in the inner disk are similar, this is not the case for $^{12}$C/$^{13}$C, when comparing central values with those near RGC of 5 kpc. As was already known, there is no $^{34}$S/$^{33}$S gradient but the average ratio of 4.35~$\pm$~0.44, derived from the $J$ = 2-1 transition lines of C$^{34}$S and C$^{33}$S, is well below previously reported values. A comparison between solar and local interstellar $^{32}$S/$^{34}$S and $^{34}$S/$^{33}$S ratios suggests that the solar system may have been formed from gas with a particularly high $^{34}$S abundance. For the first time, we report positive gradients of $^{32}$S/$^{33}$S, $^{34}$S/$^{36}$S, $^{33}$S/$^{36}$S and $^{32}{\rm S}/^{36}{\rm S}$ in our Galaxy. The predicted $^{12}$C/$^{13}$C ratios from the latest GCE models are in good agreement with our results, while $^{32}$S/$^{34}$S and $^{32}$S/$^{36}$S ratios show larger differences at larger RGC, $^{32}$S/$^{33}$S ratios show an offset across the entire inner 12 kpc of the Milky Way.