Sulfur monoxide as a tracer of the Galactic $^{32}$S/$^{34}$S gradient

To date, the Galactic interstellar radial $^{32}$S/$^{34}$S gradient has only been studied with the CS isotopologs, which may be affected by uncertainties due to the use of a single tracer. As another abundant S-bearing molecules, SO and its isotopomer $^{34}$SO could be considered as tracers of the $^{32}$S/$^{34}$S ratio. We present the first systematic observations of SO and $^{34}$SO toward a large sample of molecular clouds with accurate distances, performed with the IRAM 30 m and the 10 m Submillimeter Telescope (SMT). With the IRAM 30 m, SO $2_2-1_1$ was detected in 59 of 82 sources ($\sim$82%), and $^{34}$SO $2_2-1_1$ in 8 sources ($\sim$10%). With the SMT 10 m, SO $5_5-4_4$ was detected in 136 of 184 sources ($\sim$74%), and $^{34}$SO $5_5-4_4$ in 55 of 77 strong SO sources ($\sim$72%). SO/$^{34}$SO ratios were derived for 8 ($2_2-1_1$) and 55 ($5_5-4_4$) sources. No correlation was found between the SO/$^{34}$SO ratio and heliocentric distance or $T_k$, suggesting negligible distance and fractionation effects. Both LTE and non-LTE analyses consistently suggest that the optical depth effect is also insignificant. $^{32}$S/$^{34}$S ratios from the $2_2-1_1$ transitions follow the increasing radial trend proposed by previous CS species measurements, while those from the $5_5-4_4$ lines are systematically lower. The lower transitions of SO and $^{34}$SO may be suitable tracers of $^{32}$S/$^{34}$S, though the detections are rare. Comparisons between measurements and Galactic chemical evolution model suggest that the nucleosynthesis prescriptions need to be revised in the low-metallicity regime, but more data for the outermost Galactic regions are crucial for drawing strong conclusions.