A new measurement of the Galactic $^{12}$C/$^{13}$C gradient from sensitive HCO$^+$ absorption observations

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 suffer 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$\pm$5) is consistent with those obtained from CH$^+$. Two measurements toward the Galactic Center are 42.2$\pm$1.7 and 37.5$\pm$6.5. Though the values are a factor of 2$\sim$3 higher than those derived from dense gas tracers (e.g., H$_2$CO, complex organic molecules) toward Sagittarius (Sgr) B2 regions, our results are consistent with the absorption measurements from c-C$_3$H$_2$ toward Sgr B2 ($\sim$40), and those from CH$^+$ toward Sgr A$^*$ and Sgr B2(N) ($>$30). We calculate a new Galactic $^{12}$C/$^{13}$C gradient of (6.4$\pm$1.9)$R_{\rm GC}$/kpc+(25.9$\pm$10.5), and find an increasing trend of $^{12}$C/$^{13}$C gradient obtained from high-density to low-density gas tracers, suggesting opacity effects and chemical fractionation may have a strong impact on the isotopic ratios observed at high-density regions.