High abundance ratio of $^{13}$CO to C$^{18}$O toward photon-dominated regions in the Orion-A giant molecular cloud

Abstract : $Aims$.We derive physical properties such as the optical depths and the column densities of $^{13}$CO to C$^{18}$O to investigate the relationship between the far ultraviolet (FUV) radiation and the abundance ratios between $^{13}$CO to C$^{18}$O. $Methods$. We have carried out wide-field (0.4 deg$^2$) observations with an angular resolution of 25.8''(∼0.05 pc) in $^{13}$CO (J = 1–0) and C$^{18}$O (J = 1–0) toward the Orion-A giant molecular cloud using the Nobeyama 45 m telescope in the on-the-fly mode. $Results$. Overall distributions and velocity structures of the $^{13}$CO to C$^{18}$O emissions are similar to those of the $^{12}$CO (J = 1–0) emission. The optical depths of the $^{13}$CO to C$^{18}$O emission lines are estimated to be 0.05<$\tau_{13}_{CO}$<1.54 and 0.01<$\tau_{C}^{18}$_O$<0.18, respectively. The column densities of the $^{13}$CO and C$^{18}$O emission lines are estimated to be 0.2×10$^{16}$