A new method for direct measurement of isotopologue ratios in protoplanetary disks: a case study of the $^{12}$CO/$^{13}$CO ratio in the TW Hya disk

Planetary systems are thought to be born in protoplanetary disks. Isotope ratios are a powerful tool for investigating the material origin and evolution from molecular clouds to planetary systems via protoplanetary disks. However, it is challenging to measure the isotope (isotopologue) ratios, especially in protoplanetary disks, because the emission lines of major species are saturated. We developed a new method to overcome these challenges by using optically thin line wings induced by thermal broadening. As a first application of the method, we analyzed two carbon monoxide isotopologue lines, $^{12}$CO $3-2$ and $^{13}$CO $3-2$, from archival observations of a protoplanetary disk around TW Hya with the Atacama Large Millimeter/sub-millimeter Array. The $^{12}$CO/$^{13}$CO ratio was estimated to be ${ 20\pm5}$ at disk radii of ${ 70-110}$ au, which is significantly smaller than the value observed in the local interstellar medium, $\sim69$. It implies that an isotope exchange reaction occurs in a low-temperature environment with $\rm C/O>1$ . In contrast, it is suggested that $^{12}$CO/$^{13}$CO is higher than $\sim{ 84}$ in the outer disk ($r > { 130}$ au), which can be explained by the difference in the binding energy of the isotopologues on dust grains and the CO gas depletion processes. Our results imply that the gas-phase $^{12}$CO/$^{13}$CO can vary by a factor of ${ > 4}$ even inside a protoplanetary disk, and therefore, can be used to trace material evolution in disks.