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Planetary systems are thought to be born in protoplanetary disks. Isotoperatios are a powerful tool for investigating the material origin and evolutionfrom molecular clouds to planetary systems via protoplanetary disks. However,it is challenging to measure the isotope (isotopologue) ratios, especially inprotoplanetary disks, because the emission lines of major species aresaturated. We developed a new method to overcome these challenges by usingoptically thin line wings induced by thermal broadening. As a first applicationof the method, we analyzed two carbon monoxide isotopologue lines, $^{12}$CO$3-2$ and $^{13}$CO $3-2$, from archival observations of a protoplanetary diskaround 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 thelocal interstellar medium, $\sim69$. It implies that an isotope exchangereaction occurs in a low-temperature environment with $\rm C/O>1$ . Incontrast, 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 differencein the binding energy of the isotopologues on dust grains and the CO gasdepletion processes. Our results imply that the gas-phase $^{12}$CO/$^{13}$COcan vary by a factor of ${ > 4}$ even inside a protoplanetary disk, andtherefore, can be used to trace material evolution in disks.

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