  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.
