Rapid Evolution of Volatile CO from the Protostellar Disk Stage to the
  Protoplanetary Disk Stage
  Recent observations show that the CO gas abundance, relative to H$_2$, in
many 1-10 Myr old protoplanetary disks may be heavily depleted, by a factor of
10-100 compared to the canonical interstellar medium value of 10$^{-4}$. When
and how this depletion happens can significantly affect compositions of
planetesimals and atmospheres of giant planets. It is therefore important to
constrain if the depletion occurs already at the earliest protostellar disk
stage. Here we present spatially resolved observations of C$^{18}$O, C$^{17}$O,
and $^{13}$C$^{18}$O $J$=2-1 lines in three protostellar disks. We show that
the C$^{18}$O line emits from both the disk and the inner envelope, while
C$^{17}$O and $^{13}$C$^{18}$O lines are consistent with a disk origin. The
line ratios indicate that both C$^{18}$O and C$^{17}$O lines are optically
thick in the disk region, and only $^{13}$C$^{18}$O line is optically thin. The
line profiles of the $^{13}$C$^{18}$O emissions are best reproduced by
Keplerian gaseous disks at similar sizes as their mm-continuum emissions,
suggesting small radial separations between the gas and mm-sized grains in
these disks, in contrast to the large separation commonly seen in
protoplanetary disks. Assuming a gas-to-dust ratio of 100, we find that the CO
gas abundances in these protostellar disks are consistent with the ISM
abundance within a factor of 2, nearly one order of magnitude higher than the
average value of 1-10 Myr old disks. These results suggest that there is a
fast, $\sim$1 Myr, evolution of the abundance of CO gas from the protostellar
disk stage to the protoplanetary disk stage.
