C$^{18}$O emission as an effective measure of gas masses of protoplanetary disks.

Many astrochemical models of observed CO isotopologue line emission, earlier considered a good proxy measure of H$_2$ and hence disk gas mass, favor large deviations in the carbon and oxygen gas phase abundances and argue that severe gas phase CO depletion makes it a poor mass tracer. Here, we show that C$^{18}$O line emission is an effective measure of the gas mass, and despite its complex chemistry, a possibly better tracer than HD. Our models are able to reproduce C$^{18}$O emission from recent ALMA surveys and the TW Hya disk to within a factor of $\sim 2-3$ using carbon and oxygen abundances characteristic of the interstellar medium (C/H$=1.4 \times 10^{-4}$; O/H$=3.2\times 10^{-4}$) without having to invoke unusual chemical processing. Our gas and dust disk structure calculations considering hydrostatic pressure equilibrium and our treatment of the CO conversion on grains are primarily responsible for the very different conclusions on disk masses and CO depletion. As did previous studies, we find that a gas phase C/O of $\sim 1-2$ can explain observed hydrocarbon emission from the TW Hya disk; but significantly, we find that CO isotopologue emission is only marginally affected by the C/O ratio. We therefore conclude that C$^{18}$O emission provides estimates of disk masses that are uncertain only to within a factor of a few, and describe a simplified modeling procedure to obtain gas disk masses from C$^{18}$O emission lines.