DiskMINT: A Tool to Estimate Disk Masses with CO Isotopologues

Abstract: CO is one of the most abundant molecules in protoplanetary disks, and optically thin emission from its isotopologues has been detected in many of them. However, several past works have argued that reproducing the relatively low emission of CO isotopologues requires a very low disk mass or significant CO depletion. Here, we present a Python code, DiskMINT, which includes gas density and temperature structures that are both consistent with the thermal pressure gradient, isotope-selective chemistry, and conversion of CO into $\mathrm{CO_2}$ ice on grain-surfaces. The code generates a self-consistent disk structure, where the gas disk distribution is obtained from a Spectral Energy Distribution (SED)-derived dust disk structure with multiple grain sizes. We use DiskMINT to study the disk of RU~Lup, a high-accreting star whose disk was previously inferred to have a gas mass of only $\sim 1.5\times10<sup>{-3}\,M_\odot$ and gas-to-dust mass ratio of $\sim 4$. Our best-fit model to the long-wavelength continuum emission can explain the total $\mathrm{C<sup>{18}O}$ luminosity as well as the $\mathrm{C<sup>{18}O}$ velocity and radial intensity profiles, and obtains a gas mass of $\sim 1.2\times10<sup>{-2}\,M_\odot$, an order of magnitude higher than previous results. A disk model with parametric Gaussian vertical distribution that better matches the IR-SED can also explain the observables above with a similarly high gas mass $\sim 2.1\times10<sup>{-2}\,M_\odot$. We confirm the conclusions of Ruaud et al. (2022) that optically thin $\mathrm{C<sup>{18}O}$ rotational lines provide reasonable estimates of the disk mass and can therefore be used as gas disk tracers.