Weighing protoplanetary discs with kinematics: Physical model, method, and benchmark

Context. The mass of protoplanetary discs determines the amount of material available for planet formation, the level of coupling between gas and dust, and possibly also sets gravitational instabilities. Measuring the mass of a disc is challenging, as it is not possible to directly detect H2, and CO-based estimates remain poorly constrained. Aims. An alternative method has recently been proposed that does not rely on tracer-to-H2 ratios. It allows dynamical measurement of the disc mass together with the star mass and the disc critical radius by looking at deviations from Keplerian rotation induced by the self-gravity of the disc. So far, this method has been used to weigh three protoplanetary discs: Elias 2-27, IM Lup, and GM Aurigae. Methods. We provide a numerical benchmark of the above method. To this end, we simulated isothermal self-gravitating discs with a range of masses from 0.01 to 0.2 M with the PHANTOM code and post-processed them with radiative transfer (MCFOST) to obtain synthetic observations. Results. We find that dynamical weighing allows us to retrieve the expected disc masses as long as the disc-to-star mass ratio is larger than Md/M = 0.05. We estimate an uncertainty for the disc mass measurement of ∼25%.