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

TL;DR

This paper evaluates a dynamical method for measuring protoplanetary disc masses by simulating self-gravitating discs and analyzing deviations from Keplerian rotation, achieving about 25% accuracy for discs with mass ratios above 0.05.

Contribution

It provides a numerical benchmark for a tracer-independent method to measure disc mass using kinematic deviations, validating its accuracy and limitations.

Findings

Method accurately retrieves disc masses with >25% ratio.

Reliable for disc-to-star mass ratios >0.05.

Uncertainty in mass measurement is approximately 25%.

Abstract

The mass of protoplanetary discs sets the amount of material available for planet formation, determines the level of coupling between gas and dust, and possibly sets gravitational instabilities. Measuring mass of discs is challenging, since it is not possible to directly detect H$_2$, and CO-based estimates remain poorly constrained. An alternative method that does not rely on tracers-to-H$_2$ ratios has recently been proposed to dynamically measure the disc mass altogether 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 applied to weigh three protoplanetary discs: Elias 2-27, IM Lup and GM Aurigae. We provide here a numerical benchmark of the method by simulating isothermal self-gravitating discs with a range of masses from 0.01 to $0.2 \,M_{\odot}$ with the phantom code and post-process them with radiative transfer (mcfost) to obtain synthetic observations. We find that dynamical weighing allows to retrieve the expected value of disc masses as long as the disc-to-star mass ratio is larger than $M_d/M_\star=0.05$. The estimated uncertainty for the disc mass measurement is $\sim 25\%$.