On Kinematic Measurements of Self-Gravity in Protoplanetary Disks

Using controlled injection and recovery experiments, we devised an analysis prescription to assess the quality of dynamical measurements of protoplanetary disk gas masses based on resolved (CO) spectral line data, given observational limitations (resolution, sampling, noise), measurement bias, and ambiguities in the geometry and physical conditions. With sufficient data quality, this approach performed well for massive disks ($M_{\rm d}/M_\ast=0.1$): we inferred $M_{\rm d}$ posteriors that recovered the true values with little bias ($\lesssim$ 20%) and uncertainties within a factor of two (2$\sigma$). The gas surface density profiles for such cases are recovered with remarkable fidelity. Some experimentation indicates that this approach becomes insensitive when $M_{\rm d}/M_\ast\lesssim5$%, due primarily to degeneracies in the surface density profile parameters. Including multiple lines that probe different vertical layers, along with some improvements in the associated tools, might push that practical boundary down by another factor of $\sim$two in ideal scenarios. We also demonstrated this analysis approach using archival ALMA observations of the MWC 480 disk (\"Oberg et al. 2021): we measured $M_{\rm d}=0.13^{\: +0.04}_{\: -0.01} \: M_\odot$ (corresponding to $M_{\rm d}/M_\ast=7\pm1$%) and identified kinematic substructures consistent with surface density gaps around 65 and 135 au. Overall, this (and similar work) suggests that these dynamical measurements offer powerful new constraints with sufficient accuracy and precision to quantify gas masses and surface densities at the high end of the $M_{\rm d}/M_\ast$ distribution, and therefore can serve as key benchmarks for detailed thermo-chemical modeling. We address some prospects for improvements, and discuss various caveats and limitations to guide future work.