On the reliability of protostellar disc mass measurements and the existence of fragmenting discs

We couple non-magnetic, hydrodynamical simulations of collapsing protostellar cores with radiative transfer evolutionary models to generate synthetic observations. We then use these synthetic observations to investigate the extent to which a simple method for measuring protostellar disc masses used in the literature recovers the intrinsic masses of the discs formed in the simulations. We evaluate the effects of contamination from the surrounding core, partially resolving out the disc, optical depth, fixed assumed dust temperatures, inclination, and the dust opacity law. We show that the combination of these effects can lead to disc mass underestimates by up to factors of 2-3 at millimetre wavelengths and up to an order of magnitude or larger at submillimetre wavelengths. The optically thin portions of protostellar discs are generally cooler in the Class I stage than the Class 0 stage since Class I discs are typically larger and more optically thick, and thus more shielded. The observed disc mass distribution closely resembles the intrinsic distribution if this effect is taken into account, especially at millimetrewavelengths where optical depth effects are minimized. Approximately 50-70 per cent of protostellar discs observed to date with this method are consistent with the masses of the gravitationally unstable discs formed in the simulations, suggesting that at least some protostellar discs are likely sufficiently massive to fragment. We emphasize key future work needed to confirm these results, including assembling larger, less biased samples, and using molecular line observations to distinguish between rotationally supported, Keplerian discs and magnetically supported pseudodiscs.