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We couple non-magnetic, hydrodynamical simulations of collapsing protostellarcores with radiative transfer evolutionary models to generate syntheticobservations. We then use these synthetic observations to investigate theextent to which a simple method for measuring protostellar disc masses used inthe literature recovers the intrinsic masses of the discs formed in thesimulations. We evaluate the effects of contamination from the surroundingcore, partially resolving out the disc, optical depth, fixed assumed dusttemperatures, inclination, and the dust opacity law. We show that thecombination of these effects can lead to disc mass underestimates by up tofactors of 2-3 at millimeter wavelengths and up to an order of magnitude orlarger at submillimeter wavelengths. The optically thin portions ofprotostellar discs are generally cooler in the Class I stage than the Class 0stage since Class I discs are typically larger and more optically thick, andthus more shielded. The observed disc mass distribution closely resembles theintrinsic distribution if this effect is taken into account, especially atmillimeter wavelengths where optical depth effects are minimized. Approximately50%-70% of protostellar discs observed to date with this method are consistentwith the masses of the gravitationally unstable discs formed in thesimulations, suggesting that at least some protostellar discs are likelysufficiently massive to fragment. We emphasize key future work needed toconfirm these results, including assembling larger, less biased samples, andusing molecular line observations to distinguish between rotationallysupported, Keplerian discs and magnetically supported pseudodiscs.

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