Gravitational instabilities in a protosolar-like disc II: continuum
  emission and mass estimates
  Gravitational instabilities (GIs) are most likely a fundamental process
during the early stages of protoplanetary disc formation. Recently, there have
been detections of spiral features in young, embedded objects that appear
consistent with GI-driven structure. It is crucial to perform hydrodynamic and
radiative transfer simulations of gravitationally unstable discs in order to
assess the validity of GIs in such objects, and constrain optimal targets for
future observations. We utilise the radiative transfer code LIME to produce
continuum emission maps of a $0.17\,\mathrm{M}_{\odot}$ self-gravitating
protosolar-like disc. We note the limitations of using LIME as is and explore
methods to improve upon the default gridding. We use CASA to produce synthetic
observations of 270 continuum emission maps generated across different
frequencies, inclinations and dust opacities. We find that the spiral structure
of our protosolar-like disc model is distinguishable across the majority of our
parameter space after 1 hour of observation, and is especially prominent at
230$\,$GHz due to the favourable combination of angular resolution and
sensitivity. Disc mass derived from the observations is sensitive to the
assumed dust opacities and temperatures, and therefore can be underestimated by
a factor of at least 30 at 850$\,$GHz and 2.5 at 90$\,$GHz. As a result, this
effect could retrospectively validate GIs in discs previously thought not
massive enough to be gravitationally unstable, which could have a significant
impact on the understanding of the formation and evolution of protoplanetary
discs.
