2020MNRAS.498.4256C

We present a 3D semi-analytical model of self-gravitating discs, and include a prescription for dust trapping in the disc spiral arms. Using Monte Carlo radiative transfer, we produce synthetic ALMA (Atacama Large Millimeter/submillimeter Array) observations of these discs. In doing so, we demonstrate that our model is capable of producing observational predictions, and able to model real image data of potentially self-gravitating discs. For a disc to generate spiral structure that would be observable with ALMA requires that the disc's dust mass budget is dominated by millimetre- and centimetre-sized grains. Discs in which grains have grown to the grain fragmentation threshold may satisfy this criterion; thus, we predict that signatures of gravitational instability may be detectable in discs of lower mass than has previously been suggested. For example, we find that discs with disc-to-star mass ratios as low as 0.10 are capable of driving observable spiral arms. Substructure becomes challenging to detect in discs where no grain growth has occurred or in which grain growth has proceeded well beyond the grain fragmentation threshold. We demonstrate how we can use our model to retrieve information about dust trapping and grain growth through multiwavelength observations of discs, and using estimates of the opacity spectral index. Applying our disc model to the Elias 27, WaOph 6, and IM Lup systems, we find gravitational instability to be a plausible explanation for the observed substructure in all three discs, if sufficient grain growth has indeed occurred.