We use a suite of SPH simulations to investigate the susceptibility of protoplanetary discs to the effects of self-gravity as a function of star-disc properties. We also include passive irradiation from the host star using different models for the stellar luminosities. The critical disc-to-star mass ratio for axisymmetry (for which we produce criteria) increases significantly for low-mass stars. This could have important consequences for increasing the potential mass reservoir in a proto Trappist-1 system, since even the efficient Ormel et al. (2017) formation model will be influenced by processes like external photoevaporation, which can rapidly and dramatically deplete the dust reservoir. The aforementioned scaling of the critical M d /M * for axisymmetry occurs in part because the Toomre Q parameter has a linear dependence on surface density (which promotes instability) and only an M 1/2 * dependence on shear (which reduces instability), but also occurs because, for a given M d /M * , the thermal evolution depends on the host star mass. The early phase stellar irradiation of the disc (for which the luminosity is much higher than at the zero age main sequence, particularly at low stellar masses) can also play a key role in significantly reducing the role of self-gravity, meaning that even Solar mass stars could support axisymmetric discs a factor two higher in mass than usually considered possible. We apply our criteria to the DSHARP discs with spirals, finding that self-gravity can explain the observed spirals so long as the discs are optically thick to the host star irradiation.

We investigate how a protoplanetary disc's susceptibility to gravitational instabilities and fragmentation depends on the mass of its host star. We use 1D disc models in conjunction with 3D SPH simulations to determine the critical disc-to-star mass ratios at which discs become unstable against fragmentation, finding that discs become increasingly prone to the effects of self-gravity as we increase the host star mass. The actual limit for stability is sensitive to the disc temperature, so if the disc is optically thin stellar irradiation can dramatically stabilise discs against gravitational instability. However, even when this is the case we find that discs around 2 M stars are prone to fragmentation, which will act to produce wide-orbit giant planets and brown dwarfs. The consequences of this work are two-fold: that low mass stars could in principle support high disc-to-star mass ratios, and that higher mass stars have discs that are more prone to fragmentation, which is qualitatively consistent with observations that favour high-mass wide-orbit planets around higher mass stars. We also find that the initial masses of these planets depends on the temperature in the disc at large radii, which itself depends on the level of stellar irradiation.

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.