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.

Observations of systems hosting close in (<1 AU) giant planets and brown dwarfs (M ≳ 7 MJup) find an excess of binary star companions, indicating that stellar multiplicity may play an important role in their formation. There is now increasing evidence that some of these objects may have formed via fragmentation in gravitationally unstable discs. We present a suite of 3D smoothed particle hydrodynamics (SPH) simulations of binary star systems with circumprimary self-gravitating discs, which include a realistic approximation to radiation transport, and extensively explore the companion’s orbital parameter space for configurations which may trigger fragmentation. We identify a ‘sweet spot’ where intermediate separation binary companions (100 AU ≲ a ≲ 400 AU) can cause a marginally stable disc to fragment. The exact range of ideal binary separations is a function of the companion’s eccentricity, inclination and mass. Heating is balanced by efficient cooling, and fragmentation occurs inside a spiral mode driven by the companion. Short separation, disc penetrating binary encounters (a ≲ 100 AU) are prohibitive to fragmentation, as mass stripping and disc heating quench any instability. This is also true of binary companions with high orbital eccentricities (e ≳ 0.75). Wide separation companions (a ≳ 500 AU) have little effect on the disc properties for the setup parameters considered here. The sweet spot found is consistent with the range of binary separations which display an excess of close in giant planets and brown dwarfs. Hence we suggest that fragmentation triggered by a binary companion may contribute to the formation of these substellar objects.

Recent observations of the protoplanetary disc surrounding AB Aurigae have revealed the possible presence of two giant planets in the process of forming. The young measured age of 1 − 4 Myr for this system allows us to place strict time constraints on the formation histories of the observed planets. Hence we may be able to make a crucial distinction between formation through core accretion (CA) or the gravitational instability (GI), as CA formation timescales are typically Myrs whilst formation through GI will occur within the first ≈104 − 105 yrs of disc evolution. We focus our analysis on the 4 − 13 MJup planet observed at R ≈ 30 AU. We find CA formation timescales for such a massive planet typically exceed the system’s age. The planet’s high mass and wide orbit may instead be indicative of formation through GI. We use smoothed particle hydrodynamic simulations to determine the system’s critical disc mass for fragmentation, finding Md, crit = 0.3 M⊙. Viscous evolution models of the disc’s mass history indicate that it was likely massive enough to exceed Md, crit in the recent past, thus it is possible that a young AB Aurigae disc may have fragmented to form multiple giant gaseous protoplanets. Calculations of the Jeans mass in an AB Aurigae-like disc find that fragments may initially form with masses 1.6 − 13.3 MJup, consistent with the planets which have been observed. We therefore propose that the inferred planets in the disc surrounding AB Aurigae may be evidence of planet formation through GI.

Radial velocity (RV) measurements of transiting multiplanet systems allow us to understand the densities and compositions of planets unlike those in the solar system. Kepler-102, which consists of five tightly packed transiting planets, is a particularly interesting system since it includes a super-Earth (Kepler-102d) and a sub-Neptune-sized planet (Kepler-102e) for which masses can be measured using RVs. Previous work found a high density for Kepler-102d, suggesting a composition similar to that of Mercury, while Kepler-102e was found to have a density typical of sub-Neptune size planets; however, Kepler-102 is an active star, which can interfere with RV mass measurements. To better measure the mass of these two planets, we obtained 111 new RVs using Keck/HIRES and Telescopio Nazionale Galileo/HARPS-N and modeled Kepler-102's activity using quasiperiodic Gaussian process regression. For Kepler-102d, we report a mass upper limit M d < 5.3 M ⊕ (95% confidence), a best-fit mass M d = 2.5 ± 1.4 M ⊕, and a density ρ d = 5.6 ± 3.2 g cm−3, which is consistent with a rocky composition similar in density to the Earth. For Kepler-102e we report a mass M e = 4.7 ± 1.7 M ⊕ and a density ρ e = 1.8 ± 0.7 g cm−3. These measurements suggest that Kepler-102e has a rocky core with a thick gaseous envelope comprising 2%–4% of the planet mass and 16%–50% of its radius. Our study is yet another demonstration that accounting for stellar activity in stars with clear rotation signals can yield more accurate planet masses, enabling a more realistic interpretation of planet interiors.

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