Gravitational Instability of Protoplanetary Disks around Low-mass Stars

Gravitational instability (GI) can produce massive gas giants on wide orbits by fragmentation of protoplanetary disks (PPDs). While most previous works focus on PPDs around solar mass stars, gas giants have been observed in systems with a wide range of stellar masses including M dwarfs. We use the GIZMO code to perform global three-dimensional simulations of self-gravitating disks around low-mass stars. Our models consider heating by turbulent viscosity and stellar irradiation and the β cooling occurring over the dynamical time. We run various models with differing disk-to-star mass ratio q and disk temperature. We find that strongly gravitating disks either produce spirals or undergo fragmentation. The minimum q value for fragmentation is 0.2-0.7, with a smaller value corresponding to a more massive star and/or a smaller disk. The critical q value depends somewhat sensitively on the disk temperature, suggesting that the stellar irradiation is an important factor in determining GI. We discuss our results in comparison with previous work as well as recent ALMA observations.