Non-linear outcome of gravitational instability in an irradiated protoplanetary disc

Using local three-dimensional radiation hydrodynamics simulations, the non-linear outcome of gravitational instability in an irradiated protoplanetary disc is investigated in a parameter space of the surface density Sigma and the radius r. Starting from laminar flow, axisymmetric self-gravitating density waves grow first. Their self-gravitating degree becomes larger when Sigma is larger or the cooling time is shorter at larger radii. The density waves eventually collapse owing to non-axisymmetric instability, which results in either fragmentation or gravito-turbulence after a transient phase. The boundaries between the two are found at r similar to 75 au as well as at the Sigma that corresponds to the initial Toomre's parameter of similar to 0.2. The former boundary corresponds to the radius where the cooling time becomes short, approximating unity in terms of the inverse of the orbital frequency. Even when gravito-turbulence is established around the boundary radius, such a short cooling time inevitably makes the fluctuation of Sigma large enough to trigger fragmentation. On the other hand, when Sigma is beyond the latter boundary (i.e. the initial Toomre's parameter is less than similar to 0.2), the initial laminar flow is so unstable against self-gravity that it evolves into fragmentation regardless of the radius or, equivalently, the cooling time. Runaway collapse follows fragmentation when the mass concentration at the centre of a bound object is high enough that the temperature exceeds the H-2 dissociation temperature.