Effect of irradiation model on 2D hydrodynamic simulations of self-gravitating protoplanetary discs

Young protoplanetary discs are expected to be gravitationally unstable, which can drive angular momentum transport as well as be a potential mechanism for planet formation. Gravitational instability is most prevalent in the outer disc where cooling timescales are short. At large radii, stellar irradiation makes a significant contribution to disc heating and is expected to suppress instability. In this study, we compare two models of implementing irradiation in 2D hydrodynamic simulations of self-gravitating discs: supplying a constant heating rate per unit mass and per unit area of the disc. In the former case, instability is quenched once the stellar irradiation becomes the dominant heating source. In the latter case, we find instability persists under high levels of irradiation, despite large values of the Toomre Q parameter, in agreement with analytic predictions. Fragmentation was able to occur in this regime with the critical cooling timescale required decreasing as irradiation is increased, corresponding to a maximum threshold for the viscosity parameter: $\alpha\sim0.03-0.09$.