The importance of photosphere cooling in simulations of gravitational instability in the inner regions of protostellar discs

The fragmentation of protostellar discs via gravitational instability (GI) has been proposed as a mechanism for forming giant planets. We present methods and tests for a new implementation of radiative transfer in the Gasoline TreeSPH code with which we investigate the viability of this mechanism in the inner tens of au of discs. Accurate photosphere boundary treatments are of fundamental importance to the outcome of GI. We demonstrate that previous photosphere treatments using edge-particles overestimate the cooling rate, and present a new treatment that can accurately determine photosphere cooling, as demonstrated by its ability to satisfy the relaxation test of Boley et al. (2007b). This is the first time this test has been carried out with smoothed particle hydrodynamics. We carry out simulations of protostellar discs that are unstable in the inner tens of au and find that they do not fragment because they do not cool fast enough. One of these cases has been previously found to undergo fragmentation. The fact that we do not observe fragmentation in this simulation emphasizes the use of accurate photosphere boundary treatments and the difficulty of forming giant planets in the inner disc (inside of 40 au) via the GI mechanism.