The amount of thermal radiation produced in the grid is a function of temperature. Since sinks are a subgrid model they do not have temperature (we are not sure how big the forming star is, how fast it is growing by contraction, etc., so there isn't an easy way of assigning the sub-grid object a 'temperature'). However, we track the amount of energy that falls onto the sink. We can imagine that as material hits the surface of the star (i.e. as it is accreted by sinks), it contributes to the energy that is re-released back into the grid. That is because young stars emit energy through many means: mechanical (e.g. outflows) and various radiation processes. Since we are not modeling stellar evolution on the sub-grid scale we are not following how much energy is being released due to thermonuclear reactions in the core of our invisible star. Instead we can just imagine that as the material hits the surface of the star (i.e. passes through the sink particle) it is slowed and compressed, thereby producing thermal radiation, which we then distribute to the zones surrounding the star.

To mock this up, we will prescribe some fraction of infalling energy to be recycled back into the grid. We will have this radiative energy distributed smoothly in a kernel surrounding the sink, so that it diffuses away back into the grid through the solution of the radiative transfer equations. In this way, the sinks will act as an additional source of radiation. The kernel of cells surrounding the sinks will be stepped on each radiative time step with the values of Erad from the star.