Radiation feedback from sink particles

The amount of thermal radiation produced in the grid is a function of temperature. Since sinks are a subgrid model they themselves 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'). Similarly, we do not keep track of the amount of energy that falls onto the sink particle. Again, this is because we have no way of tracking the infall all the way down to the stellar surface that lies within the sink particle. Thus, we are left to assume gas that is accreted by surrounding zones contribute to the accretion luminosity of the forming protostar, and thus we need a way to estimate this accretion luminosity.

Thus, we will prescribe some fraction of infalling energy to be recycled back into the grid. We will have this accretion energy (E_{acc}) distributed smoothly in a kernel surrounding the sink, so that it diffuses away back into the grid via FLD radiative transfer. In this way, sinks will act as additional sources of radiation within the grid. The kernel of cells surrounding each sink will be stepped on each radiative time-step with the values of E_{acc} computed for that time-step.

Accretion Luminosity

As discussed ​here, the following equation for the accretion luminosity:

L=\frac{G M dm}{R dt}

should be a very good approximation for Astrobear to use.

Tracking accretion luminosity in the code

At each time-step i, the luminosity is computed as:

L_i=\frac{G M_i dm_i}{R ~dt}

where M_i is the mass of the sink particle at i, dm_i is the total accreted mass for that time-step, G is the gravitational constant in computational units, R is the radius of the star, taken to be 1 solar radius by default, but modifiable by the user at run-time, and dt is the hydro time-step. This luminosity is only computed after the sink particle has grown to have non-zero mass, and then will only be a source of luminosity after surrounding material has been deemed unstable and collapsing inward to the sink particle (i.e. is accreted).

Kernel

Work arrays and feeding L into the source

Tests

2D, fixed grid - radiating sink

Energy output

Different opacities

Marshak Waves

2D, fixed grid - collapsing clump