The accretion luminosity is summed up for all cells surrounding the sink particle, and the total is given by 'E_acc'. This total accretion energy is then smoothed over a kernel of cells surrounding the sink, proportionally to a decreasing exponential, such that,

Sum dE_acc | cells = E_acc

In other words, the exponential function is 'normalized'.

We also want the exponential function to go to zero at the boundary of the kernel.

So given these 2 constraints, we have the following set of equations,