Incorporating Radiative Cooling into a Cosmological Hydrodynamic Code

A possible inconsistency arising when a radiative cooling term is incorporated in a finite resolution self-gravitating hydrodynamic code is discussed. The inconsistency appears when the heating-cooling balance within the cooling and collapsing gas cloud is broken near the resolution limit of a numerical code. As the result, the cooling time of a fluid element increases enormously leading to the unphysical conclusion that the fluid element does not cool and is therefore stable against the collapse. A special cooling consistency condition is introduced which approximately restores the heating-cooling balance and leads to a numerical solution that closely mimics the exact (infinite resolution) solution.