can we get cooling to exactly balance recombination heating?

[danieljprice]

in various equation of state calls, we compute T, mu and gamma from u with some ionisation energy included, which allows for additional pressure (and hence modified dynamics) due to recombination.

In practice recombination energy is either trapped or radiated. In the case where it is radiated we would use a cooling function in order to liberate the recombination energy.

Ideally these should match so that a simulation run with recombination + relevant line cooling function should match a simulation in which recombination is not included in the equation of state

suggested test problem is a hot adiabatic wind (10^5K) where there is an analytic solution in the absence of cooling (e.g. as in Siess et al. 2022), recombination should occur in the outflow and could be then switched "off" by a cooling function that should take us back to the analytic profile

This should test the internal consistency of the cooling prescription compared to the assumed energy input in the equation of state