Heating and Cooling: “Photon Point of View” vs. “Electron Point of View”

Consideration of heating and cooling depends on the definition of the energy scale. Two different natural ways to do this are the Photon Point of View and the Electron Point of View. In the former description we keep track of the destruction and creation of photons, and a heating or cooling event corresponds to the these two processes, respectively. In the Electron Point of View we keep track of energy deposited or extracted from the electron thermal bath. The two descriptions differ owing to the internal energy associated with ionization: processes which involoving bound-bound transitions have no effect on the electron thermal bath but do emit or absorb photons. Electron impact collisions (by themselves) have no effect on the photon distribution but do heat or cool the electrons. Photoionization heats the electrons with a rate proportional to the energy of the absorbed photon above threshold; it removes photons at a rate proportional to the energy of the absorbed photons above the ion ground level. Radiative recombination differs in a corresponding way between the two descriptions. Compton heating/cooling and bremsstrahlung cooling are the same in the two descriptions.

A key point is that in the 'photon point of view' calculation there is recombination cooling even at low temperature, since every recombination releases a continuum photon and also possibly line photons. Recombination is a monotonically decreasing function of temperature, and the cooling curves have this behavior at low temperature. In constrast, the 'electron point of view' cooling rates are dominated by bremsstrahlung, which goes as $T^{1/2}$, at low and high temperatures.

It is easy to show that the two descriptions are equivalent when ionization equilibrium is achieved; the quantity heating-cooling is the same. Xstar uses the photon point of view for all its calculations of thermal balance. Traditional photoionization codes use the electron point of view. For ease of comparison, xstar (starting with version 2.54) also computes the rates per ion and total rates in the electron point of view and prints them out in the ascii file.