4.5. Testcase #5

In this example we illustrate how PopRatio may be used to calculate the cooling rate due to collisional excitation of low-lying levels of a given atom or ion.

As an example we take the ion Fe⁺, because iron is an astrophysically abundant element. The ion Fe⁺ may be the dominating ionization stage in low ionization regions, and may be an important gas coolant [30].

The cooling rate is given by [4]:

(25)

Rewriting this in terms of the total Fe⁺ density n_Fe⁺ = _i n_i and the population ratios X_i = n_i+1 / n₁:

(26)

with the energies E_i expressed in cm^-1. The Fe⁺ density will depend on its fractional abundance and on the iron elemental abundance:

(27)

Here we calculate the cooling function, defined as the right hand side of eq. (26).

Since Fe⁺ has a complicated electronic structure, several levels must be taken into account in the calculation. We employ a 16-level model ion, allowing us to calculate the cooling function for electronic densities as high as 10⁴ cm^-3.

To run this testcase the user does not need to modify function URAD, since no fluorescence transitions are loaded in.