In analogy with the line emission, recombination emission and cooling rates
are calculated using the continuum level population and
the quantities calculated from the photoionization cross section
and the Milne relation. The spontaneous recombination rates are given by
where is the LTE
density of ion
, and
is the electron density.
The continuum emissivity due to this process is given by
where is the number density of ions in
the recombining level and
is the photoionization cross
section. The cooling rate is given by the integral of this expression over
energy. These rates are calculated separately for each level
included in the multilevel calculation.
In order to account for the suppression of rates due to emission and reabsorption of recombination continua, we multiply the rates and emissivities by an escape fraction given by:
where is the optical depth at the threshold
energy for the relevant transition. This factor is used to correct
both the emission rate for the recombination events, and also the
rates in the kinetic equations determining level populations etc, and has
been found to give reasonably good fits to the results of more
detailed calculations for the case of H II region models
in which the Lyman continuum of hydrogen is optically thick
(e.g. [Harrington 1989]).