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Recombination Continuum Emission and Escape

In analogy with the line emission, recombination emission and cooling rates are calculated using the continuum level population $n_{\infty}$ and the quantities calculated from the photoionization cross section and the Milne relation. The spontaneous recombination rates are given by


\begin{displaymath}\alpha_i=({{n_i}\over{n_{i+1} n_e}})^*
\int_{\varepsilon_{th...
... \sigma_{pi}
e^{(\varepsilon_{th}-\varepsilon)/kT} \eqno{(3)} \end{displaymath}

where ${n_i}^*$ is the LTE density of ion $i$, and $n_e$ is the electron density. The continuum emissivity due to this process is given by


\begin{displaymath}j_\varepsilon=n_{upper} n_e ({{n_i}\over{n_{i+1} n_e}})^*
{{...
... \sigma_{pi}
e^{(\varepsilon_{th}-\varepsilon)/kT} \eqno{(4)} \end{displaymath}

where $n_{upper}$ is the number density of ions in the recombining level and $\sigma_{pi}$ 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:


\begin{displaymath}P_{esc., cont.}={{1}\over{1000 \tau_{cont.}+1}} \eqno{(5)} \end{displaymath}

where $\tau_{cont.}$ 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]).



Subsections
next up previous contents
Next: Line Emission and Escape Up: The Physics Behind XSTAR Previous: Thermal Equilibrium   Contents
Tim Kallman 2014-06-30