Radiative Excitation

Excitation due to absorption of continuum photons in bound-bound transitions can dominate over other mechanisms, depending on the conditions. The importance of this has been pointed out and explored by [Kinkhabwala et al.(2002),Band et al.(1990)]. Accurate treatment of this process requires that the geometry be treated carefully. This is because the net excitation rate is also affected by the radiation emitted by the decays of the excited levels. If every radiative excitation leads to a radiative deexcitation and emission of radiation which escapes the model volune then there is no net effect of this process. In the case of a stationary spherical model in which we are only interested in the total spectrum seen by a distant observer, and if radiative deexcitation is the only decay mechanism for the excited levels, then emission following radiative excitation and absorption will balance exactly. This is the scenario envisioned by classical nebular models, and for this reason these models did not generally include the effects of radiative excitation.

Radiative excitation has a cross section which can be much greater than the photoabsorption cross sections associated with photoionization. If so, it is important to accurately treat the spatial dependence of the absorption and depletion of the incident radiation in lines. This necessitates spatial steps which are small enough to resolve the line absorption, i.e. $\sim \kappa^{-1}$, where $\kappa$ is the opacity in the line. Xstar accounts for this, but using the absorption cross section binned into the continuum grid. If the grid is coarse, then there will likely be no bin close to the centers of the strongest lines, and this process will not be accurately modeled. For this reason it is recommended that a fine energy grid be used for models where radiative excitation is of interest, and where the model cloud is optically thick in the line centers.

In order to preserve the classical result in which radiative excitation is completely ignored, xstar scales the rate for this process proportional to the value of the cfrac parameter. The rate of radiative excitation of a given transition is calculated using:


\begin{displaymath}R_{lu}=\sigma_{line}F_\varepsilon\end{displaymath}

where $\sigma_{line}$ is the line mean photoabsorption cross section and $F_\varepsilon$ is the specific flux at the energy of the line. This rate is then multiplied by a factor of 1-cfrac. So, if cfrac=1 the effective rate of radiative excitation is zero. If cfrac=0 then the full rate of radiative excitaiton is included.