The continuum
radiation field is modified primarily by photoabsorption, for which
the opacity,
,
is equal to the product of the ion abundance
with the total photoionization cross section, summed over all levels.
A model is constructed by dividing the cloud into a set of concentric spherical shells. The radiation field incident on the innermost shell is the source spectrum. For each shell, starting with the innermost one, the ionization and temperature structure is calculated from the local balance equations using the radiation field incident on the inner surface. The attenuation of the incident radiation field by the shell is then calculated. The diffuse radiation emitted by the cloud is calculated using an expression of the formal solution if the equation of transfer:
where is the specific luminosity at the
cloud boundary,
is the optical depth
from
to the boundary, and
is the emissivity at
the radius
. Since our models in general have two boundaries,
we perform this calculation for radiation escaping at both the
inner and outer cloud boundaries. This calculation is performed
for each continuum energy bin, and
separately for each line. In the case of the continuum, we construct a
vector of emissivities,
which includes contributions
from the escaping fraction from all the levels which affect each
energy. For the lines, the emissivity used in this equation is the
escaping fraction for that line.