Covering Fraction (cfrac)

This parameter determines whether the geometry is a complete sphere or covers only part of the continuum source. In the former case, photons escaping the cloud in the 'inward' direction are assumed to reenter the cloud at the inner edge owing to the assumption of spherical symmetry. Default is 1.0.

cfrac is solely for deciding how the escape probabilities and optical depths are calculated. It is designed to distinguish between a plane-parallel slab where both the reflected and transmitted light is of interest (or a spherical shell with many holes so that both inward and outward light escape), vs. a closed sphere in which the only radiation which is observed is emitted outward. It does not directly affect how much total line radiation is emitted, so it is counter-intuitive in that sense. Hence it is not expected that, for example, cfrac=0.5 would produce half as much line luminosity seen by a distant observer as cfrac=1.

Here is how it works: xstar divides the radiation field into two components: inward or reflected, and outward or transmitted. At each point in the model it needs to know the escape probabilities in each of these directions in order to calculate how much of the locally emitted line radiation will escape to a distant observer, in either direction. As xstar progresses through the cloud it calculates the opacities and optical depth of the material at each radius. Thus at a given radius it knows accurately the optical depth, and hence the escape probability, in the inward or reflected direction. It does not know the optical depth in the outward direction, at least at first, because it has not calculated the ionization, temperature and opacity there yet. So it guesses at first, and assumes the optical depths are zero, and so the escape probability is 1. If you do a multi-pass model then it will use the optical depths from an earlier pass for the outward optical depth, and so it will be self-consistent. If cfrac=0 xstar follows this procedure and provides the total escaping luminosities of all the lines and rrcs in the inward and outward directions.

If cfrac=1 then xstar uses an assumption which originates from early historical photoionization models: it assumes that there is no inward or reflected radiation, and that all radiation is emitted in the outward direction. This is motivated by the assumption that the cloud is spherical, and that a sort of `Gauss's law' holds: any light emitted inward at a given radius will traverse the spherical region interior to that without interacting, and emerge at the same radius, and then have to traverse the same gas at larger radii as it would have if it were initially emitted outward. It also makes another major assumption: that the optical depth traversed in the outward direction is the same as the optical depth in the inward direction, which of course has alreay been calculated at a given radius as xstar proceeds outward in radius. So, if cfrac=1, there is no radiation escaping in the inward direction. If cfrac is between 0 and 1 then xstar does a linear interpolation between the two limits.

New in version 2.54a is the inclusion of radiative excitation. This process is discussed in more detail in section 9.D.2. The rate of radiative excitation of a given transition is calculated as described there, and 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.