The effects of inhomogeneous absorbers on the formation of intrinsic quasar absorption lines

We investigate the formation of absorption lines in an inhomogeneous medium covering an extended source, in the context of intrinsic quasar (QSO) absorption lines. We first describe a simple formalism to model the effect of having a range of column densities in front of the source. It is shown that if the probability distribution of column densities is a power law with index p, the remaining flux in a line in which the medium is very optically thick scales as tau(-(p+1)), where tau is the maximum optical depth in front of the source. This power-law behavior appears to give a better description of the observed relation between optical depth and flux near the bottom of strong intrinsic QSO absorption lines than the standard exponential behavior. The formalism provides an alternative to the model that assumes partial homogeneous covering, which is the current standard in the interpretation of intrinsic QSO absorption lines that do not show exponential behavior, and in some respects provides a better fit to the observed line strengths. We show that inhomogeneous covering can lead to an apparent velocity-dependent covering factor if the partial homogeneous covering model is applied to doublet lines. The covering factor derived from a partial homogeneous covering analysis does, however, yield information on the characteristics of the column density distribution, such as the sharpness of the edges and peaks. We apply the inhomogeneous covering formalism to two observed QSO absorption-line systems to demonstrate these effects.