A non-spherically symmetric model for absorption regions near quasars

An approximate analytic solution of the radiative-transfer equation is used to estimate upper limits on the fraction of sky covered (Omega/4pi) by absorption regions near broad absorption-line quasars. The resonance scattering of line radiation tends to 'fill in' absorption troughs, and regions with large Omega/4pi produce troughs that are severely 'filled in'. PHL 5200 and several other broad absorption line quasars have absorption troughs that are flat-bottomed and deep. It is noted that these quasars probably have small Omega/4pi. Simple solutions are obtained for the case of large optical depth and a point central source using a two-stream model for the radiation field. It is shown that the scattered radiation can produce flat-bottomed absorption troughs if the logarithmic velocity derivative in the outflow is constant. For a large class of models, Omega/4pi is approximately less than the residual intensity (the fraction left after absorption) in a deep flat-bottomed absorption trough.