Altered luminosity functions for relativistically beamed objects. II, Distribution of Lorentz factors and parent populations with complex luminosity functions

In a previous paper, Urry and Shafer (1984) showed that the observed luminosity function (LF) of objects that have part or all of their emission relativistically beamed was a double power law, flat at the faint end and steep at the bright end, so that the ratio of beamed sources to parents was a strong function of luminosity. These calculations are extended here for more realistic LFs required for actual tests of a unified theory of AGN. The observed LF of the beam-dominated objects is generally flatter than the parent LF, so that the number density ratio is a strong function of luminosity and can easily be greater than unity at high luminosities, even for gradual low-luminosity cutoffs in the parent LF. Several characteristic break points can be identified depending on the details of the parent LF. The calculations can be used to test unified theories by predicting the observed LF for aligned objects from the LF of the proposed parent population. 6 refs.