The statistics of gravitational lenses  Appaarent changes in the luminosity function of distant sources due to passage of light through a single galaxy
Abstract
We ask how the apparent distribution of fluxes (NF relation) of point sources seen behind an intervening galaxy will change due to gravitational lensing of the galaxy as a whole or due to minilenses within it. The analysis is exact in the limit that the optical depth to lensing is small. We find that there should be a significant increase in the apparent density of quasars seen near galaxies but that a sample of more than l0^{4.5} galaxies will have to be studied before a statistically significant result is found. The resulting amplification of the NF relation depends sensitively on the slope and curvature of the initial NF relation. Because of this and requirements of flux conservation, there is expected to be a decrement of very faint quasars (m> 26.5) seen near galaxies. This, coupled with the scarcity of bright quasars, implies that searches should optimally be made in the vicinity of m = 23. The apparent amplification found by Canizares with a smaller sample (N ≍ l0^{3.3}) of galaxies using relatively bright quasars (m < 16) is, if real and not a statistical anomaly, due to physical effects other than gravitational lensing.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1983
 DOI:
 10.1086/160886
 Bibcode:
 1983ApJ...267..488V
 Keywords:

 Galaxies;
 Gravitational Lenses;
 Luminosity;
 Quasars;
 Statistical Analysis;
 Cosmology;
 Integral Equations;
 Light Scattering;
 Probability Distribution Functions;
 Transfer Functions;
 Astrophysics