Probabilities for Gravitational Lensing by Point Masses in a Locally Inhomogeneous Universe
Abstract
Probability functions for gravitational lensing by point masses that incorporate Poisson statistics and flux conservation are formulated in the DyerRoeder construction. Optical depths to lensing for distant sources are calculated using both the method of Press and Gunn, which counts lenses in an otherwise empty cone, and the method of Ehlers and Schneider, which projects lensing cross sections onto the source sphere. These are then used as parameters of the probability density for lensing in the case of a critical (q_0_ = 1/2) Friedmann universe. A comparison of the probability functions indicates that the effects of angleaveraging advocated by Ehlers and Schneider can be wellapproximated by adjusting the average magnification along a random line of sight so as to conserve flux, as had been done in previous treatments by Canizares. In particular, it is demonstrated that a difference in lens populations as large as 50% between the two approaches leads to identical probabilities in the high magnification limit.
 Publication:

The Astrophysical Journal
 Pub Date:
 January 1989
 DOI:
 10.1086/167033
 Bibcode:
 1989ApJ...336..544I
 Keywords:

 Cosmology;
 Gravitational Lenses;
 Universe;
 Computational Astrophysics;
 Probability Theory;
 Astrophysics;
 COSMOLOGY;
 GRAVITATIONAL LENSES