An Analytically Soluble Problem in Fully Nonlinear Statistical Gravitational Lensing
Abstract
The amplification probability distribution p(I)dI for a point source behind a random star field which acts as the deflector exhibits a I exp3 behavior for large amplification, as can be shown from the universality of the lens equation near critical lines. In this paper it is shown that the amplitude of the I exp3 tail can be derived exactly for arbitrary mass distribution of the stars, surface mass density of stars and smoothly distributed matter, and largescale shear. This is then compared with the corresponding linear result.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1987
 DOI:
 10.1086/165428
 Bibcode:
 1987ApJ...319....9S
 Keywords:

 Computational Astrophysics;
 Gravitational Lenses;
 Point Sources;
 Probability Density Functions;
 Star Distribution;
 Density Distribution;
 Mass Distribution;
 Nonlinear Systems;
 Statistical Analysis;
 Astrophysics;
 COSMOLOGY;
 GALAXIES: STRUCTURE;
 GRAVITATION