Mathematics – Probability
Scientific paper
Nov 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991a%26a...251..393m&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 251, no. 2, Nov. 1991, p. 393-401.
Mathematics
Probability
4
Gravitational Lenses, Probability Distribution Functions, Analytic Functions, Optical Thickness, Statistical Analysis
Scientific paper
An analytical formulation for the probability distribution of magnifications due to lensing by clumps on point sources is given in the low optical depth case. A study is then made of the influence of the source size on the statistics of gravitational lensing (low optical depth), and it is predicted that the distribution of the probability of magnifications is two-peaked: the first peak occurs for small magnifications, its position being independent from the source size; the second peak occurs at maximal amplification. This is at variance with the A exp -3 tail expected in the point source case. It is found that the increase of the source size progressively transfers a fraction of the probability from the first to the second peak. The results are shown to agree with previous numerical simulations.
Marchandon S.
Nottale Laurent
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