STATISTICS OF GRAVITATIONAL LENSING - EXTENDED SOURCES

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. Then we study the influence of the source size on the statistics of gravitational lensing flow optical depth), and predict that the distribution of the probability of magnifications is two-peaked: (i) the first peak occurs for small magnifications, its position being independent from the source size; (ii) the second peak occurs at maximal amplification. This is at variance with the A-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. Our results are shown to agree with previous numerical simulations.