Statistics of Gravitational Microlensing Magnification

Details Statistics of Gravitational Microlensing Magnification Statistics of Gravitational Microlensing Magnification

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aas...189.2703l&link_type=abstract

American Astronomical Society, 189th AAS Meeting, #27.03; Bulletin of the American Astronomical Society, Vol. 28, p.1307

Astronomy and Astrophysics

Astronomy

Scientific paper

For a low optical depth (tau << 1) planar distribution of point mass lenses, we derive the macroimage magnification distribution P(A) at high magnification (A-1 >> tau (2) ) by modeling the illumination pattern as a superposition of the patterns due to individual ``point mass plus weak shear'' lenses. By convolving the magnification cross-section of the point mass plus weak shear lens with the shear distribution, we obtain a caustic-induced feature in P(A) which exhibits a simple scaling property and results in a 20% enhancement at A ~ 2/tau . We also derive P(A) for low magnification (A-1 << 1), taking into account the correlations in the magnification of the microimages. The low-A distribution has a peak of amplitude ~ 1/tau (2) at A-1 ~ tau (2) . We combine the low- and high-A results and obtain a practical semi-analytic expression for P(A). For a low optical depth three-dimensional lens distributions. we show that the multiplane lens equation near a point mass can be reduced to the single plane equation of a point mass perturbed by weak shear. This allows us to calculate the caustic-induced feature in P(A) as a weighted sum of the feature derived in the planar case. The resulting semi-analytic feature is similar to the feature in the planar case, but it does not have any simple scaling properties, and it is shifted to higher magnification. The semi-analytic distributions are compared to previous numerical results for tau ~ 0.1. They are in better agreement in the three-dimensional case. We explain this by re-examining the criterion for low optical depth. For tau ~ 0.1, a simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is ~ 20% for the three-dimensional case, much smaller than the ~ 1-exp (-8 tau ) ~ 55% for the planar case.

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