Show simple item record Petters, AO Rider, B Teguia, AM 2011-04-15T16:46:39Z 2009-12-01
dc.identifier.citation Journal of Mathematical Physics, 2009, 50 (12)
dc.identifier.issn 0022-2488
dc.description.abstract Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.
dc.language.iso en_US en_US
dc.relation.ispartof Journal of Mathematical Physics
dc.relation.isversionof 10.1063/1.3267859
dc.title A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula
dc.type Journal Article
dc.description.version Version of Record en_US 2009-12-0 en_US
duke.description.endpage 122501 en_US
duke.description.issue 12 en_US
duke.description.startpage 122501 en_US
duke.description.volume 50 en_US
dc.relation.journal Journal of Mathematical Physics en_US
pubs.issue 12
pubs.organisational-group /Duke
pubs.organisational-group /Duke/Trinity College of Arts & Sciences
pubs.organisational-group /Duke/Trinity College of Arts & Sciences/Mathematics
pubs.organisational-group /Duke/Trinity College of Arts & Sciences/Physics
pubs.publication-status Published
pubs.volume 50

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