Mathematics – Probability
Scientific paper
Jul 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986apj...306....2k&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 306, July 1, 1986, p. 2-8.
Mathematics
Probability
44
Electromagnetic Scattering, Gravitational Lenses, Random Processes, Scattering Functions, Star Distribution, Asymptotic Methods, Fourier Transformation, Probability Density Functions, Quasars, Relativity
Scientific paper
Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.
Balbus Steven
Katz Nets
Paczyński Bohdan
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