Analytic results for the gravitational lens statistics of singular isothermal spheres in general cosmologies

Details Analytic results for the gravitational lens statistics of singular isothermal spheres in general cosmologies Analytic results for the gravitational lens statistics of singular isothermal spheres in general cosmologies

Mar 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993mnras.261..453k&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 261, no. 2, p. 453-463.

Astronomy and Astrophysics

Astronomy

34

Astronomical Models, Cosmology, Gravitational Lenses, Optical Thickness, Radio Sources (Astronomy)

Scientific paper

The natural cosmological distance for the analysis of gravitational lens statistics with a singular isothermal sphere model for the lens potential is the proper motion distance. By using the proper motion distance we derive analytic expressions for the cross sections, averages of the image separations, and averages of the distances to the lens for both pointlike and resolved sources that depend only on the total density of the cosmological model and the proper motion distance to the source. The ratio of the square of the mean image separation to the mean square image separation for the lenses in a survey is a robust measure of survey completeness. The test shows that the sample of lenses in the Snapshot lens survey of bright quasars is complete within the limits of statistical errors, while the sample of lenses in the MIT-Greenbank radio survey for gravitational lenses is only 50 per cent complete. In a complete sample, the mean and mean square image separations can be used to estimate the velocity dispersion scale of galaxies.

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