Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986mnras.223..113p&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 223, Nov. 1, 1986, p. 113-128.
Astronomy and Astrophysics
Astronomy
47
Amplification, Gravitational Lenses, Quasars, Radiant Flux Density, Big Bang Cosmology, Distribution Functions, Luminosity, Optical Thickness, Point Sources
Scientific paper
This paper presents some approximate methods for calculating the amplification distribution function f(A) for a point source observed through a population of randomly placed gravitational lenses. In the limit of small lensing optical depth, the single-lens f(A) for point lenses automatically satisfies the general constraint of average flux conservation, for lenses placed either in a thin screen or throughout a Friedmann universe of arbitrary Omega0. Various approximations for extending these results to the nonlinear regime are discussed. The results are applied to quasars. Previous calculations of quasar-galaxy associations due to lensing by stars in galaxy haloes are found to have overestimated the strength of the effect. Lensing may account for the apparent evolution of the bright end of the quasar luminosity function at z greater than about 2, but only if Omega0 is less than about 0.01.
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