Mathematics – Probability
Scientific paper
Jul 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...411..513w&link_type=abstract
Astrophysical Journal - Part 1 (ISSN 0004-637X), vol. 411, no. 2, p. 513-517.
Mathematics
Probability
7
Astronomical Models, Galactic Clusters, Gravitational Lenses, Quasars, Statistical Analysis, Asymptotic Methods, Line Of Sight, Probability Theory, Radial Distribution, Velocity Distribution
Scientific paper
The theoretical average line-of-sight velocity dispersion along the radius of a spherical galaxy or cluster of galaxies tends to a variable value. Statistical lensing studies often take into account only the asymptotic value, either close to the center or at large distances, rather than the full variation: this results in significant effects in lensing properties depending on the mass density models of the lensing systems. Magnification probabilities by clusters of galaxies modeled by four well-known density profiles are calculated in this paper and the uncertainties from the variable velocity dispersions are shown. It is found that magnification probabilities span a range of about an order of magnitude among the models, which implies that it is impossible to distinguish the model differences from statistical lensing, and the present evaluation of lensing effects may also have a large uncertainty from velocity dispersions. It is suggested that a perfectly adequate estimate of lensing probabilities can be obtained by modeling galaxies and galaxy clusters as singular isothermal spheres, in which the line-of-sight velocity dispersion is in fact a constant.
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