A Technical Memorandum On Core Radii In Lens Statistics

Abstract

Quantitative estimates of lensing probabilities must be self-consistent. In particular, for asymptotically isothermal models: (1) using the $(3/2)^{1/2}$ correction for the velocity dispersion overestimates the expected number of lenses by 150\% and their average separations by 50\%, thereby introducing large cosmological errors; (2) when a core radius is added to the SIS model, the velocity dispersion must be increased; and (3) cross sections and magnification bias cannot be separated when computing the lensing probability. When we self-consistently calculate the effects of finite core radii in flat cosmological models, we find that the cosmological limits are independent of the core radius.