Gravitational Lensing by a Compound Population of Halos: Standard Models

Based on observed rotation curves of galaxies and theoretical simulations ofdark matter halos, there are reasons for believing that at least threedifferent types of dark matter halos exist in the Universe classified by theirmasses M and the inner slope of mass density -\alpha: Population A (galaxies):10^{10} h^{-1} M_\odot < M < 2 \times 10^{13} h^{-1} M_\odot, \alpha = 2;Population B (cluster halos): M > 2 \times 10^{13} h^{-1} M_\odot, \alpha =1.3; and Population C (dwarf halos): M < 10^{10} h^{-1} M_\odot, \alpha = 1.3.In this paper we calculate the lensing probability produced by such a compoundpopulation of dark halos, for both image separation and time delay, assumingthat the mass function of halos is given by the Press-Schechter function andthe Universe is described by an LCDM, OCDM, or SCDM model. The LCDM model isnormalized to the WMAP observations, OCDM and SCDM models are normalized to theabundance of rich clusters. We compare the predictions of the differentcosmological models with observational data and show that, both LCDM and OCDMmodels are marginally consistent with the current available data, but the SCDMmodel is ruled out. The fit of the compound model to the observed correlationbetween splitting angle and time delay is excellent but the fit to the numbervs splitting angle relation is only adequate using the small number of sourcesin the objective JVAS/CLASS survey. A larger survey of the same type would havegreat power in discriminating among cosmological models. Furthermore,population C in an LCDM model has a unique signature in the time domain, anadditional peak at ~3 seconds potentially observable in GRBs, which makes itdistinguishable from variants of CDM scenarios, such as warm dark matter,repulsive dark matter, or collisional dark matter.Comment: 26 pages, including 9 figure