Semianalytical Models for Lensing by Dark Halos. I. Splitting Angles

We use the semi-analytical approach to analyze gravitational lensing ofquasars by dark halos in various cold dark matter (CDM) cosmologies, in orderto determine the sensitivity of the prediction probabilities of imagesseparations to the input assumptions regarding halos and cosmologies. The massfunction of dark halos is assumed to be given by the Press-Schechter function.The mass density profile of dark halos is alternatively taken to be thesingular isothermal sphere (SIS), the Navarro-Frenk-White (NFW) profile, or thegeneralized NFW profile. The cosmologies include: the Einstein-de Sitter model(SCDM), the open model (OCDM), and the flat \Lambda-model (LCDM). As expected,we find that the lensing probability is extremely sensitive to the mass densityprofile of dark halos, and somewhat less so to the mean mass density in theuniverse, and the amplitude of primordial fluctuations. NFW halos are very muchless effective in producing multiple images than SIS halos. However, none ofthese models can completely explain the current observations: the SIS modelspredict too many large splitting lenses, while the NFW models predict too fewsmall splitting lenses. This indicates that there must be at least twopopulations of halos in the universe. A combination of SIS and NFW halos canreasonably reproduce the current observations if we choose the mass for thetransition from SIS to NFW to be ~ 10^{13} solar masses. Additionally, there isa tendency for CDM models to have too much power on small scales, i.e. too muchmass concentration; and it appears that the cures proposed for other apparentdifficulties of CDM would help here as well, an example being the warm darkmatter (WDM) variant which is shown to produce large splitting lenses fewerthan the corresponding CDM model by one order of magnitude.Comment: 46 pages, including 13 figures. Revised version with significant improvemen