AAS 199th meeting, Washington, DC, January 2002
Session 75. Gravitational Lensing and Cosmic Distances
Oral, Tuesday, January 8, 2002, 2:00-3:30pm, International Ballroom Center

## [75.02] Gravitational Lens Differential Time Delay Distributions and the Density Profile of Dark Halos

E. L. Turner (Princeton University Observatory), M. Oguri, A. Taruya, Y. Suto (Department of Physics, University of Tokyo)

The distribution of differential time delays \Delta t between images produced by strong gravitational lensing contains information on the mass distributions in the lensing objects as well as on cosmological parameters such as H0. We derive an explicit expression for the conditional probability distribution function of time delays P(\Delta t\,|\,\theta) given an image separation of multiple images \theta and related statistics assuming that the lensing halos are described by the singular isothermal sphere (SIS) and the generalization of the profile proposed by Navarro, Frenk, & White (NFW) which has the density profile of the form \rho \propto r-\alpha in the innermost region. The time delay distribution is sensitive to these profiles; steeper inner slopes tend to produce larger time delays. For example, if H0=70\,{\rm km\,s-1Mpc-1} and \Lambda-dominated cosmology are assumed, lenses with \theta=5'' induce the time delay; \Delta t[{\rm yr}]=1.2+1.4-0.7, 0.30+0.28-0.16, 0.093+0.073-0.050, and 0.040+0.031-0.021 (50% level), for SIS, generalized NFW with \alpha=1.5, \alpha=1.0, and \alpha=0.5, respectively.