**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
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## [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 H_{0}. 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 H_{0}=70\,{\rm
km\,s^{-1}Mpc^{-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.

The author(s) of this abstract have provided an email address
for comments about the abstract:
elt@astro.princeton.edu

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