Time Delays for the Giant Quadruple Lensed Quasar SDSS J1004+4112: Prospects for Determining the Density Profile of the Lensing Cluster
Abstract
We investigated the dependence of the time delays for the largeseparation gravitationally lensed quasar SDSS J1004+4112 on the inner mass profile of the lensing cluster. Adopting a mass model whose innermost density profile was parameterized as ρ ∝ r^{α}, we derived a series of mass models that can fit the observational data, and then compute the probability distribution functions of time delays. We find that larger α has longer time delays, longer tails at the higher end of the probability distribution, and larger model uncertainties. The ratios of the time delays slightly depend on the slope, α. Among others, time delays between images C and A (or B) have little dependence on the inner slope, particularly when the time delays are short. The dependence of time delays on α is well fitted by a linear form, which reflects the wellknown degeneracy between the mass profile and time delays. We performed a Monte Carlo simulation to illustrate how well the inner slope can be constrained from measurements of time delays. We found that measurements of more than one time delay resulted in reasonably tight constraints on the inner slope (σ_{α} ≲ 0.25), while only one time delay could not determine the inner slope very well. Our result indicates that time delays indeed serve as a powerful tool to determine the mass profile, despite the complexity of the lensing cluster.
 Publication:

Publications of the Astronomical Society of Japan
 Pub Date:
 April 2006
 DOI:
 10.1093/pasj/58.2.271
 arXiv:
 arXiv:astroph/0601149
 Bibcode:
 2006PASJ...58..271K
 Keywords:

 cosmology: theory;
 dark matter;
 galaxies: clusters: general;
 galaxies: halos;
 galaxies: quasars: individual (SDSS J1004+4112);
 gravitational lensing;
 Astrophysics
 EPrint:
 21 pages, 8 figures, accepted for publication in PASJ