Concordance of Kinematics and Lensing of Elliptical Galaxies with WMAP Cosmology

Abstract

We explore degeneracies in strong lensing model so to make time de- lay data consistent with the WMAP (Wilkinson Microwave Anisotropy Probe) cos- mology. Previous models using a singular isothermal lens often yield a time de- lay between the observed multiple images too small than the observed value if we hardwire the now widely quoted post-WMAP high value of the Hubble con- stant (H0 ∼ 71 ± 4k m s −1 Mpc −1 ). Alternatively, the lens density profile (star plus dark matter) is required to be locally steeper than r −2 (isothermal) profile near the Einstein radius (of the order 3 kpc) to fit the time delays; a naive extrapolation of a very steep profile to large radius would imply a lens halo with a scale length of the order only 3 kpc, too compact to be consistent with CDM. We explore more sophisti- cated, mathematically smooth, positive lens mass density profiles which are consistent with a large halo and the post-WMAP H0. Thanks to the spherical monopole degen- eracy, the reshuffling of the mass in a lens model does not affect the quality of the fit to the image positions, amplifications, and image time delays. Even better, unlike the better-known mass sheet degeneracy, the stellar mass-to-light and the H0 value are not affected either. We apply this monopole degeneracy to the quadruple imaged time-delay system PG 1115+080. Finally we discuss the implications of the time delay data on the newly proposed relativistic MOND theory.