The mass-sheet degeneracy and time-delay cosmography: Analysis of the strong lens RXJ1131-1231

Simon Birrer, Adam Amara, Alexandre Refregier

Published 2015-11-11Version 1

We present extended modeling of the strong lens system RXJ1131-1231 with archival data in two HST bands in combination with existing line-of-sight contribution and velocity dispersion estimates. We focus on the accuracy and reliability of the source reconstruction scale and lens model assumptions and its implication on time-delay cosmography. We map out the mass-sheet degeneracy and especially the degeneracy pointed out by Schneider and Sluse (2013) using the source reconstruction scale. In a second step, we fold in velocity dispersion and external convergence measurements. We then infer angular diameter distance relations for the time-delays without cosmological priors. For a flat $\Lambda$CDM cosmology, these constraints lead to constraints of the Hubble constant $H_0$ as a function of the matter density $\Omega_m$ in the form of $H_0 = H_0^*/[1 + 0.5(\Omega_m-\Omega_m^*)] \pm 5\%$ with $H_0^*= 71.7^{+3.6}_{-3.6}$ km s$^{-1}$Mpc$^{-1}$ being the value for $H_0$ at $\Omega_m^*=0.3$. This is a significant improvement in the uncertainty of the lens modeling and is consistent with recent CMB measurements. We describe the full cosmological information of the lens system RXJ1131-1231 data in an analytic form such that this information can be combined with other cosmological probes.