Lens galaxies in the Illustris simulation: power-law models and the bias of the Hubble constant from time-delays

Dandan Xu, Dominique Sluse, Peter Schneider, Volker Springel, Mark Vogelsberger, Dylan Nelson, Lars Hernquist

Published 2015-07-28Version 1

The combination of dynamical and strong gravitational lensing studies of massive galaxies shows that their total density profile in the central region (i.e. up to a few half-light radius) can be described by a power law, $\rho(r)\propto r^{-\gamma}$. Therefore, such a power-law model is employed for a large number of strong-lensing applications, including the so-called time-delay technique used to infer the Hubble constant $H_0$. However, since the radial scale at which strong lensing features are formed (i.e., the Einstein radius) corresponds to the transition from the dominance of baryonic matter to dark matter, there is no known reason why galaxies should follow a power law in density. The assumption of a power law artificially breaks the mass-sheet degeneracy, a well-known invariance transformation in gravitational lensing which affects the product of Hubble constant and time delay and can therefore cause a bias in the determination of $H_0$ from the time-delay technique. In this paper, we use the Illustris hydrodynamical simulations to estimate the amplitude of this bias, and to understand how it is related to observational properties of galaxies. Investigating a large sample of Illustris galaxies that have velocity dispersion $\sigma_{\rm SIE} \geqslant 160$ km/s at redshifts below $z=1$, we find that the bias on $H_0$ introduced by the power-law assumption can reach 20%-50%, with a scatter of 10%-30% (rms). However, we find that by selecting galaxies with an inferred power-law model slope close to isothermal, it is possible to reduce the bias on $H_0$ to <5%, and the scatter to <10%. This could potentially be used to form less biased statistical samples for $H_0$ measurements in the upcoming large survey era.