Lens galaxies in the Illustris simulation: power-law models and the bias
  of the Hubble constant from time-delays
  A power-law density model, i.e., $\rho(r) \propto r^{-\gamma'}$ has been
commonly employed in strong gravitational lensing studies, 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
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 $\sigma_{SIE}$>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.
