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A power-law density model, i.e., $\rho(r) \propto r^{-\gamma'}$ has beencommonly employed in strong gravitational lensing studies, including theso-called time-delay technique used to infer the Hubble constant $H_0$.However, since the radial scale at which strong lensing features are formedcorresponds to the transition from the dominance of baryonic matter to darkmatter, there is no known reason why galaxies should follow a power law indensity. The assumption of a power law artificially breaks the mass-sheetdegeneracy, a well-known invariance transformation in gravitational lensingwhich affects the product of Hubble constant and time delay and can thereforecause a bias in the determination of $H_0$ from the time-delay technique. Inthis paper, we use the Illustris hydrodynamical simulations to estimate theamplitude of this bias, and to understand how it is related to observationalproperties of galaxies. Investigating a large sample of Illustris galaxies thathave velocity dispersion $\sigma_{SIE}$>160 km/s at redshifts below $z=1$, wefind that the bias on $H_0$ introduced by the power-law assumption can reach20%-50%, with a scatter of $10\%-30\%$ (rms). However, we find that byselecting 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.

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