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

TL;DR

This study uses the Illustris simulation to assess how the common power-law density assumption in gravitational lensing biases the measurement of the Hubble constant, revealing significant potential errors and ways to mitigate them.

Contribution

It quantifies the bias in H_0 from power-law models in lensing and proposes selection criteria to reduce this bias using simulation data.

Findings

Bias in H_0 can reach 20%-50% due to power-law assumptions.

Selecting galaxies with near-isothermal slopes reduces bias to below 5%.

Bias and scatter depend on galaxy properties and can be mitigated.

Abstract

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.