A power-law density model , i.e. , \rho ( r ) \propto r ^ { - \gamma ^ { \prime } } 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 } \geqslant 160 { km s ^ { -1 } } 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 \la 5 \% , and the scatter to \la 10 \% .
This could potentially be used to form less biased statistical samples for H _ { 0 } measurements in the upcoming large survey era .