Caustic area biases and how to deal with them

TL;DR

This paper investigates biases affecting caustic area measurements in quadruply-imaged lensed quasars and assesses their impact on cosmological expansion rate estimates, finding the bias to be small but potentially correctable.

Contribution

It extends previous analyses by including Eddington bias effects and evaluates their impact on the Hubble constant estimation through simulations.

Findings

Bias impact on H0 is about 1% or less.

Bias depends on caustic area distribution and noise.

Proper modeling can mitigate the bias.

Abstract

Quadruply-imaged strongly lensed quasars (quads) are routinely used for measurements of the expansion rate of the Universe with time delays. It has recently been suggested that any quad lens is subject to a Malmquist-like bias that causes the inferred area enclosed within the tangential caustic to be systematically underestimated, and that such a bias might translate into a corresponding bias on the expansion parameter. In this work we extended that analysis by also considering the effect of Eddington bias. We found that the sign and amplitude of the combined bias depend on the functional form of the caustic area distribution of the lens population and on the noise associated with the caustic area estimation process. Based on simulations, we estimated that the corresponding impact on $H_0$ is on the order of a percent or smaller. If the likelihood of the lensing data is known, then the bias can be accounted for when modelling the lens population. However, ignoring the criteria used to select a quad might lead to a bias at the lens modelling stage that causes the inferred caustic area to be overestimated. Such a bias disappears for lens models that are well constrained by the data.