Efficient Mass Estimate at the Core of Strong Lensing Galaxy Clusters Using the Einstein Radius

TL;DR

This paper evaluates the accuracy of using the Einstein radius as a quick mass estimate for strong lensing galaxy clusters, quantifying its scatter and bias through simulations, and proposes corrections to improve its reliability.

Contribution

It provides the first quantitative assessment of the uncertainties in Einstein radius-based mass estimates and introduces an empirical correction to reduce bias and scatter.

Findings

Measured scatter of 13.9% in mass estimates from Einstein radius.

Identified an 8.8% positive bias in the mass estimates.

Reduced scatter to 10.1% after applying empirical correction.

Abstract

In the era of large surveys, yielding thousands of galaxy clusters, efficient mass proxies at all scales are necessary in order to fully utilize clusters as cosmological probes. At the cores of strong lensing clusters, the Einstein radius can be turned into a mass estimate. This efficient method has been routinely used in literature, in lieu of detailed mass models; however, its scatter, assumed to be $\sim30\%$, has not yet been quantified. Here, we assess this method by testing it against ray-traced images of cluster-scale halos from the Outer Rim N-body cosmological simulation. We measure a scatter of $13.9\%$ and a positive bias of $8.8\%$ in $M(<\theta_E)$, with no systematic correlation with total cluster mass, concentration, or lens or source redshifts. We find that increased deviation from spherical symmetry increases the scatter; conversely, where the lens produces arcs that cover a large fraction of its Einstein circle, both the scatter and the bias decrease. While spectroscopic redshifts of the lensed sources are critical for accurate magnifications and time delays, we show that for the purpose of estimating the total enclosed mass, the scatter introduced by source redshift uncertainty is negligible compared to other sources of error. Finally, we derive and apply an empirical correction that eliminates the bias, and reduces the scatter to $10.1\%$ without introducing new correlations with mass, redshifts, or concentration. Our analysis provides the first quantitative assessment of the uncertainties in $M(<\theta_E)$, and enables its effective use as a core mass estimator of strong lensing galaxy clusters.