TDCOSMO XIV: Practical Techniques for Estimating External Convergence of Strong Gravitational Lens Systems and Applications to the SDSS J0924+0219 System

TL;DR

This paper introduces practical techniques and a software tool for estimating the external convergence in strong gravitational lens systems, crucial for accurate Hubble Constant measurements, demonstrated on the SDSS J0924+0219 system.

Contribution

It presents a new software package for environment effect analysis and applies it to real and simulated data to estimate external convergence in lens systems.

Findings

SDSS J0924+0219 has median external convergence of -0.012

The external convergence standard deviation is 0.028

The lens field is typical compared to other lines of sight.

Abstract

Time-delay cosmography uses strong gravitational lensing of a time-variable source to infer the Hubble Constant. The measurement is independent from both traditional distance ladder and CMB measurements. An accurate measurement with this technique requires considering the effects of objects along the line of sight outside the primary lens, which is quantified by the external convergence ($\kappa_{\rm{ext}}$). In absence of such corrections, $H_0$ will be biased towards higher values in overdense fields and lower values in underdense fields. We discuss the current state of the methods used to account for environment effects. We present a new software package built for this kind of analysis and others that can leverage large astronomical survey datasets. We apply these techniques to the SDSS J0924+0219 strong lens field. We infer the relative density of the SDSS J0924+0219 field by computing weighted number counts for all galaxies in the field, and comparing to weighted number counts computed for a large number of fields in a reference survey. We then compute weighted number counts in the Millennium Simulation and compare these results to infer the external convergence of the lens field.Results. Our results show the SDSS J0924+0219 field is a fairly typical line of sight, with median $\kappa_{\rm{ext}} = -0.012$ and standard deviation $\sigma_{\kappa} = 0.028$.