# Improved Constraints on the Gravitational Lens Q0957+561. II. Strong Lensing

## TL;DR

This study uses detailed strong lensing analysis of the Q0957+561 system with HST data to refine the Hubble constant estimate and investigate the lens galaxy's mass distribution, revealing potential substructure.

## Contribution

It provides new constraints on the Hubble constant and the lens galaxy's mass profile using extensive lensing features and multi-component modeling.

## Key findings

- H_0 estimated at 85 (+14/-13) km/s/Mpc from lensing data
- The lens galaxy exhibits a rising rotation curve and an inner dark matter core
- Flux ratios suggest substructure in the lens galaxy

## Abstract

We present a detailed strong lensing analysis of an HST/ACS legacy dataset for the first gravitational lens, Q0957+561. With deep imaging we identify 24 new strongly lensed features, which we use to constrain mass models. We model the stellar component of the lens galaxy using the observed luminosity distribution, and the dark matter halo using several different density profiles. We draw on the weak lensing analysis by Nakajima et al. (2009) to constrain the mass sheet and environmental terms in the lens potential. Adopting the well-measured time delay, we find H_0 = 85 (+14/-13) km/s/Mpc (68% CL) using lensing constraints alone. The principal uncertainties in H_0 are tied to the stellar mass-to-light ratio (a variant of the radial profile degeneracy in lens models). Adding constraints from stellar population synthesis models, we obtain H_0 = 79.3 (+6.7/-8.5) km/s/Mpc (68% CL). We infer that the lens galaxy has a rising rotation curve and a dark matter distribution with an inner core. Intriguingly, we find the quasar flux ratios predicted by our models to be inconsistent with existing radio measurements, suggesting the presence of substructure in the lens.