The SLACS strong lens sample, debiased

II. Lensing-only constraints on the stellar initial mass function and dark matter contraction in early-type galaxies

¹ Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
² Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai 200240, China
³ Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China

^⋆ Corresponding author: sonnenfeld@sjtu.edu.cn

Received: 1 November 2024
Accepted: 23 March 2025

Abstract

The Sloan Lens ACS (SLACS) is the best studied sample of strong lenses to date. Much of our knowledge of the SLACS lenses has been obtained by combining strong lensing with stellar kinematics constraints. However, interpreting stellar kinematics data is difficult, as it requires reconstructing the three-dimensional structure of a galaxy and the orbits of its stars. For SLACS, the problem is exacerbated by its selection function, which caused lenses with a larger observed velocity dispersion to be overrepresented. In this work, we pursue an alternative approach to the study of galaxy structure with SLACS, based purely on gravitational lensing data. The primary goal of this study is to constrain the stellar population synthesis mismatch parameter α_sps, quantify the ratio between the true stellar mass of a galaxy and that obtained with a reference stellar population synthesis model, and identify the efficiency of the dark matter response to the infall of baryons, ϵ. We combined Einstein radius measurements from the SLACS lenses with weak lensing information from their parent sample, while accounting for selection effects. The data can be fit comparatively well by a model with log α_sps = 0.22 and ϵ = 0, corresponding to an initial mass function (IMF) slightly lighter than Salpeter and no dark matter contraction, or log α_sps = 0 and ϵ = 0.8, equivalent to a Chabrier IMF and almost maximal contraction. Selection effects, if not modelled, produce a shift in the joint posterior probability that is larger than the uncertainty. The degeneracy between α_sps and ϵ could be broken with lensing-only measurements of the projected density slope, but existing data are completely inconsistent with our model. We suspect systematic errors in the measurements to be at the origin of this discrepancy. Number density constraints would also help break the degeneracy. Because of selection effects, SLACS lenses have a larger velocity dispersion than galaxies with the same projected mass distribution, and their velocity dispersion is overestimated. These two biases combined produce a 5% upward shift in the observed velocity dispersion.