Lensing substructure quantification in RXJ1131-1231: A 2 keV lower bound on dark matter thermal relic mass

We study the substructure content of the strong gravitational lens RXJ1131-1231 through a forward modelling approach that relies on generating an extensive suite of realistic simulations. We use a semi-analytic merger tree prescription that allows us to stochastically generate substructure populations whose properties depend on the dark matter particle mass. These synthetic halos are then used as lenses to produce realistic mock images that have the same features, e.g. luminous arcs, quasar positions, instrumental noise and PSF, as the data. We then analyse the data and the simulations in the same way with summary statistics that are sensitive to the signal being targeted and are able to constrain models of dark matter statistically using Approximate Bayesian Computing (ABC) techniques. In this work, we focus on the thermal relic mass estimate and fix the semi-analytic descriptions of the substructure evolution based on recent literature. We are able, based on the HST data for RXJ1131-1231, to rule out a warm dark matter thermal relic mass below 2 keV at the 2$\sigma$ confidence level.