Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses

Abstract

We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey by Bolton et al. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift zlens ~0.2 and an average velocity dispersion seff ~270 km s-1. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc2 around the Einstein radius (Rein ~4.2 kpc). We infer a mean projected substructure mass fraction f = 0.0076+0.0208-0.0052 at the 68 per cent confidence level and a substructure mass function slopea < 2.93 at the 95 per cent confidence level for a uniform prior probability density on a. For a Gaussian prior based on cold dark matter (CDM) simulations, we infer f = 0.0064+0.0080-0.0042 and a slope of a =1.90+0.098-0.098 at the 68 per cent confidence level. Since only one substructure was detected in the full sample, we have little information on the mass function slope, which is therefore poorly constrained (i.e. the Bayes factor shows no positive preference for any of the two models). The inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at the 68 per cent confidence level. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.