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

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 aEuroz(lens)aEuro parts per thousand similar to 0.2 and an average velocity dispersion aEuro sigma(eff)aEuro parts per thousand similar to 270 km s(-1). We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc(2) around the Einstein radius (aEuroR(ein)aEuro parts per thousand similar to 4.2 kpc). We infer a mean projected substructure mass fraction f = 0.0076(0.0052)(+0.0208) at the 68 per cent confidence level and a substructure mass function slope alpha < 2.93 at the 95 per cent confidence level for a uniform prior probability density on alpha. For a Gaussian prior based on cold dark matter (CDM) simulations, we infer f = 0.0064(-0.0042)(+0.0080) and a slope of alpha = 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.