Inference of the Cold Dark Matter substructure mass function at z=0.2 using strong gravitational lenses

TL;DR

This study uses strong gravitational lensing data from 11 galaxies at z=0.2 to constrain the dark matter substructure mass function, finding results consistent with Cold Dark Matter predictions despite limited detections.

Contribution

It provides the first Bayesian constraints on the substructure mass function at low redshift using non-detections and a single detection, aligning observations with CDM models.

Findings

Inferred substructure mass fraction f ≈ 0.0064–0.0076 at 68% confidence

Substructure mass function slope α ≈ 1.90, consistent with CDM

Results agree with flux ratio anomaly inferences at 68% confidence

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. 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 z ~ 0.2 and an average velocity dispersion of 270 km/s. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc squared around the Einstein radius (~4.2 kpc). We infer a mean projected substructure mass fraction $f = 0.0076^{+0.0208}_{-0.0052}$ at the 68 percent confidence level and a substructure mass function slope $\alpha$ < 2.93 at the 95 percent confidence level for a uniform prior probability density on alpha. For a Gaussian prior based on Cold Dark Matter (CDM) simulations, we infer $f = 0 .0064^{+0.0080}_{-0.0042}$ and a slope of $\alpha$ = 1.90$^{+0.098}_{-0.098}$ at the 68 percent 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 percent confidence level.