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. 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 lens ∼ 0.2 and an average velocity dispersion σ eff ∼ 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 ( R ein ∼ 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 α < 2.93 at the 95 percent confidence level for a uniform prior probability density on α. For a Gaussian prior based on cold dark matter (CDM) simulations, we infer f = 0.0064 +0.0080 −0.0042 and a slope of α = 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.

How well can cold dark matter substructures account for the observed radio flux-ratio anomalies

“…We mention in passing that the different subhalo mass fraction between here and 0.3 per cent as in Xu et al (2009) is attributed to a richer subhalo populations of group-sized haloes considered here. These fractions are also consistent with Vegetti et al (2014), who searched for imprints of substructures in arc images of 11 gravitational lens systems from the Sloan Lens ACS Survey.…”

Constraints on the identity of the dark matter from strong gravitational lenses

“…First, we randomly sample N haloes with mass in the range [10 13 , 10 14 ] h −1 M using the mass function of the EAGLE reference simulation. This mass range is consistent with the lens sample in the SLAC (Vegetti et al 2014). For simplicity, we assume that for all the strong lens systems, z l = 0.3 and z s = 0.5, comparable to the values in the SLAC observations.…”

“…If the detection limit is 10 8 h −1 M , the test with about 100 lenses can still set a lower limit on the WDM particle mass, but it cannot rule out CDM. We stress, however, that tests assuming a more realistic sensitivity function (see Vegetti et al 2014) are required for a precise result.…”

“…In our catalogues, we will consider as 'detected subhaloes' those having a measured mass larger than M low ≡ 3σ m . We note that this definition is different from that adopted by Vegetti et al (2014), who employed a detection threshold derived from the probability density of a substructure mass, given the observed lensed data, marginalized over the host lens and background source parameters.…”

“…The technique developed by Koopmans (2005) and Vegetti & Koopmans (2009a) can detect individual subhaloes and, using the Bayesian formalism of Vegetti & Koopmans (2009b), a sample of detections can constrain the SHMF. Vegetti et al (2014) analysed 11 strong lenses in the Sloan Lens ACS Survey (SLAC; Bolton et al 2006) and obtained one detection in SDSS J0956+5110. Their estimate of the projected substructure mass fraction (i.e.…”