Lensing time delays as a substructure constraint: a case study with the cluster SDSS~J1004+4112

TL;DR

This paper introduces a method to use gravitational lensing time delays as constraints on the mass distribution in galaxy clusters, demonstrated through a case study of SDSS J1004+4112, revealing detailed matter distribution insights.

Contribution

It develops a principal-components analysis approach to isolate mass distribution constraints from time delays, enhancing understanding of dense cluster regions independently of cosmological parameters.

Findings

Time delays provide tighter constraints on dense matter regions.

Cluster SDSS J1004+4112's central region is rounder than lensed images suggest.

Additional time-delay data will improve mass distribution constraints.

Abstract

Gravitational lensing time delays are well known to depend on cosmological parameters, but they also depend on the details of the mass distribution of the lens. It is usual to model the mass distribution and use time-delay observations to infer cosmological parameters, but it is naturally also possible to take the cosmological parameters as given and use time delays as constraints on the mass distribution. This paper develops a method to isolate what exactly those constraints are, using a principal-components analysis of ensembles of free-form mass models. We find that time delays provide tighter constraints on the distribution of matter in the very high dense regions of the lensing clusters. We apply it to the cluster lens SDSS J1004+4112, whose rich lensing data includes two time delays. We find, assuming a concordance cosmology, that the time delays constrain the central region of the cluster to be rounder and less lopsided than would be allowed by lensed images alone. This detailed information about the distribution of the matter is very useful for studying the dense regions of the galaxy clusters which are very difficult to study with direct measurements. A further time-delay measurement, which is expected, will make this system even more interesting.