A New Channel for Detecting Dark Matter Substructure in Galaxies: Gravitational Lens Time Delays

TL;DR

This paper proposes using gravitational lens time delays as a new method to detect dark matter substructure, offering advantages over existing techniques by being unaffected by dust and stellar microlensing.

Contribution

It introduces a mathematical framework for analyzing time delay perturbations caused by dark matter substructure in galaxy-scale lenses.

Findings

Time delay perturbations depend on the subhalo mass function.

Time delay ratios are unaffected by lens profile degeneracies.

Substructure can alter the order of image arrival times in cusp lenses.

Abstract

We show that dark matter substructure in galaxy-scale halos perturbs the time delays between images in strong gravitational lens systems. The variance of the effect depends on the subhalo mass function, scaling as the product of the substructure mass fraction and a characteristic mass of subhalos (namely <m^2>/<m>). Time delay perturbations therefore complement gravitational lens flux ratio anomalies and astrometric perturbations by measuring a different moment of the subhalo mass function. Unlike flux ratio anomalies, "time delay millilensing" is unaffected by dust extinction or stellar microlensing in the lens galaxy. Furthermore, we show that time delay ratios are immune to the radial profile degeneracy that usually plagues lens modeling. We lay out a mathematical theory of time delay perturbations and find it to be tractable and attractive. We predict that in "cusp" lenses with close triplets of images, substructure may change the arrival-time order of the images (compared with smooth models). We discuss the possibility that this effect has already been observed in RX J1131-1231.