# Identifying Anomalies in Gravitational Lens Time Delays

## TL;DR

This paper investigates how gravitational lens time delays can reveal complex structures in lens potentials, identifying anomalies that suggest substructure or environmental effects, and provides predictions for future observations.

## Contribution

It demonstrates the use of Monte Carlo simulations to distinguish between smooth lens models and anomalies indicating substructure or complex environments.

## Key findings

- Evidence of anomalies in close image pairs in certain lenses.
- Anomalies in RX J1131-1231 indicate substructure.
- Predicted time delays for all known four-image lenses.

## Abstract

We examine the ability of gravitational lens time delays to reveal complex structure in lens potentials. In Congdon, Keeton & Nordgren (2008), we predicted how the time delay between the bright pair of images in a "fold" lens scales with the image separation, for smooth lens potentials. Here we show that the proportionality constant increases with the quadrupole moment of the lens potential, and depends only weakly on the position of the source along the caustic. We use Monte Carlo simulations to determine the range of time delays that can be produced by realistic smooth lens models consisting of isothermal ellipsoid galaxies with tidal shear. We can then identify outliers as "time delay anomalies". We find evidence for anomalies in close image pairs in the cusp lenses RX J1131$-$1231 and B1422+231. The anomalies in RX J1131$-$1231 provide strong evidence for substructure in the lens potential, while at this point the apparent anomalies in B1422+231 mainly indicate that the time delay measurements need to be improved. We also find evidence for time delay anomalies in larger-separation image pairs in the fold lenses, B1608+656 and WFI 2033$-$4723, and the cusp lens RX J0911+0551. We suggest that these anomalies are caused by some combination of substructure and a complex lens environment. Finally, to assist future monitoring campaigns we use our smooth models with shear to predict the time delays for all known four-image lenses.