Combining time delays and image positions for quadruple lenses: a moment approach

TL;DR

This paper presents an analytical method combining time delays and image positions in quadruple gravitational lenses to estimate key lens parameters quickly, aiding automated analysis in large surveys.

Contribution

It introduces simple analytical expressions linking observable quantities to lens parameters, facilitating rapid initial estimates for quadruple lens modeling.

Findings

Analytical relations accurately estimate lens parameters.

Method matches numerical results approximately.

Useful for automated lens detection in large surveys.

Abstract

Time delays in gravitational lenses can be used to determine the Hubble constant and the lens potential. In future surveys, many gravitational lenses can be discovered, and their time delays and image positions can in principle be measured. Using an elliptical power-law potential, we show that combinations of image positions and time delays for quadruple lenses yield simple analytical expressions that are connected with observable quantities. These relations can be used to obtain the approximate axis ratio q, the Einstein radius and the slope. We apply this method to RX J1131-1231, and show that our analytical results match the full numerical determinations approximately. Our approach can quickly determine rough values of lens parameters, which can then be used as initial guesses for further refinement through numerical modelling and may be useful for automated lens search in large surveys.