# Unified lensing and kinematic analysis for any elliptical mass profile

## TL;DR

This paper introduces a fast, general method for calculating gravitational lensing effects for any elliptical mass profile by decomposing it into Gaussian components, solving a long-standing computational challenge.

## Contribution

It presents a novel, efficient technique to compute lensing quantities for elliptical profiles using Gaussian decomposition, overcoming a three-decade-old computational hurdle.

## Key findings

- Method accurately computes lensing deflection and magnification for elliptical profiles.
- Decomposition into Gaussian components simplifies complex lensing calculations.
- The approach is computationally efficient and broadly applicable.

## Abstract

We demonstrate an efficient method to compute the strong-gravitational-lensing deflection angle and magnification for any elliptical surface-density profile. This method solves a numerical hurdle in lens modelling that has lacked a general solution for nearly three decades. The hurdle emerges because it is prohibitive to derive analytic expressions of the lensing quantities for most elliptical mass profiles. In our method, we first decompose an elliptical mass profile into Gaussian components. We introduce an integral transform that provides us with a fast and accurate algorithm for the Gaussian decomposition. We derive analytic expressions of the lensing quantities for a Gaussian component. As a result, we can compute these quantities for the total mass profile by adding up the contributions from the individual components. This lensing analysis self-consistently completes the kinematic description in terms of Gaussian components presented by Cappellari (2008). Our method is general without extra computational burden unlike other methods currently in use.