#### Project Title

#### Abstract/Description

The purpose of this research was to create a computer code that would numerically test a Poisson equation relating the mass distribution of a lens galaxy cluster to weak gravitational shear. Einstein’s theory of general relativity predicts that space-time is bent by massive objects, and in weak gravitational lensing, galaxy clusters act as lenses. The observable result is that galaxies far behind the gravitational lens will appear slightly more elliptical than they actually are. The ellipticity of the background galaxies is quantifiable and is directly related to the weak gravitational shear, and the shear is used to determine the mass distribution of the lensing cluster. Within the gravitational lensing community, there are two other well-known methods of determining the mass distribution of a lensing galaxy cluster from the weak gravitational shear. This new method is unique in that it uses a Poisson equation, potentially simplifying the approach to the numerical integrations required. Part of the overall goal of this project was to clarify the effectiveness of this Poisson equation method in relation to the existing methods, with the hope that the Poisson method is more accurate. The Poisson equation method described here refers to the method of numerical relaxation to determine the mass distribution of a lensing galaxy cluster by using the Poisson equation. Over 2000 lines of original C++ code were written for this project, and the code simulates a typical lensing galaxy cluster mass distribution, calculates the weak gravitational shear from the simulated cluster, adds realistic random noise to the shear data, then finally applies a second order Taylor series expansion of the Poisson equation to the noisy shear data and checks how closely the computed mass distribution matches the original simulated galaxy cluster’s distribution. This project has provided the tools needed to perform more rigorous testing of the Poisson equation.

#### Recommended Citation

Roche, Alex
(2013).
Computer Programming to Advance Gravitational Lensing.
*Undergraduate Review*, 9, 135-140.

Available at: http://vc.bridgew.edu/undergrad_rev/vol9/iss1/27

#### Rights Statement

Articles published in *The Undergraduate Review* are the property of the individual contributors and may not be reprinted, reformatted, repurposed or duplicated, without the contributor’s consent.