Mass Determination of Lens Galaxies using Einstein Rings

Abstract

Strong lensing is a gravitational phenomenon in which the light from a dis- tant source is bent and distorted by the gravitational field of an intervening massive object, such as a galaxy or a galaxy cluster, causing the source to be multiply imaged. Among the various types of strong lensing, Einstein rings are particularly intriguing and valuable for studying the characteristics of galaxies. Using Einstein rings to study the mass and environment of a galaxy is uncom- mon and can present many challenges regarding the obtention of the data, as there are many lensed systems but only a few that qualify as bonafide Einstein rings. The aim of the study is to determine the mass of lens galaxies using such rings. In this research study, we analyze data from the Gravitationally Lensed Quasar database and CASTLES database using Plotly, Matplotlib, Astropy, and pandas. By leveraging the relativistic Doppler shift and the definition of the Einstein radius, we determine the masses of ten lens galaxies. The mass range spans from 27 billion solar masses to 946 billion solar masses. We visually represent these masses through graphs, maps, and histograms. From this we figure the significance of mass in determining the Einstein radius. Furthermore, we observe a distinct pattern in the characteristics of the galaxy environment, where the majority of lens galaxies are red, contain quasars, and exhibit el- liptical shapes. Our research is significant as we apply established theories to novel observational data, allowing us to investigate Einstein rings, a rare phe- nomenon with limited available data. This study demonstrates the importance of utilizing Einstein rings as a powerful tool for studying the features of galaxies. Despite the challenges associated with data acquisition, using Einstein rings is a powerful way to measure characteristics of lensed systems.