Applying modified gravity to the lensing and Einstein ring in Abell 3827
Abstract
The lensing and Einstein ring at the core of the galaxy cluster Abell 3827 are reproduced in the modified gravity theory (MOG). The estimated effective lensing mass ${M}_{L}=(1+\ensuremath{\alpha}){M}_{b}=5.2\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ within $R=18.3\text{ }\text{ }\mathrm{kpc}$ for a baryon mass ${M}_{b}=1.0\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ within the same radius produces the observed Einstein ring angular radius ${\ensuremath{\theta}}_{E}=1{0}^{\ensuremath{'}\ensuremath{'}}$. A detailed derivation of the total lensing mass is based on modeling of the cluster configuration of galaxies, intracluster light and x-ray emission. The MOG can fit the lensing and Einstein ring in Abell 3827 without dark matter as well as general relativity with dark matter.