The Train Wreck Cluster Abell 520 and the Bullet Cluster 1E0657-558 in a Generalized Theory of Gravitation

A major hurdle for modified gravity theories is to explain the dynamics of galaxy clusters. A case is made for a generalized gravitational theory called Scalar-Tensor-Vector-Gravity (STVG) or MOG (modified gravity) to explain merging cluster dynamics. The paper presents the results of a re-analysis of the Bullet Cluster, as well as an analysis of the Train Wreck Cluster in the weak gravitational field limit without dark matter. The King-$\beta$ model is used to fit the X-ray data of both clusters, and the $\kappa$-maps are computed using the parameters of this fit. The amount of galaxies in the clusters is estimated by subtracting the predicted $\kappa$-map from the $\kappa$-map data. The estimate for the Bullet Cluster is that $14.1\%$ of the cluster is composed of galaxies. For the Train Wreck Cluster, if the Jee et al. data are used, $25.7\%$ of the cluster is composed of galaxies. The baryon matter in the galaxies and the enhanced strength of gravitation in MOG, shift the lensing peaks making them offset from the gas. The work demonstrates that this generalized gravitational theory can explain merging cluster dynamics without dark matter.