Title:The Train Wreck Cluster and Bullet Cluster explained by modified gravity without dark matter

Abstract:A major hurdle for modified gravity theories is to explain the dynamics of galaxy clusters. This paper makes the case for a generalized gravitational theory called Scalar-Tensor-Vector-Gravity (STVG) to explain merging cluster dynamics, and it will be the first of a series of papers intended to investigate this issue. The paper presents the results of a re-analysis of the Bullet Cluster as well as an analysis of the Train Wreck Cluster (using data from Jee et al. and Harvey et al.) 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 suggests that $3.2\%$ of the Bullet Cluster is composed of galaxies. For the Train Wreck Cluster, if the Jee et al. data is used, it is found that $3.5\%$ of it is galaxies, and $22\%$ if the Harvey et al. data is used. The matter in galaxies and the enhanced gravity shift the lensing peaks making the peaks offset from the X-ray gas. The work demonstrates that this generalized gravitational theory has the potential to explain merging cluster dynamics without dark matter.