The MOG Weak Field approximation II. Observational test of Chandra X-ray Clusters

Abstract: We apply the weak field approximation limit of the covariant Scalar-Tensor-Vector Gravity (STVG) theory, so-called MOdified gravity (MOG), to the dynamics of clusters of galaxies by using only baryonic matter. The MOG effective gravitational potential in the weak field approximation is composed of an attractive Newtonian term and a repulsive Yukawa term with two parameters $\alpha$ and $\mu$. The numerical values of these parameters have been obtained by fitting the predicted rotation curves of galaxies to observational data, yielding the best fit result: $\alpha = 8.89 \pm 0.34$ and $\mu= 0.042\pm 0.004$ kpc$<sup>{-1}$~\cite{rah13}. We extend the observational test of this theory to clusters of galaxies, using data for the ionized gas and the temperature profile of nearby clusters obtained by the Chandra X-ray telescope. Using the MOG virial theorem for clusters, we compare the mass profiles of clusters from observation and theory for eleven clusters. The theoretical mass profiles for the inner parts of clusters exceed the observational data. However, the observational data for the inner parts of clusters (i.e., $r&lt;0.1 r_{500}$) is scattered, but at distances larger than $\sim 300$ kpc, the observed and predicted mass profiles converge. Our results indicate that MOG as a theory of modified gravity is compatible with the observational data from the the solar system to Mega parsec scales without invoking dark matter.