Title:The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter

Abstract: A detailed analysis of the November 15, 2006 data release (Clowe et al., 2006) X-ray surface density Sigma-map and the strong and weak gravitational lensing convergence kappa-map for the Bullet Cluster 1E0657-558 is performed and the results are compared with the predictions of a modified gravity (MOG) and dark matter. Our surface density Sigma-model is computed using a King beta-model density, and a mass profile of the main cluster and an isothermal temperature profile are determined by the MOG. We find that the main cluster thermal profile is nearly isothermal. The MOG prediction of the isothermal temperature of the main cluster is T = 15.5 +- 3.9 keV, in good agreement with the experimental value T = 14.8{+2.0}{-1.7} keV. Excellent fits to the two-dimensional convergence kappa-map data are obtained without non-baryonic dark matter, accounting for the 8-sigma spatial offset between the Sigma-map and the kappa-map reported in Clowe et al. (2006). The MOG prediction for the kappa-map results in two baryonic components distributed across the Bullet Cluster 1E0657-558 with averaged mass-fraction of 83% intracluster medium (ICM) gas and 17% galaxies. Conversely, the Newtonian dark matter kappa-model has on average 76% dark matter (neglecting the indeterminant contribution due to the galaxies) and 24% ICM gas for a baryon to dark matter mass-fraction of 0.32, a statistically significant result when compared to the predicted Lambda-CDM cosmological baryon mass-fraction of 0.176{+0.019}{-0.012} (Spergel et al., 2006).