A consistent MOND modelling of the Bullet Cluster

Abstract

It is a common miss-conception that 1E 0657-56, the "Bullet Cluster", is somehow inconsistent with MOND expectations. The argument centres on the fact that the baryonic matter distribution of this system is dominated by the X-ray emitting gas, while the total projected surface density required under General Relativity to explain the observed lensing signal, centres on the observed galaxies. This is sometimes interpreted as being in conflict with MOND, as under such an interpretation, it is naively assumed that all dark matter being absent, the gravitational potential should necessarily be dominated by the largest mass distribution, that of the gas. However, just as under General Relativity, under MOND, the total gravitational potential of a system depends sensitively upon the volume density and not just on the total mass. It is shown in this {\it letter} that the surface density which QUMOND predicts will be inferred under a standard gravity framework from the total gravitational potential of the Bullet Cluster, closely matches what General Relativity inferences of lensing observations return. The close-to-point-like galaxies imply under QUMOND a relatively much larger surface density signal than what is expected from the Mpc scale gas distribution.