A detailed MOND modelling of the Bullet Cluster

Abstract

The colliding galaxy clusters system 1E 0657-56, the "Bullet Cluster", is often presented as a serious objection to modified gravity theories dispensing with dark matter in general, and in particular, to the MOND formalism. The argument centres on the fact that the baryonic matter distribution of this system is dominated by the X-ray emitting gas, while the projected surface density required under General Relativity to explain the observed lensing signal, centres on the observed galaxies. This spatial offset is interpreted as being in conflict with MOND, naively assuming that dark matter being absent, the gravitational potential should centre upon the largest mass distribution, the X-ray gas. However, as under General Relativity, under MOND, the gravitational potential of a system depends upon the volume density and not just the total mass. I here show that the surface density which QUMOND predicts will be inferred under General Relativity from the gravitational potential of the "Bullet Cluster", qualitatively matches the spatial distribution of what General Relativity inferences of lensing observations return. The close-to-point-like galaxies imply under QUMOND a relatively larger surface density signal than what is expected from the diffuse gas. As is common under MOND modeling of galaxy clusters, a mass deficit on the baryon content is obtained, in this case by a factor of 1.6. Beyond this, only small offsets on the details with respect to GR interpretations of lensing observations remain; MOND is hence shown to be no more discrepant with the "Bullet Cluster" than with any other galaxy cluster.