A test of Alzain’s modified inertia model for MOND using galaxy cluster observations

Abstract

Recently, Alzain proposed a modified inertial formalism of modified Newtonian dynamics (MOND), wherein Galiliean invariance is violated and new Lorentz transformation properties from an inertial to an accelerated frames are posited. Milgrom’s acceleration constant is then found to be invariant under the aegis of these new space-time coordinate transformations. In this model, a modified equation of hydrostatic equilibrium is proposed, which can be applied to relaxed galaxy clusters. However, when we apply this equation to a Chandra sample of 12 clusters, we find that the total dynamical mass obtained using Alzain’s model is much smaller than the baryonic mass for almost all the clusters, thereby implying that this original model is not viable. A variant of this model with a value of $$a_0$$ about two times smaller than that which fits galaxy data, is necessary in order to reconcile the missing mass problem in clusters, without the need for dark matter.