Modeling the formation of galaxy clusters in MOND

Abstract

We use a one dimensional hydrodynamical code to study the evolution of spherically symmetric perturbations in the framework of Modified Newtonian Dynamics (MOND). The code evolves spherical gaseous shells in an expanding Universe by employing a MOND-type relationship between the fluctuations in the density field and the gravitational force, $g$. We focus on the evolution of initial density perturbations of the form $δ_{i}\sim r_{i}^{-s}$ for $0<s<3$. A shell is initially cold and remains so until it encounters the shock formed by the earlier collapse of shells nearer to the centre. During the early epochs $g$ is sufficiently large and shells move according to Newtonian gravity. As the physical size of the perturbation increases with time, $g$ gets smaller and the evolution eventually becomes MOND dominated. However, the density in the inner collapsed regions is large enough that they re-enter the Newtonian regime. The evolved gas temperature and density profiles tend to a universal form that is independent of the the slope, $s$, and of the initial amplitude. An analytic explanation of this intriguing result is offered. Over a wide range of scales, the temperature, density and entropy profiles in the simulations, depend on radius roughly like $r^{0.5}$, $r^{-1.5}$ and $r^{1.5}$, respectively. We compare our results with XMM-{\it Newton} and {\it Chandra} observations of clusters. The temperature profiles of 16 observed clusters are either flat or show a mild decrease at $R\gtsim 200\rm kpc$. MOND profiles show a significant increase that cannot reconciled with the data. Our simulated MOND clusters are substantially denser than the observed clusters. It remains to be seen whether these difficulties persist in three-dimensional hydrodynamical simulations with generic initial conditions.