SPHERICAL COLLAPSE IN MODIFIED NEWTONIAN DYNAMICS

Abstract

Modeling the structure formation in the universe, we extend the spherical-collapse model in the context of modified Newtonian dynamics (MOND) starting with the linear Newtonian structure formation followed by the MONDian evolution. In MOND, the formation of structures speeds up without a need for dark matter. Starting with the top-hat overdense distribution of the matter, the structures virialize with a power-law profile of the distribution of matter. We show that the virialization process takes place gradually from the center of the structure to the outer layers. In this scenario, the smaller structures enter the MONDian regime earlier and evolve faster, hence they are older than larger structures. We also show that the virialization of the structures occurs in the MONDian regime, in which the smaller structures have stronger gravitational acceleration than the larger ones. This feature of the dynamical behavior of the structures is in agreement with the fact that the smaller structures, as the globular clusters or galactic bulges, have been formed earlier and need less dark matter in cold dark matter scenario.