Collapse of an inhomogeneous protogalaxy with random motions

Abstract

The free fall time for a galaxy collapsing inside a dark matter halo is ∼5.10 8 years while the reported age differences between halo globular clusters (even those in eccentric orbits) are of the order of a few Gigayears. The two time scales cannot be reconciled in models where the main body of the galaxy collapsed as a single unit. In this context, we examine the time taken by an inhomogeneous cloud, with gravitationally fed random motions to collapse. The collapse rate depends on the number, length scale and the degree of condensation of the inhomogeneities, and we find that for a range of values for these parameters, the protogalaxy takes significantly longer than a free fall time to collapse. We use the two component dynamic virial equation, supplemented by an evolution equation for the energy to investigate the time taken by an inhomogeneous cloud to dissipate its binding energy and collapse to one-tenth the original size, inside a dark matter halo. We find that the collapse time scales are increased to a few Gigayears and, our model suggests that the clumpy substructure of protogalaxies would have had a filling factor ∼10 −2–10 −3.