Gravitational collapse of the galactic dark matter
A spherically symmetric matter collapses under its own gravity. For the Milky Way, the time scale of collapse for a spherical halo with NFW density is ∼ 26 My which is very small compared to the age of the Milky Way. The effect of a pressure, obeying a polytrope equation of state is investigated. It is shown that for p ∝ ρ9/8, the time scale would be of the order of 1 Gy. It is also argued that such a polytrope, if considered to be in equilibrium, could explain the rotation curve of the milky way.
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