Abstract
We try to bridge the gap between the theory of linear density-velocity-gravitational perturbations in the early universe, and the relaxed galaxies we observe today. We succeed quantitatively for dark matter if dark matter is warm. The density runs of baryons and of dark matter of relaxed galaxies are well described by hydro-static equations. The evolution from initial linear perturbations to final relaxed galaxies is well described by hydro-dynamical equations. These equations necessarily include dark matter velocity dispersion. If the initial perturbation is large enough, the halo becomes self-gravitating. The adiabatic compression of the dark matter core determines the final core density, and provides a negative stabilizing feedback. The relaxed galaxy halo may form adiabatically if dark matter is warm. The galaxy halo radius continues to increase indefinitely, so has an ill-defined mass.
Highlights
Introduction and OverviewHow does a particular linear density perturbation in the early universe evolve to become a relaxed galaxy that we observe today? We approach this question in reverse chronological order
We find that the density runs ρh (r ) of the dark matter halo, and ρb (r ) of baryons, are determined by the dispersion velocities vr′h2 of dark matter particles, and vr′b2 of baryons, and by the radius req at which
The purpose of the present study is to find out how nature obtains these parameters starting from a particular linear density-velocity-gravitational perturbation in the early universe
Summary
How does a particular linear density perturbation in the early universe evolve to become a relaxed galaxy that we observe today? We approach this question in (arguably) reverse chronological order. We begin with a study of relaxed elliptical galaxies with a cusp dominated by baryons. We find that the density runs ρh (r ) of the dark matter halo, and ρb (r ) of baryons, are determined (in a limited range of the radial coordinate r) by the dispersion velocities vr′h2 of dark matter particles, and vr′b2 of baryons, and by the radius req at which ( ) ( ) ρh req = ρb req. We consider relaxed spiral galaxies with a core dominated by baryons
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