Structure and adiabatic compression of dark matter halos: Simple analytic model

An analytical model is considered for describing the inner regions of dark matter halos. This model is based on the assumption that the density of dark matter varies according to the power law. The model concerns the distribution function in phase space that is expressed in terms of the adiabatic invariants (radial action and angular momentum). Two types, narrow and broad, are suggested for the angular part of the distribution function. The model makes it possible to explicitly describe the adiabatic compression of halos due to a change induced in the gravitational potential by the condensation of baryonic matter at the center. The change in the density of the dark matter halos is calculated and it is shown that the standard algorithm for calculating the adiabatic compression overestimates the halo density, particularly for the case of strong radial anisotropy.