Friday, May 31, 2013

1305.7220 (P. H. Nguyen et al.)

Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos    [PDF]

P. H. Nguyen, J. F. Pedraza
Spherical systems with a polytropic equation of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense that their equiprobability surfaces in velocity space are non-spherical, leading to an overabundance of radial or circular orbits, depending on the parameters of the model in consideration. Among the family, we find the post-Newtonian generalization of the Plummer and Hernquist models. A close inspection of their equation of state reveals that these solutions interpolate smoothly between a polytropic sphere in the asymptotic region and an inner core that resembles an isothermal sphere. Finally, we study the thermodynamics of these models and argue for their stability.
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