Statistics – Computation
Scientific paper
Feb 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991apj...367..507m&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 367, Feb. 1, 1991, p. 507-513.
Statistics
Computation
13
Anisotropy, Computational Astrophysics, Dark Matter, Jeans Theory, Neutrinos, Density Distribution, Equations Of State, Fermions
Scientific paper
Zero central density solutions of the spherically symmetric, anisotropic Jeans equation are shown to exist for a wide range of conditions when the transverse velocity dispersion exceeds the radial one. Explicit solutions are described for generalized polytropes with distribution functions like ordinary polytropes multiplied by a power of angular momentum, and for systems with constant phase-space density in velocity ellipsoids (only the first kind of solutions are time-independent). The constant phase-space density systems obey mass-radius relations of the type MR-cubed = constant, and so do the generalized polytropes regardless of the polytropic index n, provided that the maximum value of the phase-space density is fixed. This constraint follows naturally in collisionless systems. In most cases the anisotropic solutions are more massive than their isotropic counterparts for fixed radius. One consequence of this is a weakening of phase-space constraints on the mass of fermionic dark matter, e.g. neutrinos.
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