A Family of Models for Spherical Stellar Systems

Details A Family of Models for Spherical Stellar Systems A Family of Models for Spherical Stellar Systems

1993-09-28

arxiv.org/abs/astro-ph/9309044v1

Astron.J. 107 (1994) 634

Astronomy and Astrophysics

Astrophysics

24 pages, uuencoded compressed Postscript file 0.3 Mbyte

Scientific paper

10.1086/116883

We describe a one-parameter family of models of stable spherical stellar systems in which the phase-space distribution function depends only on energy. The models have similar density profiles in their outer parts ($\rho\propto r^{-4}$) and central power-law density cusps, $\rho\propto r^{3-\eta}$, $0<\eta\le 3$. The family contains the Jaffe (1983) and Hernquist (1990) models as special cases. We evaluate the surface brightness profile, the line-of-sight velocity dispersion profile, and the distribution function, and discuss analogs of King's core-fitting formula for determining mass-to-light ratio. We also generalize the models to a two-parameter family, in which the galaxy contains a central black hole; the second parameter is the mass of the black hole. Our models can be used to estimate the detectability of central black holes and the velocity-dispersion profiles of galaxies that contain central cusps, with or without a central black hole.

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