The distribution and consumption rate of stars around a massive, collapsed object.
Abstract
The steady-state distribution and consumption rate of stars orbiting a massive object at the center of a spherical N-body stellar system are reexamined, concentrating on the manner in which stars gradually diffuse inward toward the center by repeated small-angle gravitational encounters with each other. The analysis incorporates the two-dimensional Fokker-Planck equation in energy (E) and angular-momentum (J) space, for which the approximate velocity-diffusion coefficients computed for the case of a Maxwellian field-star distribution are employed. The distribution of the stars as a function of J is determined for small J by considering the rate at which stars of fixed E enter the loss cone; a Fokker-Planck equation in E alone and containing an energy-dependent 'sink' term is obtained by integrating the two-dimensional equation over J and substituting an expression for the stellar consumption rate; and the approximate steady-state solution to this equation in the 'self-similar' regime is found along with the total rate at which the central object consumes stars. The results are applied to a massive black hole at the center of a globular cluster (M15) and an elliptical galaxy.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- January 1977
- DOI:
- 10.1086/154925
- Bibcode:
- 1977ApJ...211..244L
- Keywords:
-
- Black Holes (Astronomy);
- Elliptical Galaxies;
- Globular Clusters;
- Gravitational Collapse;
- Star Distribution;
- Stellar Systems;
- Angular Momentum;
- Diffusion Coefficient;
- Fokker-Planck Equation;
- Maxwell-Boltzmann Density Function;
- Steady State;
- Velocity Distribution;
- Astrophysics