Star clusters containing massive, central black holes: Monte Carlo simulations in twodimensional phase space.
Abstract
It is pointed out that the approximations employed by previous authors regarding the twodimensionality of the distribution function and the process of consumption in the case of the problem of a massive black hole residing at the center of a star cluster have not been very precise. A new analysis is, therefore, conducted, involving the construction of a twodimensional, Monte Carlo dynamical simulation scheme and its application to solve the FokkerPlanck equation in E and Jspace for the steady distribution and consumption of stars around a massive black hole. The key features of the Monte Carlo method used include a 'step adjustment algorithm', used to reconcile the very short dynamical time scales, associated with losscone consumption, with the rather long relaxation time scales found deep in the cusp. Another feature is a star 'creationannihilation scheme' which ensures that the results of the simulation remain statistically accurate even at large absolute values of E, deep in the cusp where the actual number of stars decreases rapidly and becomes small.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 1978
 DOI:
 10.1086/156521
 Bibcode:
 1978ApJ...225..603S
 Keywords:

 Astronomical Models;
 Black Holes (Astronomy);
 Numerical Analysis;
 Star Clusters;
 X Ray Sources;
 Angular Momentum;
 Distribution Functions;
 Dynamic Models;
 Monte Carlo Method;
 Orbit Perturbation;
 PhaseSpace Integral;
 Stellar Motions;
 Astrophysics;
 Black Hole Neighborhood:Star Distribution;
 Black Hole Neighborhood:Stellar Dynamics;
 Black Holes:Star Clusters