A numerical method for the study of the gravothermal instability in star clusters

We describe a numerical method for studying the evolution of spherical one-component star clusters. This method employs numerical integration of the moment equations derived from the Boltzman equation. In order to close this system of equations it is assumed that the energy flux tensor can be derived from an appropriate heat conduction law. We allow for a large anisotropy of the velocity distribution and include relaxation effects which are evaluated using the Fokker–Planck theory. Detailed numerical results from a study of the evolution of Plummer's model are reported. The evolution has been followed to that point where the central density ρ(0) increased by a factor of 10¹⁴. Only in the late stages of evolution the core collapse rate ($$(\dot\rho/\rho)$$) is a fixed fraction of the relaxation rate. The velocity distribution here represented by six moments seems to approach a self-similar form. The comparison of different outer boundary conditions and with former work indicates that this form is independent of the structure of the outer halo. These results provide new evidence that core collapse and the onset of the homological phase in the late stages of it is due to the gravothermal catastrophe picture of Lynden-Bell & Wood.