44 - Self-similar transport

Summary

For my part, I travel not to go anywhere, but to go. I travel for travel's sake. The great affair is to move.

R.I. Stevenson

Like Robert Louis Stevenson, the great affair of a star in a cluster is to move. When gravithermal instability sets in we want to understand how the distribution of stars evolves. Some of the earliest N-body simulations with 50 or more stars (e.g., Aarseth, 1963) already showed a clear tendency for stellar systems to form three distinct regions. At the center there is a nearly isothermal core. Its radius shrinks and its mass decreases as the system evolves. Its average density, however, increases. The stars which remain in the core bind more tightly together. Beyond the core is the halo. It contains most of the stars which diffuse from the core. Computer models of spherical systems which use the equations of stellar hydrodynamics (see Section 8) show that the halo develops a power law density distribution when all stars have the same mass (Larson, 1970). More detailed models, for isotropic velocities, which use the Fokker–Planck equation (Sections 4 and 5) confirm this power law structure (e.g., Cohn, 1980). The density in the halo ρ∝r^-α, where 2.1 ≲ α ≲ 2.4, depending on details of the model. At the outer edge of the halo an evaporation zone develops. Here the density departs from its power law and plummets to zero.