# Colisional Evolution of Stellar Systems

## Astronomy 626: Spring 1995

How do stellar-dynamical systems evolve over times longer than the
*relaxation* time,

0.1N
t_r = ---- t_c ?
ln N

At any instant a stellar system almost exactly obeys the CBE, but
stellar encounters slowly transform the system along a sequence of
near-equilibria. The discussion here focuses on the abstract problem
of a Newtonian system of `N` point masses.

## Heuristic Arguments

**Escaping stars** carry away mass and energy.

**Negative specific heat** supports an outward flow of
energy.

**Binary processes** may take over energy production.

## The Fokker-Planck Equation

**Weak encounters** dominate evolution (F-P approximation).

**Phase-space diffusion** coefficients describe effects of weak
encounters.

**Relaxation timescales** at core and median-mass radii are
derived from diffusion coefficients.

## Results for Spherical Systems

**Escape** due to ejection (insignificant) and evaporation.

**Core collapse** results from outward energy flow.

**Equipartition** between stars of different masses accelerates
core collapse.

**Expansion** of post-collapse cluster is driven by interactions
involving binary stars.

## References

- Goodman, J. 1989, in
*Dynamics of Dense Stellar Systems*.
- Heggie, D.C. 1975,
*M.N.R.A.S.* **173**, 729.
- Lynden-Bell, D. & Wood, R. 1968,
*M.N.R.A.S.*
**138**, 495.
- Spitzer, L. 1940,
*M.N.R.A.S.* **100**, 396.

Joshua E. Barnes
(barnes@zeno.ifa.hawaii.edu)
Last modified: April 27, 1995