### Violent Relaxation...

...sounds like a new form of extreme sports for the overly energetic, but it's actually a process of some importance in galaxy formation. The virial theorem relates the time average of the kinetic energy of a system of gravitationally bound particles to its potential energy: Tav = -(1/2)V. A system in which this kinetic energy is close to this average is called relaxed.

Suppose one starts with an arrangement of, say 100, mass particles with random velocities and turns on gravity. Initially, there is no particular relation between the total kinetic energy and the potential energy (except they should be bound, so T +V < 0). After a few particle crossing times (the time for a typical particle to cross the distribution under influence of other particles gravity) one should find that the ratio approaches the virial average. Such a system is said to be relaxed.

One process that leads to relaxation is gravitational encounters between pairs of individual particles, which tends to equipartition kinetic energies. The time to relaxation in such encounters depends on the density and number of particles. For an open cluster of about 100 stars, relaxation times are roughly ten million years, while for for globular cluster of 100,000 stars, the relaxation time is about half a billion years. Unsurprisingly, such systems are relaxed. For a big elliptical galaxy, though, the relaxation time may be 10^17 years, or millions of times longer than the age of the universe.

Surprisingly enough, then, such systems are also usually relaxed. Why so? Many derivations of the virial theorem depend on assuming that the moment of inertia of the system is not changing. However, if you start, say, a big mass of gas or particles from something approaching rest, and turn on gravity, it will rapidly contract, changing the moment of inertia and the overall gravitational potential. This kind of process can produce rapid ("violent") relaxation.

This kind of relaxation is thought to account for the relaxed state of most galaxies.