Hitherto in Part III, we have considered the properties of stationary relaxed stellar systems. We know such systems cannot be realistic because they are not stable. Their most obvious instability is the evaporation of high energy stars. These carry net energy away from the system; remaining stars swarm inside a deeper gravitational well and cluster more strongly together.

Even if a cluster did not evaporate, something must clearly be wrong with the assumption that it could be stable. The fact that, in a Newtonian system, more and more kinetic energy can be produced by continued gravitational concentration suggests that instability may occur wholly internally through a redistribution of the stars. In a spherical system we would expect the center to become denser, losing energy by ejecting high energy stars into the outer parts, and forming a steeper gravitational well.

A simple physical argument suggests how this instability arises. Systems satisfying the virial theorem (9.30) have 2T + W = 0 or since the total energy E = T + W, they satisfy E = – T. Although systems, or parts of systems, may not satisfy the virial theorem exactly, they are close enough that this relation describes the essential part of the physics needed to understand gravithermal instability. The kinetic energy of random motions T is proportional to the temperature. (A useful confusion of nomenclature?) Thus decreasing the energy of a gravitationally bound system, increases its temperature.