The last two chapters have assembled most of the qualitative arguments by which the evolution of the core of a stellar system can be understood. In summary, the tendency towards equipartition drives the more massive stars to smaller radii. Unless their total mass is sufficiently small, equipartition cannot be reached by the time the heavier stars become essentially self-gravitating. When that happens they are eventually subject to the gravothermal instability. It is the purpose of the present chapter to flesh out this outline, but we shall do so in two passes, as it were. First we shall examine the time scales on which these processes act, and a number of factors which modify the simple picture; and we shall explain the qualitative nature of the resulting evolution. Then we turn to a more detailed description of one case which has been studied in great detail: self-similar collapse in systems with stars of equal mass.

The big picture

The time scale for equipartition, te, was discussed in Chapter 16 (see Eq. (16.14)). It is useful to compare it with the standard relaxation time tr (Eq. (14.12)). For this purpose we evaluate the mean kinetic energy per unit mass for each species by 〈Ei〉 = v2/2, independent of mass, i.e. we assume equipartition of velocities.