Mean field fluctuations and the evolution of self-gravitating systems

This paper considers the nonlinear effects of collective fluctuations about a slowly-varying solution of the collisionless Boltzmann equation appropriate for a system of stars with a distribution of masses. It is argued that these effects should be manifest on a time-scalet _M intermediate between the violent and collisional relaxation times, inhibiting the natural progression towards equipartition induced by collisions, and favouring instead a well-mixed state, realized in numerical simulations, in which the mean square velocity is independent of the mass.