The effective stochastization time in stellar systems

Stochastization in stellar systems is analyzed in the framework of the paradigm of Krylov and Gurzadyan-Savvidi. The use of a Holtsmark distribution for the random forces with a Rastorguev-Sementsov cutoff confirms that τe/τc ∝ N1/5, where τc is the crossing time, τe is the effective stochastization time, and N is the number of stars. More oblate systems evolve more rapidly, and rotation slows stochastization. The need for a cutoff does not arise if a Petrovskaya distribution is adopted for the random forces (although applying a cutoff does not change the results). In this case, τe/τc varies with N approximately as N0.3. It is found theoretically that τe/τc ∝ N1/3/(lnN)1/2 for large N. Thus, the evolutionary scale found is close to that proposed earlier by Genkin.