Mass segregation, relaxation, and the Coulomb logarithm in N-body systems (again)

The question of the upper cutoff bmax in the " Coulomb logarithm" for self-gravitating N-body systems has been reexamined, based on both large-scale mass segregation and cumulative squared changes in orbital energies as measures of relaxation. Simulations of greater scope than those of an earlier study of the authors, together with a more sophisticated statistical procedure for estimating bmax, unequivocally support the conclu-sion of that study - namely, bmax has a roughly constant value comparable to the half-mass radius R, rather than a value ∼N-1/3R representative of the mean interparticle spacing that decreases with N. The ratios of the relaxation times observed in simulations using different softening lengths for the gravitational potential exhibit an N-dependence that agrees quantitatively with the postulate bmax ≈ R, but is conspicuously inconsistent with bmax ≈ N -1/3R. These findings do not corroborate those of Smith (1992).