Two-body relaxation

Two-body relaxation is the cumulative randomization of stellar velocities by many weak gravitational encounters. Its timescale in a system of $N$ comparable stars is of order $N/\log N$ crossing times.

The Coulomb logarithm $\log \Lambda =\log (b_{\max }/b_{\min })$ collects the logarithmically equal contributions of gravitational encounters over a wide range of impact parameters. For a self-gravitating system of $N$ comparable stars, $\Lambda$ is of order $N$.

A stellar system is collisional on a timescale of interest when its two-body relaxation time is shorter than that timescale, so discrete encounters materially alter its distribution function.