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

Numerical N-body calculations are carried out to determine the time scale for mass segregation in a cluster consisting of particles with a range of masses. Results are used to construct a simple analytic approximate expression for the time scale to use for various mass distribution functions. A convenient bimodal mass spectrum is considered, consisting of heavy and light particles whose masses differ by a factor of 10, and it is demonstrated that a convenient measure of the relaxation time may be defined in terms of the secular expansion of the cloud of light particles. An explicit prediction of the relaxation time is tested against simulations employing a Schechter-type mass function, and the expression is found to be accurate to about 25%.