On mass and velocity distributions in members of star clusters : an analytical approach

Abstract

Dynamical evolution of stellar mass distribution in star clusters is analysed by considering simultaneously the effects of dynamical friction, stochastic heating and the gravitational potential due to mass distribution in the clusters. A simple expression is suggested for the dynamical friction which adequately describes it in both high and low velocity ranges and the effect of mass distribution in the cluster on the dynamics of a test mass can be described by an anharmonic potential. With the help of energy considerations we describe the dispersions in position and in velocity for stars of different masses showing how the slowing down and mass segregation of stars evolve in the cluster. Results are presented with the parameters for the star clusters of our Galaxy.