Mass segregation (astronomy)

In astronomy, dynamical mass segregation is the process by which heavier members of a gravitationally bound system, such as a star cluster, tend to move toward the center, while lighter members tend to move farther away from the center. During a close encounter of two members of the cluster, the members exchange both energy and momentum. Although energy can be exchanged in either direction, there is a statistical tendency for the kinetic energy of the two members to equalize during an encounter; this statistical phenomenon is called equipartition, and is similar to the fact that the expected kinetic energy of the molecules of a gas are all the same at a given temperature. Since kinetic energy is proportional to mass times the square of the speed, equipartition requires the less massive members of a cluster to be moving faster. The more massive members will thus tend to sink into lower orbits (that is, orbits closer to the center of the cluster), while the less massive members will tend to rise to higher orbits. The time it takes for the kinetic energies of the cluster members to roughly equalize is called the relaxation time of the cluster. A relaxation time-scale assuming energy is exchanged through two-body interactions was approximated in the textbook by Binney & Tremaine as where is the number of stars in the cluster and is the typical time it takes for a star to cross the cluster. This is on the order of 100 million years for a typical globular cluster with radius 10 parsecs consisting of 100 thousand stars. The most massive stars in a cluster can segregate more rapidly than the less massive stars. This time-scale can be approximated using a toy model developed by Lyman Spitzer of a cluster where stars only have two possible masses ( and ). In this case, the more massive stars (mass ) will segregate in the time Outward segregation of white dwarfs was observed in the globular cluster 47 Tucanae in a HST study of the region. Primordial mass segregation is non-uniform distribution of masses present at the formation of a cluster.