Mass segregation

In astronomy, dynamical mass segregation is the process by which heavier members of a gravitationally bound system, such as a star cluster or cluster of galaxies, tend to move toward the center, while lighter members tend to move farther away from the center. Primordial mass segregation is non-uniform distribution of masses present at the formation of a cluster. After relaxation, all trace of primordial mass segregation is lost. In geochemistry, mass segregation leads to the chemical differentiation of planets above a critical size, between a heavy metallic core and a rocky outer mantle and crust.

Equipartition of kinetic energy

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, which is on the order of 100 million years for a typical globular cluster with radius 10 parsecs consisting of 100 thousand stars.

Evaporation

After relaxation, the speed of some low mass members can be greater than the escape velocity of the cluster, which results in these members being lost to the cluster. This process is called evaporation. (A similar phenomenon explains the loss of lighter gases from a planet, such as hydrogen and helium from the Earth—after equipartition, some molecules of sufficiently light gases at the top of the atmosphere will exceed the escape velocity of the planet and be lost.)

Through evaporation, most open clusters eventually dissipate, as indicated by the fact that most existing open clusters are quite young. Globular clusters, being more tightly bound, appear to be more durable.

In the Galaxy

The relaxation time of the Milky Way galaxy is approximately 10 trillion years, on the order of thousand times the age of the galaxy itself. Thus, any observed mass segregation in our galaxy must be almost entirely primordial.

See also

• Messier 67
• n-body problem
• Virial theorem
• Willman 1

References

• Ian A. Bonnell, Melvyn B. Davies (1998). "Mass segregation in young stellar clusters". Monthly Notices of the Royal Astronomical Society 295 (3): 691–698. Bibcode 1998MNRAS.295..691B. doi:10.1046/j.1365-8711.1998.01372.x. 

• E. Khalisi, P. Amaro-Seoane, R. Spurzem (2007). "A comprehensive NBODY study of mass segregation in star clusters: energy equipartition and escape". Monthly Notices of the Royal Astronomical Society 374 (2): 703–720. arXiv:astro-ph/0602570. Bibcode 2007MNRAS.374..703K. doi:10.1111/j.1365-2966.2006.11184.x. http://www3.interscience.wiley.com/cgi-bin/fulltext/117974654/HTMLSTART. 

• Spitzer, Lyman S. (Jr) (1987). Dynamical Evolution of Globular Clusters. Princeton University Press. ISBN 0691083096. 

• White, S. D. M. (April 1977). "Mass segregation and missing mass in the Coma cluster". Monthly Notices of the Royal Astronomical Society 179: 33–41. Bibcode 1977MNRAS.179...33W.