Star cluster

A star cluster is a gravitationally associated group of stars formed in a relatively compact region. Open clusters and globular clusters provide populations whose members have broadly related formation histories, making them useful laboratories for stellar evolution. Membership is tested using parallax, proper motion and, where available, radial velocity, rather than apparent proximity on the sky alone. A cluster's Hertzsprung-Russell diagram then compares stars of different masses at a shared distance; its main-sequence turnoff helps estimate stellar age. Space-based astrometry sharpens both membership selection and these evolutionary sequences, although some clusters contain multiple stellar populations.^[ref]

An open cluster is a relatively low-mass group of stars formed together, typically in a galactic disk. Two-body relaxation, stellar evaporation, and external tidal disturbances disperse many open clusters on much shorter times than the lifetimes of their low-mass member stars.

Two-body relaxation redistributes stellar energies and feeds stars above the escape threshold. The escaping population removes mass and generally nonnegative energy at infinity. Radius evolution and external tidal limits must be considered before inferring the change in cluster density.

For an isolated quasistatic cluster with near-zero escape energies, the bound negative energy is approximately fixed. The virial theorem and gravitational radius then imply $R_g\propto M^2$. A homologous mean density scales as $M^{-5}$ and increases as mass evaporates. Tidal limitation or finite positive escape energies modifies this simple model.

A globular cluster is an old, dense, approximately spheroidal star cluster whose long-term evolution is shaped by two-body relaxation and the tidal field of its host galaxy.