The Shape and Virial Theorem of a Star Cluster in the Galactic Tidal Force Field
Abstract
On the instantaneous tidal relaxation approximation, formulae are derived for the ellipticities and virial theorem of a slightly flattened homogeneous rotating cluster (the largest axis of the cluster is directed towards the Galactic center), in terms of the Galactic tidal force and the characteristic intrinsic plus orbital angular velocity. The expression for a purely tidallydetermined ellipticity is identical to that for an imcompressible fluid body of uniform density. Orbital motion generally contributes significantly to the shape of the cluster. The virial theorem is identical to that for an isolated cluster except that the gravitational potential energy is multiplied by (1  kai), where kai is a positive tidal correction term. To obtain the actual mass of a cluster, the virial theorem mass based on an isolated cluster should be multiplied by the factor 1/(1  kai). The formulae applied to open star clusters, the globular cluster omega Centauri, and dwarf elliptical galaxies in the Local Group.
 Publication:

Journal of Korean Astronomical Society
 Pub Date:
 December 1969
 Bibcode:
 1969JKAS....2....1L