Astronomy and Astrophysics – Astrophysics – Galaxy Astrophysics
Scientific paper
2011-08-26
Astronomy and Astrophysics
Astrophysics
Galaxy Astrophysics
8 pages, 6 figures, submitted to MNRAS
Scientific paper
The tidal radius is commonly analytically determined by equating the tidal field of the galaxy to the gravitational potential of the cluster. This gives a radius at which stars can move from orbiting the cluster centre to independently orbiting the galaxy. In this paper the tidal radius of a globular cluster is estimated using a novel approach from the theoretical standpoint of the general three-body problem. This is achieved by an analytical formula for the transition radius between stable and unstable orbits in a globular cluster. A stability analysis, outlined by Mardling (2008), is used here to predict the occurrence of unstable stellar orbits in the outermost region of a globular cluster in a distant orbit around a galaxy. It is found that the eccentricity of the cluster-galaxy orbit has a far more significant effect on the tidal radius of globular clusters than previous theoretical results have found. A simple analytical formula is given for determining the transition between stable and unstable orbits, which is analogous to the tidal radius for a globular cluster. This tidal radius estimate is interior to previous estimates and gives the innermost region from which stars can random walk to their eventual escape from the cluster.
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