THE DISTRIBUTION FUNCTIONS OF STAR CLUSTERS.
Abstract
Two model globular clusters are constructed, each consistent with a given analytical surface density law known to fit well actual star clusters. One model is described by an isotropic distribution function (IDF) which depends on energy alone. The other model is described by the maximum energy distribution (MEDF) consistent with the given surface density. At small energies the IDF is exponential while at high energies it linearly approaches a finite value at the cutoff energy. The coefficient in the exponential approaches a constant as the concentration of the cluster increases, explaining the failure of the model to fit spherical galaxies. Arguments in favor of the abrupt cutoff are advanced which are based on the relaxation time being long compared with the circumgalactic orbital period, and on the change in the total escape energy as a cluster executes an elliptical circumgalactic orbit. It is shown that the truncated Maxwellian distribution in an MEDF is the distribution which is zero above the escape energy and constant below. For the given surface density the MEDF is computed by constructing a set of perturbing distribution functions which do not contribute to the density. These are added to the IDF in such a way as to maximize the entropy. Six perturbing functions were constructed and then used in finding the MEDF. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1969
- Accession Number
- AD0701085
Entities
People
- John Broderick
Organizations
- Brandeis University