Relativistic, Spherically Symmetric Star Clusters.IV. a Sufficient Condition for Instability of Isotropic Clusters against Radial Perturbations

Abstract

view Abstract Citations (34) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Relativistic, Spherically Symmetric Star Clusters.IV. a Sufficient Condition for Instability of Isotropic Clusters against Radial Perturbations Fackerell, Edward D. Abstract In this paper a one-dimensional eigenvalue equation of the Sturm-Liouville type is obtained which optimizes the trial functions used by Ipser in Paper III of this series to analyze the stability against radial perturbations of isotropic, spherically symmetric, relativistic star clusters. This eigenequation provides a very powerful, sufficient criterion for the instability of such a star cluster. Using this criterion, we show that a polytropic star cluster of indices n = 4 and P4 = 45 is unstable if the redshift of a photon emitted from its center and received at infinity is greater than 0.7302. This result is important because such a cluster has an extreme core-halo density distribution (mean density divided by central density equal to 1.6 X 10-13), and no previous stability analyses have been capable of handling clusters with extreme core-halo distributions. Publication: The Astrophysical Journal Pub Date: June 1970 DOI: 10.1086/150477 Bibcode: 1970ApJ...160..859F full text sources ADS | Related Materials (4) Part 1: 1968ApJ...154..251I Part 2: 1969ApJ...156..509I Part 3: 1969ApJ...158...17I Part 5: 1971ApJ...165..489F