Other
Scientific paper
May 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978ap%26ss..55..351s&link_type=abstract
Astrophysics and Space Science, vol. 55, no. 2, May 1978, p. 351-382.
Other
Calculus Of Variations, Dynamic Stability, Isotropic Media, Relativistic Effects, Star Clusters, Functions (Mathematics), Isothermal Processes, Polytropic Processes, Rayleigh-Ritz Method, Red Shift, Variational Principles
Scientific paper
A multiterm trial function technique is developed for studying the dynamic stability of isotropic relativistic star clusters by using the variational principle originated by Ipser and Thorne (1968). The technique is applied to n = 4 polytropic clusters and low-temperature isothermal clusters. These two types of cluster have pronounced core-halo structures and have both proved difficult to analyze with single-term trial-function methods. The n = 4 polytropic clusters are proved to be dynamically unstable if their central redshifts are greater than 0.412. This is quite close to the point on their sequence with a central redshift of 0.41, where their fractional binding energy peaks. Strong evidence is obtained that all isothermal clusters with no dispersion in the stellar rest mass become dynamically unstable near the region where their fractional binding energy peaks, and that none of these clusters is dynamically stable if their central redshift exceeds a value of approximately 0.53.
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