Expansion versus contraction in the evolution of a star cluster.

Abstract

view Abstract Citations (1) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Expansion versus contraction in the evolution of a star cluster. King, Ivan Abstract During its evolution a star cluster is subjected simultaneously to expansive and contractive influences. In a loose cluster the expansive influences are dominant, and the consequent expansion accentuates this dominance. Spitzer (1958) has shown that under such circumstances the lifetime of a cluster is short. On the other hand, the evolution of a dense cluster is dominated by the contractive influence of the ejection of stars. This process also accelerates itself, and again the lifetime of the cluster is sharply limited (King 1958). The present paper treats a cluster of intermediate density, where both expansive and contractive influences operate simultaneously. Application of the virial theorem and the law of conservation of energy leads to differential equations for the rates of change of the number of stars n and the cluster radius R. As is to be expected, the analysis shows that loose clusters become looser and dense clusters become denser. The dividing line is characterized by a certain value of the ratio R9/n. The dependence on R is so strong that there is practically a critical radius, which varies only as the ninth root of n. For a given n the critical radius characterizes the cluster in which the expansive and contractive influences remain most closely balanced. This cluster has a longer life than any other with the same initial number of stars. There is thus an upper limit to the lifetime of a galactic cluster. Furthermore, numerical calculations show that the balance between expansive and contractive influences is so extremely unstable that it is all but impossible for a cluster's lifetime to attain that idealized upper limit. The practical upper limit is thus even lower; it is about io~ years for a cluster containing 100 stars and 5 X I0~ years for 1000 stars. The critical radius in either case is a little over a parsec. Finally, an estimate may be made of how much these results are likely to be changed by the inclusion of other ~ffects in the evolution of a cluster. King, I. 1958, A. J. 63, ii8. Spitzer, L. 1958, Ap. J. 127, 17. University of Illinois Observatory, Urbana, Ill. Publication: The Astronomical Journal Pub Date: September 1958 DOI: 10.1086/107755 Bibcode: 1958AJ.....63..306K full text sources ADS |