The dynamical lifetime of a star cluster.

Abstract

view Abstract Citations (6) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The dynamical lifetime of a star cluster. King, Ivan Abstract It is well known that a cluster will eject stars as a result of encounters between its members. It has also been recognized that the cluster will consequently contract and the contraction will increase the rate of ejection. The purpose of the present paper is to calculate the effect of the contraction on the lifetime of the cluster. The starting point is the instantaneous rate of ejection of stars, as calculated by Ambartsumian (1938), Spitzer (1940), and Chandrasekhar (1943), who have shown that the cluster loses just under one per cent of its stars in a time equal to the time of relaxation. This principle can be combined with the theory of the time of relaxation, the law of conservation of energy, and the virial theorem to give a differential equation for the number of stars in the cluster as a function of time. The equation is easily solved. The solution depends slightly on the assumption made about the amount of energy that the escaping stars carry away. It is shown to be reasonable to assume that they carry away zero energy; this assumption sets an upper bound on the life of the cluster. The resulting evolution of the cluster may be compared with the exponential decay that would follow from assuming that the time of relaxation remains constant. For an exponential decay the time required for half the stars to escape is 93 TO, where TO is the initial time of relaxation; while consideration of the contraction reduces this time to 39 TO. The corresponding times required for nine-tenths of the stars to escape are 300 TO and 42 TO. All these time intervals are inversely proportional to the initial instantaneous rate of ejection of stars. Any future refinements in the theory of the ejection rate will change the estimate of the lifetime of a cluster but will not affect the conclusion that its lifetime is considerably reduced by evolutionary contraction of the cluster. Ambartsumian, V. A. 1938, Ann. Leningrad State Univ., No. 22, issue 4, p. 19. Chandrasdchar, S. 1943, Ap. J. 98, 54. Spitzer, L. 1940, Al. N. 100, 396 = Harvard Reprint No. 204. University of Illinois Observatory, Urbana, Ill. Publication: The Astronomical Journal Pub Date: July 1957 DOI: 10.1086/107496 Bibcode: 1957AJ.....62..144K full text sources ADS |