A study on the structure of globular clusters.
It is aimed at to investigate changes of structures of globular clusters with time, and to examine whether they are actually in non-equilibrium states. In Chapter I, a model process for energy exchange is considered instead of treating the Fokker Planck equation, and an approximate equation for distribution of velocity is derived. The distribution function Ψ of total mechanical energy, H, and angular momentum, J, of a star is considered to be more reasonable for studying globular clusters rather than distribution function of velocity itself. An equation for Ψ is derived. It is found that the rate of escape of stars from a spherical cluster can be expressed in a similar form to that of an infinitely extended homogeneous cluster, and it is determined only by the mean of local rates of escape. On the basis of an assumption that the initial cluster was restricted in a finite region with a finite mass, the possibility of structure change and expansion is suggested, and it is seen for the cluster to tend to equilibrium asymptotically as t to oo. In Chapter II, timely change of structure of a model cluster of stars with an equal mass and of uniform rate of energy exchange is investigated. It is shown in this case that the distribution of stars changes accompanying envelope formation from its initial one to a truncated isothermal distribution having a finite mass and radius. The computed result agrees considerably well with observations. The 'change of radius of a cluster with time is also discussed, and it is found to increase at early stages of its evolution. It is concluded: (1) large clusters, e.g., ω Cen might be still in non-equilibrium states, and its peculiar distribution could be explained only as in an non-equilibrium state, (2) medium size clusters like M3 or M15 are close to equilibrium but have not completely reached it, (3) the clusters are generally still in expanding stages. The ages of the clusters are estimated from the characteristics of density distribution. For M2, M3, M5, M13, M15, M22, M92 and ω Cen, the results are 8.1, 6.5, 11, 6.6, 6.2, 8.3, 4.6 and 5.1 in 109 years, respectively. The results are generally fairly coincident with those obtained from the theory of stellar evolution.
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| Format: | Journal Contribution biblioteca |
| Language: | English |
| Published: |
1962
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| Online Access: | http://hdl.handle.net/1834/16926 |
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| Summary: | It is aimed at to investigate changes of structures of globular clusters with time, and to examine whether they are actually in non-equilibrium states. In Chapter I,
a model process for energy exchange is considered instead of treating the Fokker Planck equation, and an approximate equation for distribution of velocity is derived.
The distribution function Ψ of total mechanical energy, H, and angular momentum, J, of a star is considered to be more reasonable for studying globular clusters rather
than distribution function of velocity itself. An equation for Ψ is derived. It is found that the rate of escape of stars from a spherical cluster can be expressed in a similar
form to that of an infinitely extended homogeneous cluster, and it is determined only by the mean of local rates of escape. On the basis of an assumption that
the initial cluster was restricted in a finite region with a finite mass, the possibility of structure change and expansion is suggested, and it is seen for the cluster to tend to equilibrium asymptotically as t to oo. In Chapter II, timely change of structure of a model cluster of stars with an equal mass and of uniform rate of energy exchange
is investigated. It is shown in this case that the distribution of stars changes accompanying envelope formation from its initial one to a truncated isothermal distribution having a finite mass and radius. The computed result agrees considerably well with observations. The 'change of radius of a cluster with time is also discussed, and it is found to increase at early stages of its evolution. It is concluded: (1) large clusters, e.g., ω Cen might be still in non-equilibrium states, and its peculiar distribution could be explained only as in an non-equilibrium state, (2) medium size clusters like M3 or M15 are close to equilibrium but have not completely reached it,
(3) the clusters are generally still in expanding stages. The ages of the clusters are estimated from the characteristics of density distribution. For M2, M3, M5, M13, M15, M22, M92 and ω Cen, the results are 8.1, 6.5, 11, 6.6, 6.2, 8.3, 4.6 and 5.1 in 109 years, respectively. The results are generally fairly coincident with those obtained from the theory of stellar evolution. |
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