Secular stability of isothermal two-component star clusters is studied in terms of thermodynamics, by using a linear-series method. The unperturbed clusters are confined in spherical vessels. It is shown that thermodynamic treatment for the stability is possible even to self-gravitating stellar systems if the systems evolve in accordance with the Fokker-Planck equation. The applicability of the linear-series method is proved. Results of the stability analyses show that a cluster is unstable when both its self-gravitating core and the extended halo develop well. If the total mass ratio of the massive stars to the less massive ones, M2!M1, is in a certain range (the range depends on the mass ratio of the individual stars, m2!m1), the stability criteria are almost independent of the boundary conditions at the surface. This is because the less massive components behave like a heat bath to the centrally condensed self-gravitating massive components. When M2 1M1 0.25(m0/m1)- , the cluster in a plastic wall with a fixed pressure has no thermodynamic equilibrium configuration bounded by its self-gravity, although it has configurations bounded by its surface pressure. This is another manifestation of Spitzer's (1969) theorem on the absence of equilibrium of isolated two-component clusters. Mutual relations among the secular instability, the core-halo structure, and Spitzer's (1969) theorem are discussed. Key words: Core-halo structure; Linear-series method; Secular stability; Two-component star clusters.
Publications of the Astronomical Society of Japan
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