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The Dynamical Evolution of Binaries in Clusters
[chapter]

D. C. Heggie

1975
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Dynamics of Stellar System
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Using information on the rates at which binaries suffer encounters in a stellar system (Heggie, 1974a), we here study the effects of such processes on the evolution of the system itself. First considering systems with no binaries initially, we show that low-energy pairs attain a quasi-equilibrium distribution comparatively quickly. Their effect on the evolution of the cluster is negligible compared with that of two-body relaxation. In small systems energetic pairs may form sufficiently quickly
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... fficiently quickly to exercise a substan tial effect on its development and on the escape rate, but in large systems their appearance is delayed until the evolution of the core is well advanced. In that case they appear to be responsible for arresting the collapse of the core at some stage. Binaries of low energy, even if present initially in large numbers, are likely to have at most only a temporary effect on the evolution of the system. High-energy pairs are not easily destroyed, and so, if present initially, their effect is persistent. It competes with two-body relaxation especially when the fraction of such pairs and the total number-density are high, as in the core, where, in addition, binaries tend to congregate by mass segregation. When encounters with binaries become important, being mostly 'superelastic' they enhance escape and lead to ejection of mass from the core into the halo, thus accelerating the rate at which mass is lost by tidal forces. It is difficult to decide observationally whether globular clusters possess sufficiently large numbers of binaries for these effects to be important. facts on the formation and evolution of binaries in clusters. If we define 'soft' binaries to be those with binding energies x satisfying /?xl, the argument differs, for these may absorb binding energy, but Spitzer and Hart showed, by a calculation to orders of magnitude, that the number of such pairs forming per unit relaxation time must vary approximately as N~ *, where N is the total number of particles in the system. Since the evolution of the cluster will be over after at most a hundred relaxation times, the conclusion is that the formation of hard pairs can be entirely ignored, provided that the system is of sufficient size. Since considerable theoretical effort has been applied to a detailed, independent investigation of dynamical processes involving binaries, the rate of their occurrence can now be stated with some accuracy in most cases (Heggie, 1974a). In this paper these newly available results are applied to a re-examination of the role played by binaries in the evolution of clusters, with especial regard to the questions discussed by Spitzer and Hart. In the next two sections, devoted respectively to soft and hard pairs, the arguments will be seen to differ in some respects from those quoted above, although the broad conclusions of Spitzer and Hart are preserved. In particular it is confirmed that in a large system there is insufficient time for the formation of enough binaries to affect significantly the evolution of the system. In the fourth section we consider how these conclusions must be modified if we do not wait for the binaries to form by these inefficient dynamical processes: supposing that there may already exist numbers of binaries when the star cluster has formed, we enquire how abundant and how energetic they need to be in order to exert a significant in fluence on the dynamical evolution of the whole cluster. Throughout most of the paper, except where otherwise stated, the discussion is restricted to systems whose members all have the same mass, m, and so the final section indicates certain avenues which require exploration before the results may be applied to real systems, with especial regard to the effects of a mass-spectrum. At this point some suggestions are made for contact with observations. First, however, we remark on the assumptions and approximations made in order to arrive at the 'reaction rates' which we shall quote, though full details will be found elsewhere (Heggie, 1974a) . The results are expressed in terms of rate functions Q(x, y), analogous to those of atomic physics, defined thus: Let n be the number-density of single stars near a binary having 'internal' binding energy x > 0. Then the probability that, during an encounter with a single star, the binary suffers a change in its binding energy lying in the range (y, y + dy) during the time interval (t, t + dt) is defined to be nQ(x, y) dy dt. This definition is easily extended to accommodate the case in which stars with different masses are present, but we note that the encounter responsible for a certain change in energy is idealised to occur instantaneously. Since only the local numberavailable at https://www.cambridge.org/core/terms. https://doi.

doi:10.1007/978-94-010-1818-0_9
fatcat:hfm25qp2ffdfvoygntyinx4xoa