Tidal-shock relaxation: A reexamination of tidal shocks in stellar systems

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Abstract
The phenomenon of ''tidal-shock relaxation'' is defined and quantitatively estimated. We show that the second-order term [(Delta E)(2)](ts), which has usually been neglected in the treatment of tidal shocks, is typically far more important than the first-order term [(Delta E)](ts). The latter has been found by Aguilar, Ostriker, and Hut (1988) to be the dominant physical process driving the evolution of the Galactic system of globular clusters. The reason is simply that \upsilon.Delta upsilon\, which contributes to the second-order term, is usually much larger than \Delta upsilon\(2), the basis of the first-order term. Near the tidal radius the tidal-shock relaxation term [(Delta E)(2)](ts) will accelerate mass loss, and near the half-mass radius it competes with the two-body relaxation [(Delta E)(2)](rel) in driving the evolution of the internal structure in the cluster. Formulae for the evaluation of the second-order term are computed for the idealized case treated by Spitzer (1987) of stars in harmonic potential. For typical parameters of global clusters we find that even at the half-mass point, tidal-shock relaxation may be competitive with two-body relaxation.

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