The role of chaos in the circularization of tidal capture binaries. II. Long-time evolution

We examine the long-time dynamical evolution of binaries formed by tidal capture using a self-consistent normal mode analysis. An efficient method for handling very long period orbits is developed which allows us to examine the highly eccentric phase following capture. We start with an adiabatic analysis and show that the orbital eccentricity performs a random walk between the initial eccentricity (≥1) and some nonzero minimum value. The existence of a minimum eccentricity in turn restricts the maximum tidal energy the system is capable of acquiring. We then examine dissipative systems by introducing an artificial mode damping mechanism and show that tidal capture binaries go through two distinct phases. Following capture is a short violent chaotic phase during which the dynamical behavior is as described by the adiabatic analysis. Huge tides are raised, and the tidal luminosity is likely to be large if nonlinear dissipative processes are efficient. Given that the binary survives this phase, it must dissipate a prescribed amount of energy before it enters the second phase during which the orbital behavior is no longer chaotic and the orbital eccentricity varies quasi-periodically. During this long quiescent phase, the tides are small and the binary circularizes only via dissipative processes. The prescribed energy loss and the eccentricity at the beginning of this phase depend on the periastron separation at capture. For example, for equal mass stars with an initial periastron separation of 3 stellar radii, the system starts this phase with an eccentricity of 0.8. For such a system, the quiescent circularization phase is estimated to be at least 10⁷ yr, in contrast to a circularization time predicted by the standard model of 10 yr (McMillan, McDermott, & Taam 1987). Since capture orbits are chaotic, there exists the possibility of a binary returning to an unbound state. We show that the majority of tidal capture binaries are stable against self-ionization. We discuss the various destructive processes which the stars must be stable against during the chaotic phase in order to enter the quiescent phase intact. We also discuss the implications for the formation of low-mass X-ray binaries and related objects and the role of tidal capture binaries in globular cluster evolution.