THE DYNAMIC EVOLUTION OF TIDAL CAPTURE BINARIES

The formation of a binary by the tidal capture of a main-sequence star (mass M1, radius R1) by a neutron star (mass M2) is an extremely violent dynamical event. The star, which can be characterized as an irrotational Ricmann ellipsoid in which the change in energy is proportional to the change in angular momentum, emerges from the first pericentric passage with both a large oscillation and a bulk rotation. If the energy in the oscillation exceeds approximately 0.15GM perpendicular-to 2/R1, the star becomes dynamically unstable during the encounter, and either disrupts or loses a substantial fraction of its mass. This occurs on the first orbit if the initial pericenter, R(p), is less than R(p)/R1 less-than-or-similar-to 1.3(M1BAR/2M1)1/3, where M(T) = M1 + M2. The star exceeds this limit on later orbits for pericenters R(p)/R1 less-than-or-similar-to 1.7(M2/M1) + 0.5(M(T)/2M2)1/2. Viscosity is unimportant until late in the evolution (ellipticity e less-than-or-similar-to 0.5), and in most cases nonlinear sources of viscosity such as mode-mode coupling in the atmosphere of the star are the dominant source of viscosity. The energy of the oscillations is stored in only a few modes, and their amplitudes evolve in a slowly damped random walk, which leads to large fluctuations in the orbital binding energy. The time scale for the evolution of the system is dominated by the fluctuations into low-energy, long-period orbits. A small fraction (1%-2%) of the binaries become unbound as a result of de-excitation or heating from encounters with other stars. Another 2%-5% remain bound but are scattered into orbits with pericenters R(p)/R1 > 50 owing to angular momentum transfer during encounters with other stars. While these represent a small fraction of tidal encounters, they can be a large fraction of nonmerging encounters, and they represent all of the objects which in the traditional picture of tidal encounters form binaries with orbital radii of 6R1-10R1.