Secular dynamics of binaries in stellar clusters - II. Dynamical evolution

Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources) and blue stragglers. We investigate the secular dynamics of a binary system driven by the global tidal field of an axisymmetric stellar cluster in which the binary orbits. In a companion paper we developed a general Hamiltonian framework describing such systems. The effective (doubly-averaged) Hamiltonian derived there encapsulates all information about the tidal potential experienced by the binary in its orbit around the cluster in a single parameter Gamma. Here we provide a thorough exploration of the phase-space of the corresponding secular problem as Gamma is varied. We find that for Gamma > 1/5 the phase-space structure and the evolution of binary orbital elements are qualitatively similar to the Lidov-Kozai problem. However, this is only one of four possible regimes, because the dynamics are qualitatively changed by bifurcations at Gamma = 1/5, 0, -1/5. We show how the dynamics are altered in each regime and calculate characteristics such as the secular evolution time-scale and maximum possible eccentricity. We verify the predictions of our doubly-averaged formalism numerically and find it to be very accurate when its underlying assumptions are fulfilled, typically meaning that the secular time-scale should exceed the period of the binary around the cluster by greater than or similar to 10-10(2) (depending on the cluster potential and binary orbit). Our results may be relevant for understanding the nature of a variety of exotic systems harboured by stellar clusters.