Secular dynamics of binaries in stellar clusters II: dynamical evolution

Chris Hamilton, Roman R. Rafikov

Published 2019-02-04Version 1

Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. 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 (Hamilton \& Rafikov 2019a) 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 binary orbital elements evolution are qualitatively similar 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 in detail how the dynamics are altered in each regime and calculate their characteristics such as secular evolution timescale, maximum possible eccentricity, etc. We verify the predictions of this doubly-averaged formalism numerically and find it to be very accurate when its underlying assumptions are fulfilled, typically meaning that the secular timescale should exceed the period of the binary in the cluster by $\gtrsim 10-10^2$ (depending on the cluster potential and binary orbit). Our results may be relevant for understanding the nature of a variety of exotic systems harbored by dense stellar clusters.