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

Abstract

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 (doublyaveraged) Hamiltonian derived there encapsulates all information about the tidal potential experienced by the binary in its orbit around the cluster in a single parameter Γ. Here we provide a thorough exploration of the phase-space of the corresponding secular problem as Γ is varied. We find that for Γ > 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 Γ = 1/5, 0, −1/5. We show how the dynamics are altered in each regime and calculate characteristics such as secular evolution timescale, maximum possible eccentricity, etc. 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 timescale should exceed the period of the binary around the cluster by 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.1 To sufficient accuracy, the binary's barycentre follows the trajectory of a test particle, d 2 Rg/dt 2 = −∇Φ where Φ is the smooth cluster potential.

Compact-object Mergers in the Galactic Center: Evolution in Triaxial Clusters

“…In this section, we examine the dynamics of binaries whose outer orbits densely fill an axisymmetric torus on timescales shorter than those at which the inner binary is torqued by the tidal field. This problem was studied in detail by Hamilton & Rafikov (2019b, 2019c, who develop a general formalism to describe the dynamics of torus-filling binaries in axisymmetric potentials, generalizing previous results regarding the effect of galactic tides on stellar binaries (e.g., Heisler & Tremaine 1986). Here, we demonstrate that our simulations are consistent with the results of Hamilton & Rafikov (2019b, 2019c and examine the additional effect of an SMBH on these considerations.…”

“…In this section, we discuss the dynamics of binaries in axisymmetric potentials whose outer orbits fail to densely fill a torus within the secular timescale. In this regime, the analytic formalism of Hamilton & Rafikov (2019b, 2019c breaks down, and we observe substantially different behavior. Most interestingly, this regime can give rise to secular chaos in the evolution of the inner orbit, as previously studied by Petrovich & Antonini (2017).…”

“…However, the authors treated the cluster potential as a small perturbation to a three-body system and did not explore the full extent of the cluster, but rather limited themselves to the central ∼0.5 pc of a single ad hoc potential. Second, in a series of papers, Hamilton & Rafikov (2019a, 2019b, 2019c explored the secular dynamics for the full extent of the cluster and overcame the technical limitations of Petrovich & Antonini (2017) by fully accounting for the cluster tidal field in the binary's evolution. However, the authors restricted themselves to non-triaxial clusters without an SMBH.…”

“…in is a constant of motion and the potential is integrable. Using the conservation of j z and the secular energy, Hamilton & Rafikov (2019c) show that a nearly circular inner orbit with » j i cos (e.g., Kozai 1962;Lidov 1962). As we will see in Section 3.2, the presence of an SMBH conspires to keep Γ>1/5 in most regimes.…”

Long-term orbital dynamics of trans-Neptunian objects

“…Moreover, Ω G is always decreasing if I G < 90 o and always increasing if I G > 90 o (the period of its linear part can be found in Higuchi et al 2007). Finally, as noted by Hamilton and Rafikov (2019) about the same Hamiltonian in a different context, for K 2 G < 4/5 the eccentricity value at the stable equilibrium points (see Eq. 33) is a lower bound of the maximum eccentricity reached by any trajectory.…”