Secular dynamics of binaries in stellar clusters I: general formulation and dependence on cluster potential
arXiv:1902.01344 · doi:10.1093/mnras/stz1730
Abstract
Orbital evolution of binary systems in dense stellar clusters is important in a variety of contexts: origin of blue stragglers, progenitors of compact object mergers, millisecond pulsars, and so on. Here we consider the general problem of secular evolution of the orbital elements of a binary system driven by the smooth tidal field of an axisymmetric stellar cluster (globular, nuclear, etc.) in which the binary orbits. We derive a secular Hamiltonian (averaged over both the inner Keplerian orbit of the binary and its outer orbit within the cluster) valid to quadrupole order for an arbitrary cluster potential and explore its characteristics. This doubly-averaged 'tidal' Hamiltonian depends on just two parameters, which fully absorb the information about the background cluster potential and the binary's orbit within it: a dimensional parameter setting the secular timescale, and a dimensionless parameter which determines the phase portrait of the binary's inner orbital evolution. We examine the dependence of and on cluster potential (both spherical and axisymmetric) and on the binary orbit within the cluster. Our theory reproduces known secular results - such as Lidov-Kozai evolution and the effect of the Galactic tide on Oort Cloud comets - in appropriate limits, but is more general. It provides a universal framework for understanding dynamical evolution of various types of binaries driven by the smooth tidal field of any axisymmetric potential. In a companion paper (Hamilton & Rafikov 2019b) we provide a detailed exploration of the resulting orbital dynamics.
arXiv comment24 pages, 13 figures. Final version accepted for publication in MNRAS
References in corpus (59)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- galpy: A Python Library for Galactic Dynamics
- Shrinking binary and planetary orbits by Kozai cycles with tidal friction
- The Eccentric Kozai-Lidov Effect and Its Applications
- Binary Black Hole Mergers from Globular Clusters: Masses, Merger Rates, and the Impact of Stellar Evolution
- Hot Jupiters from Secular Planet--Planet Interactions
- Secular evolution of compact binaries near massive black holes: gravitational wave sources and other exotica
- Secular Dynamics in Hierarchical Three-Body Systems
- Binary Black Hole Mergers from Globular Clusters: Implications for Advanced LIGO
- Resonant Relaxation in Stellar Systems
- On the Eccentricity Distribution of Coalescing Black Hole Binaries Driven by the Kozai Mechanism in Globular Clusters
- MOCCA-SURVEY Database I: Coalescing Binary Black Holes Originating From Globular Clusters
- Eccentric Black Hole Mergers Forming in Globular Clusters
- Binary black hole mergers from field triples: properties, rates and the impact of stellar evolution
- Binary Mergers and Growth of Black Holes in Dense Star Clusters
- Accelerating Compact Object Mergers in Triple Systems with the Kozai Resonance: A Mechanism for "Prompt" Type Ia Supernovae, Gamma-Ray Bursts, and Other Exotica
- Lidov-Kozai Cycles with Gravitational Radiation: Merging Black Holes in Isolated Triple Systems
- Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai-Lidov Effect
- On the triple origin of blue stragglers
- The Eccentric Kozai Mechanism for a Test Particle
- Dynamical Formation of the GW150914 Binary Black Hole
- Long-Term Cycling of Kozai-Lidov Cycles: Extreme Eccentricities and Inclinations Excited by a Distant Eccentric Perturber
- Black hole mergers and blue stragglers from hierarchical triples formed in globular clusters
- Eccentricity growth and orbit flip in coplanar hierarchical three body systems
- Black hole mergers from an evolving population of globular clusters
- Steady-state planet migration by the Kozai-Lidov mechanism in stellar binaries
- Greatly enhanced merger rates of compact-object binaries in non-spherical nuclear star clusters
- On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening
- Mergers of Stellar-Mass Black Holes in Nuclear Star Clusters
- Rapid Eccentricity Oscillations and the Mergers of Compact Objects in Hierarchical Triples
- The Evolution of Wide Binary Stars
- A Binary Origin for Blue Stragglers in Globular Clusters
- The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole
- The Effect of Encounters on the Eccentricity of Binaries in Clusters
- The impact of vector resonant relaxation on the evolution of binaries near a massive black hole: implications for gravitational wave sources
- Compact Binaries Ejected from Globular Clusters as GW Sources
- Binary Black Holes in Dense Star Clusters: Exploring the Theoretical Uncertainties
- The rate of WD-WD head-on collisions in isolated triples is too low to explain standard type Ia supernovae
- Stellar Dynamics around Black Holes in Galactic Nuclei
- THE ORBITAL ECCENTRICITIES OF BINARY MILLISECOND PULSARS IN GLOBULAR CLUSTERS
- Origin of the S Stars in the Galactic Center
- Exoplanets Beyond the Solar Neighbourhood: Galactic Tidal Perturbations
- Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure. II. External perturbations: flybys and supernovae
- A Unified Theory for the Effects of Stellar Perturbations and Galactic Tides on Oort Cloud Comets
- The Effectiveness of the Kozai Mechanism in the Galactic Centre
- Secular dynamics of binaries in stellar clusters II: dynamical evolution
- Revisiting relaxation in globular clusters
- Levy Flights of Binary Orbits due to Impulsive Encounters
- Compact object binary mergers driven by cluster tides: a new channel for LIGO/Virgo gravitational wave events
- On the formation of hot and warm Jupiters via secular high-eccentricity migration in stellar triples
- Secular theory of the orbital evolution of the young stellar disc in the Galactic Centre
- Planetary Orbital Equations in Externally-Perturbed Systems: Position and Velocity-Dependent Forces
- A new insight into the Galactic potential: A simple secular model for the evolution of binary systems in the solar neighbourhood
- Diffusion and mixing in globular clusters
- Exponential growth of eccentricity in secular theory
- Computing secular motion under slowly rotating quadratic perturbation
- Eccentricity Boost of Stars Around Shrinking Massive Black Hole Binaries
- Probabilistic eccentricity bifurcation for stars around shrinking massive black hole binaries
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- Single-single gravitational-wave captures in globular clusters: Eccentric deci-Hertz sources observable by DECIGO and Tian-Qin
- Chaotic dynamics of wide triples induced by galactic tides: a novel channel for producing compact binaries, mergers, and collisions
- Dynamics of Planetary Systems Within Star Clusters: Aspects of the Solar System's Early Evolution
- On the Correlation between Hot Jupiters and Stellar Clustering: High-eccentricity Migration Induced by Stellar Flybys
- Secular dynamics of binaries in stellar clusters II: dynamical evolution
- Compact-Object Mergers in the Galactic Center: Evolution in Triaxial Clusters
- Close Encounters of Wide Binaries Induced by the Galactic Tide: Implications for Stellar Mergers and Gravitational-Wave Sources
- Anomalies in the gravitational recoil of eccentric black-hole mergers with unequal mass ratios
- Eccentricity dynamics of wide binaries -- I. The effect of Galactic tides
- On the phase-mixed eccentricity and inclination distributions of wide binaries in the Galaxy
- On the pollution of white dwarfs by exo-Oort cloud comets
- Secular dynamics of binaries in stellar clusters -- III. Doubly-averaged dynamics in the presence of general relativistic precession
- Intermediate mass black holes' effect on compact object binaries
- Evolution of binary stars in the early evolutionary phases of ultra-faint dwarf galaxies
- Binary mergers in the centers of galaxies: synergy between stellar flybys and tidal fields
- Astrophysics with the Laser Interferometer Space Antenna
- The evolution of a supermassive binary black hole in an non-spherical nuclear star cluster
- The eccentricity distribution of wide binaries and their individual measurements