Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure. III. Suborbital effects: hybrid integration techniques and orbit-averaging corrections

Abstract

The SecularMultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested binaries. In the formalism underlying SecularMultiple, we previously averaged over all orbits in the system. This approximation significantly speeds up numerical integration of the equations of motion, making large population synthesis studies possible. However, the orbit averaging approximation can break down when the secular evolution timescale of the system is comparable to or shorter than any of the orbital periods in the system. Here, we present an update to SecularMultiple in which we incorporate hybrid integration techniques, and orbit-averaging corrections. With this update, the user can specify which orbits should be integrated directly (without averaging), or assuming averaged orbits. For orbits that are integrated directly, we implemented two integration techniques, one which is based on the regularised Kustaanheimo-Stiefel equations of motion in element form. We also implemented analytical orbit-averaging corrections for pairwise interactions to quadrupole order. The updates presented here provide more flexibility for integrating the long-term dynamical evolution of hierarchical multiple systems. By effectively combining direct integration and orbit averaging the long-term evolution can be accurately computed, but with significantly lower computational cost compared to existing direct N-body codes. We give a number of examples in which the new features are beneficial. Our updated code, which is written in C++ supplemented with a user-friendly interface in Python, is freely available.

arXiv commentAccepted for publication in MNRAS. 15 pages, 4 figures. Code can be found at https://github.com/hamers/secularmultiple

References in corpus (62)

• A Survey of Stellar Families: Multiplicity of Solar-Type Stars
• Shrinking binary and planetary orbits by Kozai cycles with tidal friction
• Mind your Ps and Qs: the Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars
• REBOUND: An open-source multi-purpose N-body code for collisional dynamics
• The Occurrence and Architecture of Exoplanetary Systems
• IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits
• Planet Migration and Binary Companions: the case of HD 80606b
• Secular evolution of compact binaries near massive black holes: gravitational wave sources and other exotica
• Evolution in Binary and Triple Stars, with an application to SS Lac
• Secular Dynamics in Hierarchical Three-Body Systems
• From binaries to multiples II: hierarchical multiplicity of F and G dwarfs
• The Kozai Mechanism and the Evolution of Binary Supermassive Black Holes
• Binary black hole mergers from field triples: properties, rates and the impact of stellar evolution
• 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
• On the Formation of Hot Jupiters in Stellar Binaries
• Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai-Lidov Effect
• On the triple origin of blue stragglers
• Mergers and Obliquities in Stellar Triples
• Multi-physics simulations using a hierarchical interchangeable software interface
• Black hole mergers and blue stragglers from hierarchical triples formed in globular clusters
• The Astrophysical Multipurpose Software Environment
• Planet Hunters: A Transiting Circumbinary Planet in a Quadruple Star System
• Black hole triple dynamics: breakdown of the orbit average approximation and implications for gravitational wave detections
• From binaries to multiples I: Data on F and G dwarfs within 67 pc of the Sun
• Implementing Few-Body Algorithmic Regularization with Post-Newtonian Terms
• Merging Binaries in the Galactic Center: The eccentric Kozai-Lidov mechanism with stellar evolution
• Satellite dynamics on the Laplace surface
• Steady-state planet migration by the Kozai-Lidov mechanism in stellar binaries
• Formation and Stellar Spin-Orbit Misalignment of Hot Jupiters from Lidov-Kozai Oscillations in Stellar Binaries
• Black Hole and Neutron Star Binary Mergers in Triple Systems: Merger Fraction and Spin-Orbit Misalignment
• The Kozai-Lidov Mechanism in Hydrodynamical Disks
• Warm Jupiters from secular planet-planet interactions
• Black hole mergers from quadruples
• The triple evolution dynamical instability: Stellar collisions in the field and the formation of exotic binaries
• Population synthesis of triple systems in the context of mergers of carbon-oxygen white dwarfs
• Algorithmic regularization with velocity-dependent forces
• Double-Averaging Can Fail to Characterize the Long-Term Evolution of Lidov-Kozai Cycles & Derivation of an Analytical Correction
• Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure. First applications to multiplanet and multistar systems
• Enhanced Black-Hole Mergers in Binary-Binary Interactions
• Quasi-secular evolution of mildly hierarchical triple systems: analytics and applications for GW-sources and hot Jupiters
• Greatly Enhanced Eccentricity Oscillations in Quadruple Systems Composed of Two Binaries: Implications for Stars, Planets, and Transients
• Black hole-neutron star mergers from triples
• Spin-Orbit Misalignment of Merging Black-Hole Binaries with Tertiary Companions
• An Analytical Portrait of Binary Mergers in Hierarchical Triple Systems
• The rate of WD-WD head-on collisions in isolated triples is too low to explain standard type Ia supernovae
• Secular dynamics of hierarchical quadruple systems: the case of a triple system orbited by a fourth body
• Induced Ellipticity for Inspiraling Binary Systems
• Secular chaotic dynamics in hierarchical quadruple systems, with applications to hot Jupiters in stellar binaries and triples
• A slow-down time-transformed symplectic integrator for solving the few-body problem
• Dynamics of Quadruple Systems Composed of Two Binaries: Stars, White Dwarfs, and Implications for Ia Supernovae
• MSTAR -- a fast parallelised algorithmically regularised integrator with minimum spanning tree coordinates
• 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
• Effects of Disk Warping on the Inclination Evolution of Star-Disk-Binary Systems
• The Kozai-Lidov Mechanism in Hydrodynamical Disks. III. Effects of Disk Mass and Self-Gravity
• Chaotic quadruple secular evolution and the production of misaligned exomoons and Warm Jupiters in stellar multiples
• Misaligned accretion disc formation via Kozai-Lidov oscillations
• Lidov-Kozai Mechanism in Hydrodynamical Disks: Linear Stability Analysis
• Kozai-Lidov Disc Instability
• Massive binary star mergers in galactic nuclei: implications for blue stragglers, binary S-stars and gravitational waves
• The frequency of Kozai-Lidov disc oscillation driven giant outbursts in Be/X-ray binaries
• A census of main-sequence interactions in the Multiple Star Catalog

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• The ominous fate of exomoons around hot Jupiters in the high-eccentricity migration scenario
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