Dynamics of Black Hole Pairs I: Periodic Tables

Abstract

Although the orbits of comparable mass, spinning black holes seem to defy simple decoding, we find a means to decipher all such orbits. The dynamics is complicated by extreme perihelion precession compounded by spin-induced precession. We are able to quantitatively define and describe the fully three dimensional motion of comparable mass binaries with one black hole spinning and expose an underlying simplicity. To do so, we untangle the dynamics by capturing the motion in the orbital plane. Our results are twofold: (1) We derive highly simplified equations of motion in a non-orthogonal orbital basis, and (2) we define a complete taxonomy for fully three-dimensional orbits. More than just a naming system, the taxonomy provides unambiguous and quantitative descriptions of the orbits, including a determination of the zoom-whirliness of any given orbit. Through a correspondence with the rationals, we are able to show that zoom-whirl behavior is prevalent in comparable mass binaries in the strong-field regime. A first significant conclusion that can be drawn from this analysis is that all generic orbits in the final stages of inspiral under gravitational radiation losses are characterized by precessing clovers with few leaves and that no orbit will behave like the tightly precessing ellipse of Mercury. The gravitational waveform produced by these low-leaf clovers will reflect the natural harmonics of the orbital basis -- harmonics that, importantly, depend only on radius. The significance for gravitational wave astronomy will depend on the number of windings the pair executes in the strong-field regime and could be more conspicuous for intermediate mass pairs than for stellar mass pairs.

19 pages, lots of figures

References in corpus (14)

• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Gravitational wave snapshots of generic extreme mass ratio inspirals
• Solving Einstein's Equations With Dual Coordinate Frames
• Spin Flips and Precession in Black-Hole-Binary Mergers
• A Periodic Table for Black Hole Orbits
• Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
• Black Hole Mergers and Unstable Circular Orbits
• High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants
• Resurvey of order and chaos in spinning compact binaries
• Revisit on "Ruling out chaos in compact binary systems"
• Chaos and Order in Models of Black Hole Pairs
• Binary black holes on a budget: Simulations using workstations
• Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
• Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling

Cited by in corpus (8)

• Zoom-Whirl Orbits in Black Hole Binaries
• How to observe a non-Kerr spacetime
• Periodic orbits around a spherically symmetric naked singularity
• Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
• A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
• Inspiral of Generic Black Hole Binaries: Spin, Precession, and Eccentricity
• Spinning compact binary dynamics and chameleon orbits
• Spinning compact binary inspiral II: Conservative angular dynamics