A Stability Timescale for Non-Hierarchical Three-Body Systems

Abstract

The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital distances are well-separated. However, instability, which is often associated with significant energy exchange between orbits, takes time to develop. Assuming two massive objects in a circular orbit and a test particle in an eccentric orbit, we develop an analytical formula estimating the time it takes for the test particle's orbital energy to change by an order of itself. We show its consistency with results from N-body simulations. For eccentric orbits in particular, the instability is primarily driven not by close encounters of the test particle with one of the other bodies, but by the fundamental susceptibility of eccentric orbits to exchange energy at their periapsis. Motivated by recent suggestions that the galactic center may host an intermediate-mass black hole (IMBH) as a companion to the massive black hole Sgr A*, we use our timescale to explore the parameter space that could harbor an IMBH for the lifetime of the S-cluster of stars surrounding Sgr A*. Furthermore, we show that the orbit of an S-star can be stable for long timescales in the presence of other orbital crossing stars, thus suggesting that the S-cluster may be stable for the lifetimes of its member stars.

16 pages, 8 figures, Submitted ApJ - Comments welcome

References in corpus (22)

• Binary interaction dominates the evolution of massive stars
• GW190521: A Binary Black Hole Merger with a Total Mass of $150M_{\odot }$
• Dynamical Outcomes of Planet-Planet Scattering
• Properties and astrophysical implications of the 150 Msun binary black hole merger GW190521
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• An Update on Monitoring Stellar Orbits in the Galactic Center
• Two Suns in The Sky: Stellar Multiplicity in Exoplanet Systems
• Large eccentricity, low mutual inclination: the three-dimensional architecture of a hierarchical system of giant planets
• Generalized Hill-Stability Criteria for Hierarchical Three-Body Systems at Arbitrary Inclinations
• The Formation of Intermediate Mass Black Holes in Galactic Nuclei
• The Photoeccentric Effect and Proto-Hot Jupiters II. KOI-1474.01, a candidate eccentric planet perturbed by an unseen companion
• The S-Star Cluster at the Center of the Milky Way: On the nature of diffuse NIR emission in the inner tenth of a parsec
• Higher-order effects in the dynamics of hierarchical triple systems. Quadrupole-squared terms
• Algebraic and machine learning approach to hierarchical triple-star stability
• Formation of Dark Matter Torii Around Supermassive Black Holes Via The Eccentric Kozai-Lidov Mechanism
• Empirical Stability Boundary for Hierarchical Triples
• The influence of the secular perturbation of an intermediate-mass companion: I. Eccentricity excitation of disk stars at the Galactic center
• A Simple Random-Walk Model Explains the Disruption Process of Hierarchical, Eccentric 3-Body Systems
• Binaries are softer than they seem: Effects of an external potential on the scattering dynamics of binaries
• Dynamical disruption timescales and chaotic behavior of hierarchical triple systems
• Lagrange vs. Lyapunov stability of hierarchical triple systems: dependence on the mutual inclination between inner and outer orbits
• The Origin of Kepler-419b: A Path to Tidal Migration Via Four-body Secular Interactions

Cited by in corpus (4)

• Constraining a companion of the galactic center black hole, Sgr A*
• 10,000 Resolved Triples from Gaia: Empirical Constraints on Triple Star Populations
• Partial disruption of a planet around a white dwarf: the effect of perturbation from the remnant planet on the accretion
• Repeating X-ray bursts: Interaction between a neutron star and clumps partially disrupted from a planet