Resonant Dynamical Friction Around a Super-Massive Black Hole: Analytical Description

Abstract

We derive an analytical model for the so-called phenomenon of `resonant dynamical friction', where a disc of stars around a super-massive black hole interacts with a massive perturber, so as to align its inclination with the disc's orientation. We show that it stems from a singular behaviour of the orbit-averaged equations of motion, which leads to a rapid alignment of the argument of the ascending node $\Omega$ of each of the disc stars, with that of the perturber, ${\Omega }_{\mathrm{p}}$, with a phase-difference of $90^{\circ }$. This phenomenon occurs for all stars whose maximum possible $\dot{\Omega }$ (maximised over all values of $\Omega$ for all the disc stars), is greater than ${\dot{\Omega }}_{\mathrm{p}}$; this corresponds approximately to all stars whose semi-major axes are less than twice that of the perturber. The rate at which the perturber's inclination decreases with time is proportional to its mass and is shown to be much faster than Chandrasekhar's dynamical friction. We find that the total alignment time is inversely proportional to the root of the perturber's mass. This persists until the perturber enters the disc. The predictions of this model agree with a suite of numerical $N$-body simulations which we perform to explore this phenomenon, for a wide range of initial conditions, masses, \emph{etc.}, and are an instance of a general phenomenon. Similar effects could occur in the context of planetary systems, too.

(v1) Submitted for publication. Comments welcome. (v2) Updated to match version accepted to MNRAS

References in corpus (22)

• The Two Young Star Disks in the Central Parsec of the Galaxy: Properties, Dynamics and Formation
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Intermediate mass black holes in AGN disks II. Model predictions & observational constraints
• Performance Analysis of Direct N-Body Algorithms on Special-Purpose Supercomputers
• Large scale kinematics and dynamical modelling of the Milky Way nuclear star cluster
• Twelve years of spectroscopic monitoring in the Galactic Center: the closest look at S-stars near the black hole
• The Milky Way's nuclear star cluster: Old, metal-rich, and cuspy
• A numerical study of vector resonant relaxation
• The young stars in the Galactic Center
• Kinematic Structure of the Galactic Center S-cluster
• A Self-Consistent, Time-Dependent Treatment of Dynamical Friction: New Insights regarding Core Stalling and Dynamical Buoyancy
• Higher-order effects in the dynamics of hierarchical triple systems. Quadrupole-squared terms
• SMBH in Galactic Nuclei with Tidal Disruption of Stars
• The Thermodynamics of Rotating Black-Hole Star Clusters
• The bound mass of Dehnen models with centrally peaked star formation efficiency
• Star formation at the Galactic Centre: coevolution of multiple young stellar discs
• Analytic solution to the dynamical friction acting on circularly moving perturbers
• A numerical study of stellar discs in galactic nuclei
• Stellar dynamics in the periodic cube
• Resonant friction on discs in galactic nuclei
• Anisotropic mass segregation: two-component mean-field model

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