Relativistic dynamics of stars near a supermassive black hole

Abstract

General relativistic precession limits the ability of gravitational encounters to increase the eccentricity $e$ of orbits near a supermassive black hole (SBH). This "Schwarzschild barrier" (SB) has been shown to play an important role in the orbital evolution of stars like the galactic center S-stars. However, the evolution of orbits below the SB, $e>e_{\mathrm{SB}}$, is not well understood; the main current limitation is the computational complexity of detailed simulations. Here we present an $N$-body algorithm that allows us to efficiently integrate orbits of test stars around a SBH including general relativistic corrections to the equations of motion and interactions with a large ($\gtrsim 10^3$) number of field stars. We apply our algorithm to the S-stars and extract diffusion coefficients describing the evolution in angular momentum $L$. We identify three angular momentum regimes, in which the diffusion coefficients depend in functionally different ways on $L$. Regimes of lowest and highest $L$ are well-described in terms of non-resonant relaxation (NRR) and resonant relaxation (RR), respectively. In addition, we find a new regime of "anomalous relaxation" (AR). We present analytic expressions, in terms of physical parameters, that describe the diffusion coefficients in all three regimes, and propose a new, empirical criterion for the location of the SB in terms of the $L$-dependence of the diffusion coefficients. Subsequently we apply our results to obtain the steady-state distribution of angular momentum for orbits near a SBH.

Accepted for publication in MNRAS. 34 pages, 32 figures

References in corpus (6)

• Implementing Few-Body Algorithmic Regularization with Post-Newtonian Terms
• 6th and 8th Order Hermite Integrator for N-body Simulations
• Resonant relaxation near a massive black hole: the dependence on eccentricity
• Cluster Core Dynamics at the Galactic Center
• Capture of non-relativistic particles in eccentric orbits by a Kerr black hole
• Spin Evolution of Supermassive Black Holes and Galactic Nuclei

Cited by in corpus (13)

• The nuclear cluster of the Milky Way: Our primary testbed for the interaction of a dense star cluster with a massive black hole
• Illuminating Massive Black Holes With White Dwarfs: Orbital Dynamics and High Energy Transients from Tidal Interactions
• Importance of transient resonances in extreme-mass-ratio inspirals
• A new Monte Carlo method for dynamical evolution of non-spherical stellar systems
• Relativistic orbits around spinning supermassive black holes. Secular evolution to 4.5 post-Newtonian order
• Analytic computation of the secular effects of encounters on a binary: features arising from second-order perturbation theory
• Can supernova kicks trigger EMRIs in the Galactic Centre?
• Chaos in self-gravitating many-body systems: Lyapunov time dependence of $N$ and the influence of general relativity
• Secular Dynamics around a Supermassive Black Hole via Multipole Expansion
• Evolution of eccentric stellar disks around supermassive black holes: the complex disk disruption dynamics and the milliparsec stars
• Sculpting the Stellar Cusp in the Galactic Center
• Astrophysics with the Laser Interferometer Space Antenna
• Relativistic dynamical friction in stellar systems