171 research outputs found
A numerical study of vector resonant relaxation
Stars bound to a supermassive black hole interact gravitationally. Persistent
torques acting between stellar orbits lead to the rapid resonant relaxation of
the orbital orientation vectors ("vector" resonant relaxation) and slower
relaxation of the eccentricities ("scalar" resonant relaxation), both at rates
much faster than two-body or non-resonant relaxation. We describe a new
parallel symplectic integrator, N-ring, which follows the dynamical evolution
of a cluster of N stars through vector resonant relaxation, by averaging the
pairwise interactions over the orbital period and periapsis-precession
timescale. We use N-ring to follow the evolution of clusters containing over
10^4 stars for tens of relaxation times. Among other results, we find that the
evolution is dominated by torques among stars with radially overlapping orbits,
and that resonant relaxation can be modelled as a random walk of the orbit
normals on the sphere, with angular step size ranging from 0.5-1 radian. The
relaxation rate in a cluster with a fixed number of stars is proportional to
the RMS mass of the stars. The RMS torque generated by the cluster stars is
reduced below the torque between Kepler orbits due to apsidal precession and
declines weakly with the eccentricity of the perturbed orbit. However since the
angular momentum of an orbit also decreases with eccentricity, the relaxation
rate is approximately eccentricity-independent for e<0.7 and grows rapidly with
eccentricity for e>0.8. We quantify the relaxation using the autocorrelation
function of the spherical multipole moments; this decays exponentially and the
e-folding time may be identified with the vector resonant relaxation timescale.Comment: 35 pages, 13 figures, accepted for publication in MNRA
Resonant relaxation in globular clusters
Resonant relaxation has been discussed as an efficient process that changes
the angular momenta of stars orbiting around a central supermassive black hole
due to the fluctuating gravitational field of the stellar cluster. Other
spherical stellar systems, such as globular clusters, exhibit a restricted form
of this effect where enhanced relaxation rate only occurs in the directions of
the angular momentum vectors, but not in their magnitudes; this is called
vector resonant relaxation (VRR). To explore this effect, we performed a large
set of direct N-body simulations, with up to 512k particles and ~500 dynamical
times. Contrasting our simulations with Spitzer-style Monte Carlo simulations,
that by design only exhibit 2-body relaxation, we show that the temporal
behavior of the angular momentum vectors in -body simulations cannot be
explained by 2-body relaxation alone. VRR operates efficiently in globular
clusters with . The fact that VRR operates in globular clusters may
open way to use powerful tools in statistical physics for their description. In
particular, since the distribution of orbital planes relaxes much more rapidly
than the distribution of the magnitude of angular momentum and the radial
action, the relaxation process reaches an internal statistical equilibrium in
the corresponding part of phase space while the whole cluster is generally out
of equilibrium, in a state of quenched disorder. We point out the need to
include effects of VRR in Monte Carlo simulations of globular clusters.Comment: Submitted to Ap
Parameter estimation for inspiraling eccentric compact binaries including pericenter precession
Inspiraling supermassive black hole binary systems with high orbital
eccentricity are important sources for space-based gravitational wave (GW)
observatories like the Laser Interferometer Space Antenna (LISA). Eccentricity
adds orbital harmonics to the Fourier transform of the GW signal and
relativistic pericenter precession leads to a three-way splitting of each
harmonic peak. We study the parameter estimation accuracy for such waveforms
with different initial eccentricity using the Fisher matrix method and a Monte
Carlo sampling of the initial binary orientation. The eccentricity improves the
parameter estimation by breaking degeneracies between different parameters. In
particular, we find that the source localization precision improves
significantly for higher-mass binaries due to eccentricity. The typical sky
position errors are deg for a nonspinning, equal-mass
binary at redshift , if the initial eccentricity 1 yr before merger is
. Pericenter precession does not affect the source localization
accuracy significantly, but it does further improve the mass and eccentricity
estimation accuracy systematically by a factor of 3--10 for masses between
and for .Comment: 14 two-column pages, 12 figures, expanded version; contains the proof
correction
Imprint of Accretion Disk-Induced Migration on Gravitational Waves from Extreme Mass Ratio Inspirals
We study the effects of a thin gaseous accretion disk on the inspiral of a
stellar--mass black hole into a supermassive black hole. We construct a
phenomenological angular momentum transport equation that reproduces known disk
effects. Disk torques modify the gravitational wave phase evolution to
detectable levels with LISA for reasonable disk parameters. The Fourier
transform of disk-modified waveforms acquires a correction with a different
frequency trend than post-Newtonian vacuum terms. Such inspirals could be used
to detect accretion disks with LISA and to probe their physical parameters.Comment: 4 pages, 2 figures, submitted to Physical Review Letter
Implications of the Eccentric Kozai-Lidov Mechanism for Stars Surrounding Supermassive Black Hole Binaries
An enhanced rate of stellar tidal disruption events (TDEs) may be an
important characteristic of supermassive black hole (SMBH) binaries at close
separations. Here we study the evolution of the distribution of stars around a
SMBH binary due to the eccentric Kozai-Lidov (EKL) mechanism, including
octupole effects and apsidal precession caused by the stellar mass distribution
and general relativity. We identify a region around one of the SMBHs in the
binary where the EKL mechanism drives stars to high eccentricities, which
ultimately causes the stars to either scatter off the second SMBH or get
disrupted. For SMBH masses 10^7 Msun and 10^8 Msun, the TDE rate can reach
10^{-2} yr and deplete a region of the stellar cusp around the secondary SMBH
in ~0.5 Myr. As a result, the final geometry of the stellar distribution
between 0.01 and 0.1 pc around the secondary SMBH is a torus. These effects may
be even more prominent in nuclear stellar clusters hosting a supermassive and
an intermediate mass black hole.Comment: 11 pages, 10 figures accepted for publication in MNRA
Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei
The Laser Interferometer Gravitational-Wave Observatory, LIGO, found direct
evidence for double black hole binaries emitting gravitational waves. Galactic
nuclei are expected to harbor the densest population of stellar-mass black
holes. A significant fraction () of these black holes can reside in
binaries. We examine the fate of the black hole binaries in active galactic
nuclei, which get trapped in the inner region of the accretion disk around the
central supermassive black hole. We show that binary black holes can migrate
into and then rapidly merge within the disk well within a Salpeter time. The
binaries may also accrete a significant amount of gas from the disk, well above
the Eddington rate. This could lead to detectable X-ray or gamma-ray emission,
but would require hyper-Eddington accretion with a few percent radiative
efficiency, comparable to thin disks. We discuss implications for gravitational
wave observations and black hole population studies. We estimate that Advanced
LIGO may detect such, gas-induced binary mergers per year.Comment: 9 pages, 2 figure
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