30,704 research outputs found
Binary black holes on a budget: Simulations using workstations
Binary black hole simulations have traditionally been computationally very
expensive: current simulations are performed in supercomputers involving dozens
if not hundreds of processors, thus systematic studies of the parameter space
of binary black hole encounters still seem prohibitive with current technology.
Here we show how the multi-layered refinement level code BAM can be used on
dual processor workstations to simulate certain binary black hole systems. BAM,
based on the moving punctures method, provides grid structures composed of
boxes of increasing resolution near the center of the grid. In the case of
binaries, the highest resolution boxes are placed around each black hole and
they track them in their orbits until the final merger when a single set of
levels surrounds the black hole remnant. This is particularly useful when
simulating spinning black holes since the gravitational fields gradients are
larger. We present simulations of binaries with equal mass black holes with
spins parallel to the binary axis and intrinsic magnitude of S/m^2= 0.75. Our
results compare favorably to those of previous simulations of this particular
system. We show that the moving punctures method produces stable simulations at
maximum spatial resolutions up to M/160 and for durations of up to the
equivalent of 20 orbital periods.Comment: 20 pages, 8 figures. Final version, to appear in a special issue of
Class. Quantum Grav. based on the New Frontiers in Numerical Relativity
Conference, Golm, July 200
Collisional dynamics around binary black holes in galactic centers
We follow the sinking of two massive black holes in a spherical stellar
system where the black holes become bound under the influence of dynamical
friction. Once bound, the binary hardens by three-body encounters with
surrounding stars. We find that the binary wanders inside the core, providing
an enhanced supply of reaction partners for the hardening. The binary evolves
into a highly eccentric orbit leading to coalescence well beyond a Hubble time.
These are the first results from a hybrid ``self consistent field'' (SCF) and
direct Aarseth N-body integrator (NBODY6), which combines the advantages of the
direct force calculation with the efficiency of the field method. The code is
designed for use on parallel architectures and is therefore applicable to
collisional N-body integrations with extraordinarily large particle numbers (>
10^5). This creates the possibility of simulating the dynamics of both globular
clusters with realistic collisional relaxation and stellar systems surrounding
supermassive black holes in galactic nuclei.Comment: 38 pages, 13 figures, submitted to ApJ, accepted, revised text and
added figure
Tracking the precession of compact binaries from their gravitational-wave signal
We present a simple method to track the precession of a black-hole-binary
system, using only information from the gravitational-wave (GW) signal. Our
method consists of locating the frame from which the magnitude of the
modes is maximized, which we denote the "quadrupole-aligned"
frame. We demonstrate the efficacy of this method when applied to waveforms
from numerical simulations. In the test case of an equal-mass nonspinning
binary, our method locates the direction of the orbital angular momentum to
within . We then
apply the method to a binary that exhibits significant
precession. In general a spinning binary's orbital angular momentum
is \emph{not} orthogonal to the orbital plane. Evidence that our
method locates the direction of rather than the normal of the
orbital plane is provided by comparison with post-Newtonian (PN) results. Also,
we observe that it accurately reproduces similar higher-mode amplitudes to a
comparable non-spinning (and therefore non-precessing) binary, and that the
frequency of the modes is consistent with the "total
frequency" of the binary's motion. The simple form of the quadrupole-aligned
waveform will be useful in attempts to analytically model the
inspiral-merger-ringdown (IMR) signal of precessing binaries, and in
standardizing the representation of waveforms for studies of accuracy and
consistency of source modelling efforts, both numerical and analytical.Comment: 11 pages, 12 figures, 1 tabl
Simulations of black-hole binaries with unequal masses or non-precessing spins: accuracy, physical properties, and comparison with post-Newtonian results
We present gravitational waveforms for the last orbits and merger of
black-hole-binary (BBH) systems along two branches of the BBH parameter space:
equal-mass binaries with equal non-precessing spins, and nonspinning
unequal-mass binaries. The waveforms are calculated from numerical solutions of
Einstein's equations for black-hole binaries that complete between six and ten
orbits before merger. Along the equal-mass spinning branch, the spin parameter
of each BH is , and along the unequal-mass
branch the mass ratio is . We discuss the construction of
low-eccentricity puncture initial data for these cases, the properties of the
final merged BH, and compare the last 8-10 GW cycles up to with
the phase and amplitude predicted by standard post-Newtonian (PN) approximants.
As in previous studies, we find that the phase from the 3.5PN TaylorT4
approximant is most accurate for nonspinning binaries. For equal-mass spinning
binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN
order) gives the most robust performance, but it is possible to treat TaylorT4
in such a way that it gives the best accuracy for spins . When
high-order amplitude corrections are included, the PN amplitude of the
modes is larger than the NR amplitude by between 2-4%.Comment: 21 pages, 9 figures, 6 tables. Version accepted by PR
Evolution of Massive Black Hole Binaries
We present the result of large-scale N-body simulations of the
stellar-dynamical evolution of a massive black-hole binary at the center of a
spherical galaxy. We focus on the dependence of the hardening rate on the
relaxation timescale of the parent galaxy. A simple theoretical argument
predicts that a binary black hole creates the ``loss cone'' around it. Once the
loss cone is formed, the hardening rate is determined by the rate at which
field stars diffuse into the loss cone. Therefore the hardening timescale
becomes proportional to the relaxation timescale. Recent N-body simulations,
however, have failed to confirm this theory and various explanations have been
proposed. By performing simulations with sufficiently large N (up to )
for sufficiently long time, we found that the hardening rate does depend on N.
Our result is consistent with the simple theoretical prediction that the
hardening timescale is proportional to the relaxation timescale. This
dependence implies that most massive black hole binaries are unlikely to merge
within the Hubble time through interaction with field stars and gravitational
wave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear
in the February 10, 2004 issu
Black-hole binaries, gravitational waves, and numerical relativity
Understanding the predictions of general relativity for the dynamical
interactions of two black holes has been a long-standing unsolved problem in
theoretical physics. Black-hole mergers are monumental astrophysical events,
releasing tremendous amounts of energy in the form of gravitational radiation,
and are key sources for both ground- and space-based gravitational-wave
detectors. The black-hole merger dynamics and the resulting gravitational
waveforms can only be calculated through numerical simulations of Einstein's
equations of general relativity. For many years, numerical relativists
attempting to model these mergers encountered a host of problems, causing their
codes to crash after just a fraction of a binary orbit could be simulated.
Recently, however, a series of dramatic advances in numerical relativity has
allowed stable, robust black-hole merger simulations. This remarkable progress
in the rapidly maturing field of numerical relativity, and the new
understanding of black-hole binary dynamics that is emerging is chronicled.
Important applications of these fundamental physics results to astrophysics, to
gravitational-wave astronomy, and in other areas are also discussed.Comment: 54 pages, 42 figures. Some typos corrected & references updated.
Essentially final published versio
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