84 research outputs found
Impact of LISA's low frequency sensitivity on observations of massive black hole mergers
LISA will be able to detect gravitational waves from inspiralling massive
black hole (MBH) binaries out to redshifts z > 10. If the binary masses and
luminosity distances can be extracted from the LISA data stream, this
information can be used to reveal the merger history of MBH binaries and their
host galaxies in the evolving universe. Since this parameter extraction
generally requires that LISA observe the inspiral for a significant fraction of
its yearly orbit, carrying out this program requires adequate sensitivity at
low frequencies, f < 10^{-4} Hz. Using several candidate low frequency
sensitivities, we examine LISA's potential for characterizing MBH binary
coalescences at redshifts z > 1.Comment: Submitted to the Proceedings of the 5th International LISA Symposium,
Classical and Quantum Gravit
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
Consistency of post-Newtonian waveforms with numerical relativity
General relativity predicts the gravitational wave signatures of coalescing
binary black holes. Explicit waveform predictions for such systems, required
for optimal analysis of observational data, have so far been achieved using the
post-Newtonian (PN) approximation. The quality of this treatment is unclear,
however, for the important late-inspiral portion. We derive late-inspiral
waveforms via a complementary approach, direct numerical simulation of
Einstein's equations. We compare waveform phasing from simulations of the last
cycles of gravitational radiation from equal-mass, nonspinning black
holes with the corresponding 2.5PN, 3PN, and 3.5PN orbital phasing. We find
phasing agreement consistent with internal error estimates based on either
approach, suggesting that PN waveforms for this system are effective until the
last orbit prior to final merger.Comment: Replaced with published version -- one figure removed, text and other
figures updated for clarity of discussio
Anatomy of the binary black hole recoil: A multipolar analysis
We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of ``anti-kick'' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes
Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
We present an accurate approximation of the full gravitational radiation
waveforms generated in the merger of non-eccentric systems of two non-spinning
black holes. Utilizing information from recent numerical relativity simulations
and the natural flexibility of the effective-one-body (EOB) model, we extend
the latter so that it can successfully match the numerical relativity waveforms
during the last stages of inspiral, merger and ringdown. By ``successfully''
here, we mean with phase differences < 8% of a gravitational-wave cycle
accumulated by the end of the ringdown phase, maximizing only over time of
arrival and initial phase. We obtain this result by simply adding a
4-post-Newtonian order correction in the EOB radial potential and determining
the (constant) coefficient by imposing high-matching performances with
numerical waveforms of mass ratios m1/m2 = 1, 3/2, 2 and 4, m1 and m2 being the
individual black-hole masses. The final black-hole mass and spin predicted by
the numerical simulations are used to determine the ringdown frequency and
decay time of three quasi-normal-mode damped sinusoids that are attached to the
EOB inspiral-(plunge) waveform at the EOB light-ring. The EOB waveforms might
be tested and further improved in the future by comparison with extremely long
and accurate inspiral numerical-relativity waveforms. They may already be
employed for coherent searches and parameter estimation of gravitational waves
emitted by non-spinning coalescing binary black holes with ground-based
laser-interferometer detectors.Comment: 15 pages, 9 figure
A data-analysis driven comparison of analytic and numerical coalescing binary waveforms: nonspinning case
We compare waveforms obtained by numerically evolving nonspinning binary black holes to post-Newtonian (PN) template families currently used in the search for gravitational waves by ground-based detectors. We find that the time-domain 3.5PN template family, which includes the inspiral phase, has fitting factors (FFs) >= 0.96 for binary systems with total mass M = 10 ~ 20 Msun. The time-domain 3.5PN effective-one-body template family, which includes the inspiral, merger and ring-down phases, gives satisfactory signal-matching performance with FFs >= 0.96 for binary systems with total mass M = 10 ~ 120 Msun. If we introduce a cutoff frequency properly adjusted to the final black-hole ring-down frequency, we find that the frequency-domain stationary-phase-approximated template family at 3.5PN order has FFs >= 0.96 for binary systems with total mass M = 10 ~ 20 Msun. However, to obtain high matching performances for larger binary masses, we need to either extend this family to unphysical regions of the parameter space or introduce a 4PN order coefficient in the frequency-domain GW phase. Finally, we find that the phenomenological Buonanno-Chen-Vallisneri family has FFs >= 0.97 with total mass M=10 ~ 120Msun. The main analyses use the noise spectral-density of LIGO, but several tests are extended to VIRGO and advanced LIGO noise-spectral densities
Binary black hole late inspiral: Simulations for gravitational wave observations
Coalescing binary black hole mergers are expected to be the strongest
gravitational wave sources for ground-based interferometers, such as the LIGO,
VIRGO, and GEO600, as well as the space-based interferometer LISA. Until
recently it has been impossible to reliably derive the predictions of General
Relativity for the final merger stage, which takes place in the strong-field
regime. Recent progress in numerical relativity simulations is, however,
revolutionizing our understanding of these systems. We examine here the
specific case of merging equal-mass Schwarzschild black holes in detail,
presenting new simulations in which the black holes start in the late inspiral
stage on orbits with very low eccentricity and evolve for ~1200M through ~7
orbits before merging. We study the accuracy and consistency of our simulations
and the resulting gravitational waveforms, which encompass ~14 cycles before
merger, and highlight the importance of using frequency (rather than time) to
set the physical reference when comparing models. Matching our results to PN
calculations for the earlier parts of the inspiral provides a combined waveform
with less than half a cycle of accumulated phase error through the entire
coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs)
for iLIGO, adLIGO, and LISA, highlighting the contributions from the
late-inspiral and merger-ringdown parts of the waveform which can now be
simulated numerically. Contour plots of SNR as a function of z and M show that
adLIGO can achieve SNR >~ 10 for some intermediate-mass binary black holes
(IMBBHs) out to z ~ 1, and that LISA can see massive binary black holes (MBBHs)
in the range 3x10^4 100 out to the earliest epochs
of structure formation at z > 15.Comment: 17 pages, 20 figures. Final published versio
Modeling kicks from the merger of generic black-hole binaries
Recent numerical relativistic results demonstrate that the merger of
comparable-mass spinning black holes has a maximum ``recoil kick'' of up to
\sim 4000 \kms. However the scaling of these recoil velocities with mass
ratio is poorly understood. We present new runs showing that the maximum
possible kick perpendicular to the orbital plane does not scale as
(where is the symmetric mass ratio), as previously proposed, but is more
consistent with , at least for systems with low orbital precession.
We discuss the effect of this dependence on galactic ejection scenarios and
retention of intermediate-mass black holes in globular clusters.Comment: 5 pages, 1 figure, 3 tables. Version published in Astrophys. J. Let
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