70 research outputs found
Notes on the spheroidal harmonic multipole moments of gravitational radiation
The estimation of gravitational radiation's multipole moments is a central
problem in gravitational wave theory, with essential applications in
gravitational wave signal modeling and data analysis. This problem is
complicated by most astrophysically relevant systems' not having angular modes
that are analytically understood. A ubiquitous workaround is to use spin
weighted spherical harmonics to estimate multipole moments; however, these are
only related to the natural modes of non-spinning spacetimes, thus obscuring
the behavior of radiative modes when the source has angular momentum. In such
cases, radiative modes are spheroidal in nature. Here, common approaches to the
estimation of spheroidal harmonic multipole moments are unified under a simple
framework. This framework leads to a new class of spin weighted spheroidal
harmonic functions. Adjoint-spheroidal harmonics are introduced and used to
motivate the general estimation of spheroidal harmonic multipole moments via
bi-orthogonal decomposition with overtone subsets. In turn, the
adjoint-spheroidal harmonics are used to construct a single linear operator for
which all spheroidal harmonics are eigenfunctions. Implications of these
results on gravitational wave theory are discussed.Comment: 20 pages, 4 figure
Exploring the Use of Numerical Relativity Waveforms in Burst Analysis of Precessing Black Hole Mergers
Recent years have witnessed tremendous progress in numerical relativity and
an ever improving performance of ground-based interferometric gravitational
wave detectors. In preparation for Advanced LIGO and a new era in gravitational
wave astronomy, the numerical relativity and gravitational wave data analysis
communities are collaborating to ascertain the most useful role for numerical
relativity waveforms in the detection and characterization of binary black hole
coalescences. In this paper, we explore the detectability of equal mass,
merging black hole binaries with precessing spins and total mass M_T in
[80,350]Msol, using numerical relativity waveforms and template-less search
algorithms designed for gravitational wave bursts. In particular, we present a
systematic study using waveforms produced by the MAYAKRANC code that are added
to colored, Gaussian noise and analyzed with the Omega burst search algorithm.
Detection efficiency is weighed against the orientation of one of the
black-hole's spin axes. We find a strong correlation between the detection
efficiency and the radiated energy and angular momentum, and that the inclusion
of the l=2, m=+/-1,0 modes, at a minimum, is necessary to account for the full
dynamics of precessing systems.Comment: 9 pages, 15 figure
First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries
Gravitational-wave observations of binary black holes currently rely on
theoretical models that predict the dominant multipoles (l,m) of the radiation
during inspiral, merger and ringdown. We introduce a simple method to include
the subdominant multipoles to binary black hole gravitational waveforms, given
a frequency-domain model for the dominant multipoles. The amplitude and phase
of the original model are appropriately stretched and rescaled using
post-Newtonian results (for the inspiral), perturbation theory (for the
ringdown), and a smooth transition between the two. No additional tuning to
numerical-relativity simulations is required. We apply a variant of this method
to the non-precessing PhenomD model. The result, PhenomHM, constitutes the
first higher-multipole model of spinning black-hole binaries, and currently
includes the (l,m) = (2,2), (3,3), (4,4), (2,1), (3,2), (4,3) radiative
moments. Comparisons with numerical-relativity waveforms demonstrate that
PhenomHM is more accurate than dominant-multipole-only models for all binary
configurations, and typically improves the measurement of binary properties.Comment: 4 pages, 4 figure
Testing general relativity using golden black-hole binaries
The coalescences of stellar-mass black-hole binaries through their inspiral,
merger, and ringdown are among the most promising sources for ground-based
gravitational-wave (GW) detectors. If a GW signal is observed with sufficient
signal-to-noise ratio, the masses and spins of the black holes can be estimated
from just the inspiral part of the signal. Using these estimates of the initial
parameters of the binary, the mass and spin of the final black hole can be
uniquely predicted making use of general-relativistic numerical simulations. In
addition, the mass and spin of the final black hole can be independently
estimated from the merger--ringdown part of the signal. If the binary black
hole dynamics is correctly described by general relativity (GR), these
independent estimates have to be consistent with each other. We present a
Bayesian implementation of such a test of general relativity, which allows us
to combine the constraints from multiple observations. Using kludge modified GR
waveforms, we demonstrate that this test can detect sufficiently large
deviations from GR, and outline the expected constraints from upcoming GW
observations using the second-generation of ground-based GW detectors.Comment: 5 pages, 2 fig
The most powerful astrophysical events: Gravitational-wave peak luminosity of binary black holes as predicted by numerical relativity
For a brief moment, a binary black hole (BBH) merger can be the most powerful astrophysical event in the visible Universe. Here we present a model fit for this gravitational-wave peak luminosity of nonprecessing quasicircular BBH systems as a function of the masses and spins of the component black holes, based on numerical relativity (NR) simulations and the hierarchical fitting approach introduced by X. Jiménez-Forteza et al. [Phys. Rev. D 95, 064024 (2017).]. This fit improves over previous results in accuracy and parameter-space coverage and can be used to infer posterior distributions for the peak luminosity of future astrophysical signals like GW150914 and GW151226. The model is calibrated to the ℓ≤6 modes of 378 nonprecessing NR simulations up to mass ratios of 18 and dimensionless spin magnitudes up to 0.995, and includes unequal-spin effects. We also constrain the fit to perturbative numerical results for large mass ratios. Studies of key contributions to the uncertainty in NR peak luminosities, such as (i) mode selection, (ii) finite resolution, (iii) finite extraction radius, and (iv) different methods for converting NR waveforms to luminosity, allow us to use NR simulations from four different codes as a homogeneous calibration set. This study of systematic fits to combined NR and large-mass-ratio data, including higher modes, also paves the way for improved inspiral-merger-ringdown waveform models
Phenomenological gravitational-wave model for precessing black-hole binaries with higher multipoles and asymmetries
In this work we introduce phenomxo4a, the first phenomenological, frequency-domain gravitational waveform model to incorporate multipole asymmetries and precession angles tuned to numerical relativity. We build upon the modeling work that produced the phenompnr model and incorporate our additions into the imrphenomx framework, retuning the coprecessing frame model and extending the tuned precession angles to higher signal multipoles. We also include, for the first time in frequency-domain models, a recent model for spin-precession-induced multipolar asymmetry in the coprecessing frame to the dominant gravitational-wave multipoles. The accuracy of the full model and its constituent components is assessed through comparison to numerical relativity and numerical relativity surrogate waveforms by computing mismatches and performing parameter estimation studies. We show that, for the dominant signal multipole, we retain the modeling improvements seen in the phenompnr model. We find that the relative accuracy of current full IMR models varies depending on location in parameter space and the comparison metric, and on average they are of comparable accuracy. However, we find that variations in the pointwise accuracy do not necessarily translate into large biases in the parameter estimation recoveries
Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a
joint effort between members of the numerical relativity, analytical relativity
and gravitational-wave data analysis communities. The goal of the NRAR
collaboration is to produce numerical-relativity simulations of compact
binaries and use them to develop accurate analytical templates for the
LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and
extracting astrophysical information from them. We describe the results of the
first stage of the NRAR project, which focused on producing an initial set of
numerical waveforms from binary black holes with moderate mass ratios and
spins, as well as one non-spinning binary configuration which has a mass ratio
of 10. All of the numerical waveforms are analysed in a uniform and consistent
manner, with numerical errors evaluated using an analysis code created by
members of the NRAR collaboration. We compare previously-calibrated,
non-precessing analytical waveforms, notably the effective-one-body (EOB) and
phenomenological template families, to the newly-produced numerical waveforms.
We find that when the binary's total mass is ~100-200 solar masses, current EOB
and phenomenological models of spinning, non-precessing binary waveforms have
overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary
numerical waveforms with mass ratios <= 4, when maximizing over binary
parameters. This implies that the loss of event rate due to modelling error is
below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to
five non-spinning waveforms with mass ratio smaller than 6 have overlaps above
99.7% with the numerical waveform with a mass ratio of 10, without even
maximizing on the binary parameters.Comment: 51 pages, 10 figures; published versio
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