57 research outputs found
Use of Singular-Value Decomposition in Gravitational-Wave Data Analysis
Singular-value decomposition is a powerful technique that has been used in
the analysis of matrices in many fields. In this paper, we summarize how it has
been applied to the analysis of gravitational-wave data. These include
producing basis waveforms for matched filtering, decreasing the computational
cost of searching for many waveforms, improving parameter estimation, and
providing a method of waveform interpolation.Comment: 7 pages, Third Galileo - Xu Guangqi Conference Proceeding
The balancing act of template bank construction: inspiral waveform template banks for gravitational-wave detectors and optimizations at fixed computational cost
Gravitational-wave searches for signals from inspiralling compact binaries
have relied on matched filtering banks of waveforms (called template banks) to
try to extract the signal waveforms from the detector data. These template
banks have been constructed using four main considerations, the region of
parameter space of interest, the sensitivity of the detector, the matched
filtering bandwidth, and the sensitivity one is willing to lose due to the
granularity of template placement, the latter of which is governed by the
minimal match. In this work we describe how the choice of the lower frequency
cutoff, the lower end of the matched filter frequency band, can be optimized
for detection. We also show how the minimal match can be optimally chosen in
the case of limited computational resources. These techniques are applied to
searches for binary neutron star signals that have been previously performed
when analyzing Initial LIGO and Virgo data and will be performed analyzing
Advanced LIGO and Advanced Virgo data using the expected detector sensitivity.
By following the algorithms put forward here, the volume sensitivity of these
searches is predicted to improve without increasing the computational cost of
performing the search.Comment: 12 pages, 8 figures, 4 table
A method to estimate the significance of coincident gravitational-wave observations from compact binary coalescence
Coalescing compact binary systems consisting of neutron stars and/or black
holes should be detectable with upcoming advanced gravitational-wave detectors
such as LIGO, Virgo, GEO and {KAGRA}. Gravitational-wave experiments to date
have been riddled with non-Gaussian, non-stationary noise that makes it
challenging to ascertain the significance of an event. A popular method to
estimate significance is to time shift the events collected between detectors
in order to establish a false coincidence rate. Here we propose a method for
estimating the false alarm probability of events using variables commonly
available to search candidates that does not rely on explicitly time shifting
the events while still capturing the non-Gaussianity of the data. We present a
method for establishing a statistical detection of events in the case where
several silver-plated (3--5) events exist but not necessarily any
gold-plated () events. We use LIGO data and a simulated, realistic,
blind signal population to test our method
Interpolating compact binary waveforms using the singular value decomposition
Compact binary systems with total masses between tens and hundreds of solar
masses will produce gravitational waves during their merger phase that are
detectable by second-generation ground-based gravitational-wave detectors. In
order to model the gravitational waveform of the merger epoch of compact binary
coalescence, the full Einstein equations must be solved numerically for the
entire mass and spin parameter space. However, this is computationally
expensive. Several models have been proposed to interpolate the results of
numerical relativity simulations. In this paper we propose a numerical
interpolation scheme that stems from the singular value decomposition. This
algorithm shows promise in allowing one to construct arbitrary waveforms within
a certain parameter space given a sufficient density of numerical simulations
covering the same parameter space. We also investigate how similar approaches
could be used to interpolate waveforms in the context of parameter estimation.Comment: 5 pages, 3 figures, presented at the joint 9th Edoardo Amaldi
Conference on Gravitational Waves and 2011 Numerical Relativity - Data
Analysis (NRDA) meetin
Momentum flow in black-hole binaries. I. Post-Newtonian analysis of the inspiral and spin-induced bobbing
A brief overview is presented of a new Caltech/Cornell research program that is exploring the nonlinear dynamics of curved spacetime in binary black-hole collisions and mergers, and of an initial project in this program aimed at elucidating the flow of linear momentum in binary black holes (BBHs). The âgauge-dependenceâ (arbitrariness) in the localization of linear momentum in BBHs is discussed, along with the hope that the qualitative behavior of linear momentum will be gauge-independent. Harmonic coordinates are suggested as a possibly preferred foundation for fixing the gauge associated with linear momentum. For a BBH or other compact binary, the Landau-Lifshitz formalism is used to define the momenta of the binaryâs individual bodies in terms of integrals over the bodiesâ surfaces or interiors, and define the momentum of the gravitational field (spacetime curvature) outside the bodies as a volume integral over the fieldâs momentum density. These definitions will be used in subsequent papers that explore the internal nonlinear dynamics of BBHs via numerical relativity. This formalism is then used, in the 1.5 post-Newtonian approximation, to explore momentum flow between a binaryâs bodies and its gravitational field during the binaryâs orbital inspiral. Special attention is paid to momentum flow and conservation associated with synchronous spin-induced bobbing of the black holes, in the so-called âextreme-kick configurationâ (where two identical black holes have their spins lying in their orbital plane and antialigned)
Parameter space metric for 3.5 post-Newtonian gravitational-waves from compact binary inspirals
We derive the metric on the parameter space of 3.5 post-Newtonian (3.5PN)
stationary phase compact binary inspiral waveforms for a single detector,
neglecting spin, eccentricity, and finite-body effects. We demonstrate that
this leads to better template placement than the current practice of using the
2PN metric to place 3.5PN templates: The recovered event rate is improved by
about 10% at a cost of nearly doubling the number of templates. The
cross-correlations between mass parameters are also more accurate, which will
result in better coincidence tests.Comment: 10 pages, 7 figure
Interpolation in waveform space: enhancing the accuracy of gravitational waveform families using numerical relativity
Matched-filtering for the identification of compact object mergers in
gravitational-wave antenna data involves the comparison of the data stream to a
bank of template gravitational waveforms. Typically the template bank is
constructed from phenomenological waveform models since these can be evaluated
for an arbitrary choice of physical parameters. Recently it has been proposed
that singular value decomposition (SVD) can be used to reduce the number of
templates required for detection. As we show here, another benefit of SVD is
its removal of biases from the phenomenological templates along with a
corresponding improvement in their ability to represent waveform signals
obtained from numerical relativity (NR) simulations. Using these ideas, we
present a method that calibrates a reduced SVD basis of phenomenological
waveforms against NR waveforms in order to construct a new waveform approximant
with improved accuracy and faithfulness compared to the original
phenomenological model. The new waveform family is given numerically through
the interpolation of the projection coefficients of NR waveforms expanded onto
the reduced basis and provides a generalized scheme for enhancing
phenomenological models.Comment: 10 pages, 7 figure
Efficiently enclosing the compact binary parameter space by singular-value decomposition
Gravitational-wave searches for the merger of compact binaries use
matched-filtering as the method of detecting signals and estimating parameters.
Such searches construct a fine mesh of filters covering a signal parameter
space at high density. Previously it has been shown that singular value
decomposition can reduce the effective number of filters required to search the
data. Here we study how the basis provided by the singular value decomposition
changes dimension as a function of template bank density. We will demonstrate
that it is sufficient to use the basis provided by the singular value
decomposition of a low density bank to accurately reconstruct arbitrary points
within the boundaries of the template bank. Since this technique is purely
numerical it may have applications to interpolating the space of numerical
relativity waveforms.Comment: 5 pages, 6 figure
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