217 research outputs found
Data analysis strategies for the detection of gravitational waves in non-Gaussian noise
In order to analyze data produced by the kilometer-scale gravitational wave
detectors that will begin operation early next century, one needs to develop
robust statistical tools capable of extracting weak signals from the detector
noise. This noise will likely have non-stationary and non-Gaussian components.
To facilitate the construction of robust detection techniques, I present a
simple two-component noise model that consists of a background of Gaussian
noise as well as stochastic noise bursts. The optimal detection statistic
obtained for such a noise model incorporates a natural veto which suppresses
spurious events that would be caused by the noise bursts. When two detectors
are present, I show that the optimal statistic for the non-Gaussian noise model
can be approximated by a simple coincidence detection strategy. For simulated
detector noise containing noise bursts, I compare the operating characteristics
of (i) a locally optimal detection statistic (which has nearly-optimal behavior
for small signal amplitudes) for the non-Gaussian noise model, (ii) a standard
coincidence-style detection strategy, and (iii) the optimal statistic for
Gaussian noise.Comment: 5 pages RevTeX, 4 figure
Template banks to search for compact binaries with spinning components in gravitational wave data
Gravitational waves from coalescing compact binaries are one of the most
promising sources for detectors such as LIGO, Virgo and GEO600. If the
components of the binary posess significant angular momentum (spin), as is
likely to be the case if one component is a black hole, spin-induced precession
of a binary's orbital plane causes modulation of the gravitational-wave
amplitude and phase. If the templates used in a matched-filter search do not
accurately model these effects then the sensitivity, and hence the detection
rate, will be reduced. We investigate the ability of several search pipelines
to detect gravitational waves from compact binaries with spin. We use the
post-Newtonian approximation to model the inspiral phase of the signal and
construct two new template banks using the phenomenological waveforms of
Buonanno, Chen and Vallisneri. We compare the performance of these template
banks to that of banks constructed using the stationary phase approximation to
the non-spinning post-Newtonian inspiral waveform currently used by LIGO and
Virgo in the search for compact binary coalescence. We find that, at the same
false alarm rate, a search pipeline using phenomenological templates is no more
effective than a pipeline which uses non-spinning templates. We recommend the
continued use of the non-spinning stationary phase template bank until the
false alarm rate associated with templates which include spin effects can be
substantially reduced.Comment: 11 pages, 3 figure
Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope
General relativity has very specific predictions for the gravitational
waveforms from inspiralling compact binaries obtained using the post-Newtonian
(PN) approximation. We investigate the extent to which the measurement of the
PN coefficients, possible with the second generation gravitationalwave
detectors such as the Advanced Laser Interferometer Gravitational-Wave
Observatory (LIGO) and the third generation gravitational-wave detectors such
as the Einstein Telescope (ET), could be used to test post-Newtonian theory and
to put bounds on a subclass of parametrized-post-Einstein theories which differ
from general relativity in a parametrized sense. We demonstrate this
possibility by employing the best inspiralling waveform model for nonspinning
compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within
the class of theories considered, Advanced LIGO can test the theory at 1.5PN
and thus the leading tail term. Future observations of stellar mass black hole
binaries by ET can test the consistency between the various PN coefficients in
the gravitational-wave phasing over the mass range of 11-44 Msun. The choice of
the lower frequency cut off is important for testing post-Newtonian theory
using the ET. The bias in the test arising from the assumption of nonspinning
binaries is indicated.Comment: 18 pages, 11 figures, Matches with the published versio
Black-hole hair loss: learning about binary progenitors from ringdown signals
Perturbed Kerr black holes emit gravitational radiation, which (for the
practical purposes of gravitational-wave astronomy) consists of a superposition
of damped sinusoids termed quasi-normal modes. The frequencies and
time-constants of the modes depend only on the mass and spin of the black hole
- a consequence of the no-hair theorem. It has been proposed that a measurement
of two or more quasi-normal modes could be used to confirm that the source is a
black hole and to test if general relativity continues to hold in ultra-strong
gravitational fields. In this paper we propose a practical approach to testing
general relativity with quasi-normal modes. We will also argue that the
relative amplitudes of the various quasi-normal modes encode important
information about the origin of the perturbation that caused them. This helps
in inferring the nature of the perturbation from an observation of the emitted
quasi-normal modes. In particular, we will show that the relative amplitudes of
the different quasi-normal modes emitted in the process of the merger of a pair
of nonspinning black holes can be used to measure the component masses of the
progenitor binary.Comment: 24 pages, 9 figures, 4 tables, accepted for publication in Physical
Review
A coherent triggered search for single spin compact binary coalescences in gravitational wave data
In this paper we present a method for conducting a coherent search for single
spin compact binary coalescences in gravitational wave data and compare this
search to the existing coincidence method for single spin searches. We propose
a method to characterize the regions of the parameter space where the single
spin search, both coincident and coherent, will increase detection efficiency
over the existing non-precessing search. We also show example results of the
coherent search on a stretch of data from LIGO's fourth science run but note
that a set of signal based vetoes will be needed before this search can be run
to try to make detections.Comment: 14 pages, 4 figure
Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform
We prove that the oft-used stationary-phase method gives a very accurate
expression for the Fourier transform of the gravitational-wave signal produced
by an inspiraling compact binary. We give three arguments. First, we
analytically calculate the next-order correction to the stationary-phase
approximation, and show that it is small. This calculation is essentially an
application of the steepest-descent method to evaluate integrals. Second, we
numerically compare the stationary-phase expression to the results obtained by
Fast Fourier Transform. We show that the differences can be fully attributed to
the windowing of the time series, and that they have nothing to do with an
intrinsic failure of the stationary-phase method. And third, we show that these
differences are negligible for the practical application of matched filtering.Comment: 8 pages, ReVTeX, 4 figure
LISA Data Analysis using MCMC methods
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously
detect many thousands of low frequency gravitational wave signals. This
presents a data analysis challenge that is very different to the one
encountered in ground based gravitational wave astronomy. LISA data analysis
requires the identification of individual signals from a data stream containing
an unknown number of overlapping signals. Because of the signal overlaps, a
global fit to all the signals has to be performed in order to avoid biasing the
solution. However, performing such a global fit requires the exploration of an
enormous parameter space with a dimension upwards of 50,000. Markov Chain Monte
Carlo (MCMC) methods offer a very promising solution to the LISA data analysis
problem. MCMC algorithms are able to efficiently explore large parameter
spaces, simultaneously providing parameter estimates, error analyses and even
model selection. Here we present the first application of MCMC methods to
simulated LISA data and demonstrate the great potential of the MCMC approach.
Our implementation uses a generalized F-statistic to evaluate the likelihoods,
and simulated annealing to speed convergence of the Markov chains. As a final
step we super-cool the chains to extract maximum likelihood estimates, and
estimates of the Bayes factors for competing models. We find that the MCMC
approach is able to correctly identify the number of signals present, extract
the source parameters, and return error estimates consistent with Fisher
information matrix predictions.Comment: 14 pages, 7 figure
Angular Resolution of the LISA Gravitational Wave Detector
We calculate the angular resolution of the planned LISA detector, a
space-based laser interferometer for measuring low-frequency gravitational
waves from galactic and extragalactic sources. LISA is not a pointed
instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will
measure simultaneously both polarization components of incoming gravitational
waves, so the data will consist of two time series. All physical properties of
the source, including its position, must be extracted from these time series.
LISA's angular resolution is therefore not a fixed quantity, but rather depends
on the type of signal and on how much other information must be extracted.
Information about the source position will be encoded in the measured signal in
three ways: 1) through the relative amplitudes and phases of the two
polarization components, 2) through the periodic Doppler shift imposed on the
signal by the detector's motion around the Sun, and 3) through the further
modulation of the signal caused by the detector's time-varying orientation. We
derive the basic formulae required to calculate the LISA's angular resolution
for a given source. We then evaluate for
two sources of particular interest: monchromatic sources and mergers of
supermassive black holes. For these two types of sources, we calculate (in the
high signal-to-noise approximation) the full variance-covariance matrix, which
gives the accuracy to which all source parameters can be measured. Since our
results on LISA's angular resolution depend mainly on gross features of the
detector geometry, orbit, and noise curve, we expect these results to be fairly
insensitive to modest changes in detector design that may occur between now and
launch. We also expect that our calculations could be easily modified to apply
to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil
Searching for Gravitational Waves from Binary Inspirals with LIGO
We describe the current status of the search for gravitational waves from
inspiralling compact binary systems in LIGO data. We review the result from the
first scientific run of LIGO (S1). We present the goals of the search of data
taken in the second scientific run (S2) and describe the differences between
the methods used in S1 and S2.Comment: 9 pages, 2 figures. Published in proceedings of the 8th Gravitational
Wave Data Analysis Workshop, Milwaukee, WI, USA, 17-20 December 200
Gravitational waves from inspiraling compact binaries: Second post-Newtonian waveforms as search templates
We ascertain the effectiveness of the second post-Newtonian approximation to
the gravitational waves emitted during the adiabatic inspiral of a compact
binary system as templates for signal searches with kilometer-scale
interferometric detectors. The reference signal is obtained by solving the
Teukolsky equation for a small mass moving on a circular orbit around a large
nonrotating black hole. Fitting factors computed from this signal and these
templates, for various types of binary systems, are all above the 90% mark.
According to Apostolatos' criterion, second post-Newtonian waveforms should
make acceptably effective search templates.Comment: LaTeX, one eps figure. Hires and color versions are available from
http://jovian.physics.uoguelph.ca/~droz/uni/papers/search.htm
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