3,810 research outputs found
Computational Resources to Filter Gravitational Wave Data with P-approximant Templates
The prior knowledge of the gravitational waveform from compact binary systems
makes matched filtering an attractive detection strategy. This detection method
involves the filtering of the detector output with a set of theoretical
waveforms or templates. One of the most important factors in this strategy is
knowing how many templates are needed in order to reduce the loss of possible
signals. In this study we calculate the number of templates and computational
power needed for a one-step search for gravitational waves from inspiralling
binary systems. We build on previous works by firstly expanding the
post-Newtonian waveforms to 2.5-PN order and secondly, for the first time,
calculating the number of templates needed when using P-approximant waveforms.
The analysis is carried out for the four main first-generation interferometers,
LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the
computational cost of generating banks of templates for filtering GW data. We
carry out the calculations for two initial conditions. In the first case we
assume a minimum individual mass of and in the second, we assume
a minimum individual mass of . We find that, in general, we need
more P-approximant templates to carry out a search than if we use standard PN
templates. This increase varies according to the order of PN-approximation, but
can be as high as a factor of 3 and is explained by the smaller span of the
P-approximant templates as we go to higher masses. The promising outcome is
that for 2-PN templates the increase is small and is outweighed by the known
robustness of the 2-PN P-approximant templates.Comment: 17 pages, 8 figures, Submitted to Class.Quant.Gra
The Cauchy convergence of T and P-approximant templates for test-mass Kerr binary systems
In this work we examine the Cauchy convergence of both post-Newtonian
(T-approximant) and re-summed post-Newtonian (P-approximant) templates for the
case of a test-mass orbiting a Kerr black hole along a circular equatorial
orbit. The Cauchy criterion demands that the inner product between the and
order approximation approaches unity, as we increase the order of
approximation. In previous works, it has been shown that we achieve greater
fitting factors and better parameter estimation using the P-approximant
templates for both Schwarzschild and Kerr black holes. In this work, we show
that the P-approximant templates also display a faster Cauchy convergence
making them a superior template to the standard post-Newtonian templates.Comment: 5 pages, Replaced with shortened published versio
Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
The two-body dynamics in general relativity has been solved perturbatively
using the post-Newtonian (PN) approximation. The evolution of the orbital phase
and the emitted gravitational radiation are now known to a rather high order up
to O(v^8), v being the characteristic velocity of the binary. The orbital
evolution, however, cannot be specified uniquely due to the inherent freedom in
the choice of parameter used in the PN expansion as well as the method pursued
in solving the relevant differential equations. The goal of this paper is to
determine the (dis)agreement between different PN waveform families in the
context of initial and advanced gravitational-wave detectors. The waveforms
employed in our analysis are those that are currently used by Initial
LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3,
TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the
Fourier-domain representation TaylorF2. We examine the overlaps of these models
with one another and with the prototype effective one-body model (calibrated to
numerical relativity simulations, as currently used by initial LIGO) for a
number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their
differences and to help us decide whether there exist preferred families that
are the most appropriate as search templates. We conclude that as long as the
total mass remains less than a certain upper limit M_crit, all template
families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the
purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial,
Enhanced and Advanced LIGO. From a purely computational point of view we
recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to
numerical relativity simulations be used for total binary mass M > Mcrit.Comment: 27 pages, 8 figures, 4 tables, submitted to PR
Length requirements for numerical-relativity waveforms
One way to produce complete inspiral-merger-ringdown gravitational waveforms
from black-hole-binary systems is to connect post-Newtonian (PN) and
numerical-relativity (NR) results to create "hybrid" waveforms. Hybrid
waveforms are central to the construction of some phenomenological models for
GW search templates, and for tests of GW search pipelines. The dominant error
source in hybrid waveforms arises from the PN contribution, and can be reduced
by increasing the number of NR GW cycles that are included in the hybrid.
Hybrid waveforms are considered sufficiently accurate for GW detection if their
mismatch error is below 3% (i.e., a fitting factor about 0.97). We address the
question of the length requirements of NR waveforms such that the final hybrid
waveforms meet this requirement, considering nonspinning binaries with q =
M_2/M_1 \in [1,4] and equal-mass binaries with \chi = S_i/M_i^2 \in [-0.5,0.5].
We conclude that for the cases we study simulations must contain between three
(in the equal-mass nonspinning case) and ten (the \chi = 0.5 case) orbits
before merger, but there is also evidence that these are the regions of
parameter space for which the least number of cycles will be needed.Comment: Corrected some typo
Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums
Periodic orbit quantization requires an analytic continuation of
non-convergent semiclassical trace formulae. We propose a method for
semiclassical quantization based upon the Pade approximant to the periodic
orbit sums. The Pade approximant allows the re-summation of the typically
exponentially divergent periodic orbit terms. The technique does not depend on
the existence of a symbolic dynamics and can be applied to both bound and open
systems. Numerical results are presented for two different systems with chaotic
and regular classical dynamics, viz. the three-disk scattering system and the
circle billiard.Comment: 7 pages, 3 figures, submitted to Europhys. Let
How Many Templates for GW Chirp Detection? The Minimal-Match Issue Revisited
In a recent paper dealing with maximum likelihood detection of gravitational
wave chirps from coalescing binaries with unknown parameters we introduced an
accurate representation of the no-signal cumulative distribution of the
supremum of the whole correlator bank. This result can be used to derive a
refined estimate of the number of templates yielding the best tradeoff between
detector's performance (in terms of lost signals among those potentially
detectable) and computational burden.Comment: submitted to Class. Quantum Grav. Typing error in eq. (4.8) fixed;
figure replaced in version
A Comparison of search templates for gravitational waves from binary inspiral
We compare the performances of the templates defined by three different types
of approaches: traditional post-Newtonian templates (Taylor-approximants),
``resummed'' post-Newtonian templates assuming the adiabatic approximation and
stopping before the plunge (P-approximants), and further ``resummed''
post-Newtonian templates going beyond the adiabatic approximation and
incorporating the plunge with its transition from the inspiral
(Effective-one-body approximants). The signal to noise ratio is significantly
enhanced (mainly because of the inclusion of the plunge signal) by using these
new effective-one-body templates relative to the usual post-Newtonian ones for
binary masses greater than , the most likely sources for initial
laser interferometers. Independently of the question of the plunge signal, the
comparison of the various templates confirms the usefulness of using
resummation methods. The paper also summarizes the key elements of the
construction of various templates and thus can serve as a resource for those
involved in writing inspiral search software.Comment: eta-dependent tail terms corrected after related errata by Blanchet
(2005
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