431 research outputs found
Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters
The paper deals with issues pertaining the detection of gravitational waves
from coalescing binaries. We introduce the application of differential geometry
to the problem of optimal detection of the `chirp signal'. We have also carried
out extensive Monte Carlo simulations to understand the errors in the
estimation of parameters of the binary system. We find that the errors are much
more than those predicted by the covariance matrix even at a high SNR of 10-15.
We also introduce the idea of using the instant of coalescence rather than the
time of arrival to determine the direction to the source.Comment: 28 pages, REVTEX, 12 figures (bundled via uufiles command along with
this paper) submitted to Phys. Rev.
Gravitational Waves from coalescing binaries: Estimation of parameters
The paper presents a statistical model which reproduces the results of Monte
Carlo simulations to estimate the parameters of the gravitational wave signal
from a coalesing binary system. The model however is quite general and would be
useful in other parameter estimation problems.Comment: LaTeX with RevTeX macros, 4 figure
Estimation of parameters of gravitational waves from coalescing binaries
In this paper we deal with the measurement of the parameters of the
gravitational wave signal emitted by a coalescing binary signal.
We present the results of Monte Carlo simulations carried out for the case of
the initial LIGO, incorporating the first post-Newtonian corrections into the
waveform. Using the parameters so determined, we estimate the direction to the
source. We stress the use of the time-of-coalescence rather than the
time-of-arrival of the signal to determine the direction of the source. We show
that this can considerably reduce the errors in the determination of the
direction of the source.Comment: 5 pages, REVTEX, 2 figures (bundled via uufiles command along with
this paper) submitted to Praman
Hypercontractivity on the -Araki-Woods algebras
Extending a work of Carlen and Lieb, Biane has obtained the optimal
hypercontractivity of the -Ornstein-Uhlenbeck semigroup on the
-deformation of the free group algebra. In this note, we look for an
extension of this result to the type III situation, that is for the
-Araki-Woods algebras. We show that hypercontractivity from to
can occur if and only if the generator of the deformation is bounded.Comment: 17 page
Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?
The most promising source of gravitational waves for the planned detectors
LIGO and VIRGO are merging compact binaries, i.e., neutron star/neutron star
(NS/NS), neutron star/black hole (NS/BH), and black hole/black-hole (BH/BH)
binaries. We investigate how accurately the distance to the source and the
masses and spins of the two bodies will be measured from the gravitational wave
signals by the three detector LIGO/VIRGO network using ``advanced detectors''
(those present a few years after initial operation). The combination of the masses of the two bodies is
measurable with an accuracy . The reduced mass is measurable
to for NS/NS and NS/BH binaries, and for BH/BH
binaries (assuming BH's). Measurements of the masses and spins are
strongly correlated; there is a combination of and the spin angular
momenta that is measured to within . We also estimate that distance
measurement accuracies will be for of the detected
signals, and for of the signals, for the LIGO/VIRGO
3-detector network.Comment: 103 pages, 20 figures, submitted to Phys Rev D, uses revtex macros,
Caltech preprint GRP-36
Role of initial data in spherical collapse
We bring out here the role of initial data in causing the black hole and
naked singularity phases as the final end state of a continual gravitational
collapse. The collapse of a type I general matter field is considered, which
includes most of the known physical forms of matter. It is shown that given the
distribution of the density and pressure profiles at the initial surface from
which the collapse evolves, there is a freedom in choosing rest of the free
functions, such as the velocities of the collapsing shells, so that the end
state could be either a black hole or a naked singularity depending on this
choice. It is thus seen that it is the initial data that determines the end
state of spherical collapse in terms of these outcomes, and we get a good
picture of how these phases come about.Comment: 5 pages, Revtex4, Revised version, To appear in Physical Review
Gravitational collapse in asymptotically Anti-de Sitter/de Sitter backgrounds
We study here the gravitational collapse of a matter cloud with a
non-vanishing tangential pressure in the presence of a non-zero cosmological
term. Conditions for bounce and singularity formation are derived for the
model. It is also shown that when the tangential pressures vanish, the bounce
and singularity conditions reduce to that of the dust case studied earlier. The
collapsing interior is matched with an exterior which is asymptotically de
Sitter or anti de Sitter, depending on the sign of cosmological constant. The
junction conditions for matching the cloud to exterior are specified. The
effect of the cosmological term on apparent horizons is studied in some detail,
and the nature of central singularity is analyzed. We also discuss here the
visibility of the singularity and implications for the cosmic censorship
conjecture.Comment: 11 pages, 1 figure, Revtex
Optimal statistic for detecting gravitational wave signals from binary inspirals with LISA
A binary compact object early in its inspiral phase will be picked up by its
nearly monochromatic gravitational radiation by LISA. But even this innocuous
appearing candidate poses interesting detection challenges. The data that will
be scanned for such sources will be a set of three functions of LISA's twelve
data streams obtained through time-delay interferometry, which is necessary to
cancel the noise contributions from laser-frequency fluctuations and
optical-bench motions to these data streams. We call these three functions
pseudo-detectors. The sensitivity of any pseudo-detector to a given sky
position is a function of LISA's orbital position. Moreover, at a given point
in LISA's orbit, each pseudo-detector has a different sensitivity to the same
sky position. In this work, we obtain the optimal statistic for detecting
gravitational wave signals, such as from compact binaries early in their
inspiral stage, in LISA data. We also present how the sensitivity of LISA,
defined by this optimal statistic, varies as a function of sky position and
LISA's orbital location. Finally, we show how a real-time search for inspiral
signals can be implemented on the LISA data by constructing a bank of templates
in the sky positions.Comment: 22 pages, 15 eps figures, Latex, uses iopart style/class files. Based
on talk given at the 8th Gravitational Wave Data Analysis Workshop,
Milwaukee, USA, December 17-20, 2003. Accepted for publication in Class.
Quant. Gra
Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals
A global network of laser interferometric gravitational wave detectors is
projected to be in operation by around the turn of the century. Here, the noisy
output of a single instrument is examined. A gravitational wave is assumed to
have been detected in the data and we deal with the subsequent problem of
parameter estimation. Specifically, we investigate theoretical lower bounds on
the minimum mean-square errors associated with measuring the parameters of the
inspiral waveform generated by an orbiting system of neutron stars/black holes.
Three theoretical lower bounds on parameter estimation accuracy are considered:
the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai
bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing
binary waveform, and compare them with published CRB and numerical Monte-Carlo
results. At large SNR, we find that the theoretical bounds are all identical
and are attained by the Monte-Carlo results. As SNR gradually drops below 10,
the WWB and ZZB are both found to provide increasingly tighter lower bounds
than the CRB. However, at these levels of moderate SNR, there is a significant
departure between all the bounds and the numerical Monte-Carlo results.Comment: 17 pages (LaTeX), 4 figures. Submitted to Physical Review
Detection, Measurement and Gravitational Radiation
Here I examine how to determine the sensitivity of the LIGO, VIRGO, and LAGOS
gravitational wave detectors to sources of gravitational radiation by
considering the process by which data are analyzed in a noisy detector. By
constructing the probability that the detector output is consistent with the
presence of a signal, I show how to (1) quantify the uncertainty that the
output contains a signal and is not simply noise, and (2) construct the
probability distribution that the signal parameterization has a certain value.
From the distribution and its mode I determine volumes in parameter
space such that actual signal parameters are in with probability . If
we are {\em designing} a detector, or determining the suitability of an
existing detector for observing a new source, then we don't have detector
output to analyze but are interested in the ``most likely'' response of the
detector to a signal. I exploit the techniques just described to determine the
``most likely'' volumes for detector output corresponding to the source.
Finally, as an example, I apply these techniques to anticipate the sensitivity
of the LIGO and LAGOS detectors to the gravitational radiation from a perturbed
Kerr black hole.Comment: 37 pages (plus 6 figures), LaTeX/REVTE
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