6 research outputs found
Detecting gravitational waves from inspiraling binaries with a network of detectors : coherent strategies by correlated detectors
We discuss the coherent search strategy to detect gravitational waves from
inspiraling compact binaries by a network of correlated laser interferometric
detectors. From the maximum likelihood ratio statistic, we obtain a coherent
statistic which is slightly different from and generally better than what we
obtained in our previous work. In the special case when the cross spectrum of
two detectors normalized by the power spectrum density is constant, the new
statistic agrees with the old one. The quantitative difference of the detection
probability for a given false alarm rate is also evaluated in a simple case.Comment: 4 pages, 1 Postscript figures, uses revtex4.st
The cross-correlation search for periodic gravitational waves
In this paper we study the use of cross-correlations between multiple
gravitational wave (GW) data streams for detecting long-lived periodic signals.
Cross-correlation searches between data from multiple detectors have
traditionally been used to search for stochastic GW signals, but recently they
have also been used in directed searches for periodic GWs. Here we further
adapt the cross-correlation statistic for periodic GW searches by taking into
account both the non-stationarity and the long term-phase coherence of the
signal. We study the statistical properties and sensitivity of this search, its
relation to existing periodic wave searches, and describe the precise way in
which the cross-correlation statistic interpolates between semi-coherent and
fully-coherent methods. Depending on the maximum duration over we wish to
preserve phase coherence, the cross-correlation statistic can be tuned to go
from a standard cross-correlation statistic using data from distinct detectors,
to the semi-coherent time-frequency methods with increasing coherent time
baselines, and all the way to a full coherent search. This leads to a unified
framework for studying periodic wave searches and can be used to make informed
trade-offs between computational cost, sensitivity, and robustness against
signal uncertainties.Comment: 17 pages, 1 figure, RevTeX
Detecting gravitational waves from inspiraling binaries with a network of detectors : coherent versus coincident strategies
We compare two strategies of multi-detector detection of compact binary
inspiral signals, namely, the coincidence and the coherent. For simplicity we
consider here two identical detectors having the same power spectral density of
noise, that of initial LIGO, located in the same place and having the same
orientation. We consider the cases of independent noise as well as that of
correlated noise. The coincident strategy involves separately making two
candidate event lists, one for each detector, and from these choosing those
pairs of events from the two lists which lie within a suitable parameter
window, which then are called as coincidence detections. The coherent strategy
on the other hand involves combining the data phase coherently, so as to obtain
a single network statistic which is then compared with a single threshold. Here
we attempt to shed light on the question as to which strategy is better. We
compare the performances of the two methods by plotting the Receiver Operating
Characteristics (ROC) for the two strategies. Several of the results are
obtained analytically in order to gain insight. Further we perform numerical
simulations in order to determine certain parameters in the analytic formulae
and thus obtain the final complete results. We consider here several cases from
the relatively simple to the astrophysically more relevant in order to
establish our results. The bottom line is that the coherent strategy although
more computationally expensive in general than the coincidence strategy, is
superior to the coincidence strategy - considerably less false dismissal
probability for the same false alarm probability in the viable false alarm
regime.Comment: 18 pages, 10 figures, typo correcte
Spectrum of rotating black holes and its implications for Hawking radiation
The reduced phase space formalism for quantising black holes has recently
been extended to find the area and angular momentum spectra of four dimensional
Kerr black holes. We extend this further to rotating black holes in all
spacetime dimensions and show that although as in four dimensions the spectrum
is discrete, it is not equispaced in general. As a result, Hawking radiation
spectra from these black holes are continuous, as opposed to the discrete
spectrum predicted for four dimensional black holes.Comment: 11 pages, Revtex4. Minor changes to match version to appear in Class.
Quant. Gra
Quantum state preparation and macroscopic entanglement in gravitational-wave detectors
Long-baseline laser-interferometer gravitational-wave detectors are operating
at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within
a broad frequency band. Such a low classical noise budget has already allowed
the creation of a controlled 2.7 kg macroscopic oscillator with an effective
eigenfrequency of 150 Hz and an occupation number of 200. This result, along
with the prospect for further improvements, heralds the new possibility of
experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical
behavior of objects in the realm of everyday experience - using
gravitational-wave detectors. In this paper, we provide the mathematical
foundation for the first step of a MQM experiment: the preparation of a
macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum
state, which is possible if the interferometer's classical noise beats the SQL
in a broad frequency band. Our formalism, based on Wiener filtering, allows a
straightforward conversion from the classical noise budget of a laser
interferometer, in terms of noise spectra, into the strategy for quantum state
preparation, and the quality of the prepared state. Using this formalism, we
consider how Gaussian entanglement can be built among two macroscopic test
masses, and the performance of the planned Advanced LIGO interferometers in
quantum-state preparation
Detecting gravitational waves from inspiraling binaries with a network of geographically separated detectors: coherent versus coincident strategies
We compare two strategies of multidetector detection of compact binary inspiral signals, namely, the coincidence and the coherent for the realistic case of geographically separated detectors. The naive coincident strategy treats the detectors as if they are isolated— compares individual detector statistics with their respective thresholds while the coherent strategy combines the detector network data coherently to obtain a single detection statistic which is then compared with a single threshold. We also consider an enhanced coincidence strategy which is intermediate in the sense that though the individual statistics are added in quadrature and the sum compared with a single threshold, the estimated parameters are also checked for consistency. For simplicity, we consider detector pairs having the same power spectral density of noise, as that of initial LIGO and also assume the noise to be stationary and Gaussian. Further, since we consider the detectors to be widely separated on Earth, we take the instrumental noises to be uncorrelated; the wide separation implicitly means that since the detector arms must lie parallel to the Earth's surface, the detectors necessarily have different orientations. We compare the performances of the methods by plotting the receiver operating characteristics for the strategies. Several results are derived analytically in order to gain insight. Simulations are performed in order to plot the receiver operating characteristic (ROC) curves. A single astrophysical source as well as a distribution of sources is considered. We assume a 1 yr data train and a mass range of 1-40M<SUB>⊙</SUB> for the case of astrophysically distributed sources. We find that the coherent strategy is superior to the two coincident strategies that we consider. Remarkably, the detection probability of the coherent strategy is 50% better than the naive coincident strategy. One the other hand, the difference in performance between the coherent strategy and enhanced coincident strategy is not very large. Even in this situation, it is not difficult to perform the real data analysis with the coherent strategy. The bottom line is that the coherent strategy is a good detection strategy