928 research outputs found
The mathematical theory of resonant transducers in a spherical gravity wave antenna
The rigoruos mathematical theory of the coupling and response of a spherical
gravitational wave detector endowed with a set of resonant transducers is
presented and developed. A perturbative series in ascending powers of the
square root of the ratio of the resonator to the sphere mass is seen to be the
key to the solution of the problem. General layouts of arbitrary numbers of
transducers can be assessed, and a specific proposal (PHC), alternative to the
highly symmetric TIGA of Merkowitz and Johnson, is described in detail.
Frequency spectra of the coupled system are seen to be theoretically recovered
in full agreement with experimental determinations.Comment: 31 pages, 7 figures, LaTeX2e, \usepackage{graphicx,deleq
Radiation Pressure Induced Instabilities in Laser Interferometric Detectors of Gravitational Waves
The large scale interferometric gravitational wave detectors consist of
Fabry-Perot cavities operating at very high powers ranging from tens of kW to
MW for next generations. The high powers may result in several nonlinear
effects which would affect the performance of the detector. In this paper, we
investigate the effects of radiation pressure, which tend to displace the
mirrors from their resonant position resulting in the detuning of the cavity.
We observe a remarkable effect, namely, that the freely hanging mirrors gain
energy continuously and swing with increasing amplitude. It is found that the
`time delay', that is, the time taken for the field to adjust to its
instantaneous equilibrium value, when the mirrors are in motion, is responsible
for this effect. This effect is likely to be important in the optimal operation
of the full-scale interferometers such as VIRGO and LIGO.Comment: 27 pages, 11 figures, RevTex styl
Optimising the directional sensitivity of LISA
It was shown in a previous work that the data combinations canceling laser
frequency noise constitute a module - the module of syzygies. The cancellation
of laser frequency noise is crucial for obtaining the requisite sensitivity for
LISA. In this work we show how the sensitivity of LISA can be optimised for a
monochromatic source - a compact binary - whose direction is known, by using
appropriate data combinations in the module. A stationary source in the
barycentric frame appears to move in the LISA frame and our strategy consists
of "coherently tracking" the source by appropriately "switching" the data
combinations so that they remain optimal at all times. Assuming that the
polarisation of the source is not known, we average the signal over the
polarisations. We find that the best statistic is the `network' statistic, in
which case LISA can be construed of as two independent detectors. We compare
our results with the Michelson combination, which has been used for obtaining
the standard sensitivity curve for LISA, and with the observable obtained by
optimally switching the three Michelson combinations. We find that for sources
lying in the ecliptic plane the improvement in SNR increases from 34% at low
frequencies to nearly 90% at around 20 mHz. Finally we present the
signal-to-noise ratios for some known binaries in our galaxy. We also show
that, if at low frequencies SNRs of both polarisations can be measured, the
inclination angle of the plane of the orbit of the binary can be estimated.Comment: 16 pages, 8 figures, submitted to Phys Rev
Improving the Sensitivity of LISA
It has been shown in the past, that the six Doppler data streams obtained
LISA configuration can be combined by appropriately delaying the data streams
for cancelling the laser frequency noise. Raw laser noise is several orders of
magnitude above the other noises and thus it is essential to bring it down to
the level of shot, acceleration noises. A rigorous and systematic formalism
using the techniques of computational commutative algebra was developed which
generates all the data combinations cancelling the laser frequency noise. The
relevant data combinations form a first module of syzygies. In this paper we
use this formalism for optimisation of the LISA sensitivity by analysing the
noise and signal covariance matrices. The signal covariance matrix, averaged
over polarisations and directions, is calculated for binaries whose frequency
changes at most adiabatically. We then present the extremal SNR curves for all
the data combinations in the module. They correspond to the eigenvectors of the
noise and signal covariance matrices. We construct LISA `network' SNR by
combining the outputs of the eigenvectors which improves the LISA sensitivity
substantially. The maximum SNR curve can yield an improvement upto 70 % over
the Michelson, mainly at high frequencies, while the improvement using the
network SNR ranges from 40 % to over 100 %. Finally, we describe a simple toy
model, in which LISA rotates in a plane. In this analysis, we estimate the
improvement in the LISA sensitivity, if one switches from one data combination
to another as it rotates. Here the improvement in sensitivity, if one switches
optimally over three cyclic data combinations of the eigenvector is about 55 %
on an average over the LISA band-width. The corresponding SNR improvement is 60
%, if one maximises over the module.Comment: 16 pages, 10 figures, Submitted to Class. Quant. Gravit
Observing Gravitational Waves with a Single Detector
A major challenge of any search for gravitational waves is to distinguish
true astrophysical signals from those of terrestrial origin. Gravitational-wave
experiments therefore make use of multiple detectors, considering only those
signals which appear in coincidence in two or more instruments. It is unclear,
however, how to interpret loud gravitational-wave candidates observed when only
one detector is operational. In this paper, we demonstrate that the observed
rate of binary black hole mergers can be leveraged in order to make confident
detections of gravitational-wave signals with one detector alone. We quantify
detection confidences in terms of the probability that a signal
candidate is of astrophysical origin. We find that, at current levels of
instrumental sensitivity, loud signal candidates observed with a single
Advanced LIGO detector can be assigned . In the future,
Advanced LIGO may be able to observe single-detector events with confidences
exceeding .Comment: 8 pages, 4 figures; published in CQG; minor updates to match
published versio
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