4,474 research outputs found
New Coordinates for the Amplitude Parameter Space of Continuous Gravitational Waves
The parameter space for continuous gravitational waves (GWs) can be divided
into amplitude parameters (signal amplitude, inclination and polarization
angles describing the orientation of the source, and an initial phase) and
phase-evolution parameters. The division is useful in part because the
Jaranowski-Krolak-Schutz (JKS) coordinates on the four-dimensional amplitude
parameter space allow the GW signal to be written as a linear combination of
four template waveforms with the JKS coordinates as coefficients. We define a
new set of coordinates on the amplitude parameter space, with the same
properties, which is more closely connected to the physical amplitude
parameters. These naturally divide into two pairs of Cartesian-like coordinates
on two-dimensional subspaces, one corresponding to left- and the other to
right-circular polarization. We thus refer to these as CPF (circular
polarization factored) coordinates. The corresponding two sets of polar
coordinates (known as CPF-polar) can be related in a simple way to the physical
parameters. We illustrate some simplifying applications for these various
coordinate systems, such as: a calculation of Jacobians between various
coordinate systems; an illustration of the signal coordinate singularities
associated with left- and right-circular polarization, which correspond to the
origins of the two two-dimensional subspaces; and an elucidation of the form of
the log-likelihood ratio between hypotheses of Gaussian noise with and without
a continuous GW signal. These are used to illustrate some of the prospects for
approximate evaluation of a Bayesian detection statistic defined by
marginalization over the physical parameter space. Additionally, in the
presence of simplifying assumptions about the observing geometry, we are able
to explicitly evaluate the integral for the Bayesian detection statistic, and
compare it to the approximate results.Comment: REVTeX, 18 pages, 8 image files included in 7 figure
Macular Bioaccelerometers on Earth and in Space
Space flight offers the opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Macular research in space is particularly important to NASA because the bioaccelerometers are proving to be weighted neural networks in which information is distributed for parallel processing. Neural networks are plastic and highly adaptive to new environments. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, 3-dimensional reconstruction of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes. The results of such a combined effort could usher in a new era in understanding vestibular function on Earth and in space. They can also provide a rational basis for counter-measures to space motion sickness, which may prove troublesome as space voyager encounter new gravitational fields on planets, or must re-adapt to 1 g upon return to earth
Improved filters for gravitational waves from inspiralling compact binaries
The order of the post-Newtonian expansion needed, to extract in a reliable
and accurate manner the fully general relativistic gravitational wave signal
from inspiralling compact binaries, is explored. A class of approximate wave
forms, called P-approximants, is constructed based on the following two inputs:
(a) The introduction of two new energy-type and flux-type functions e(v) and
f(v), respectively, (b) the systematic use of Pade approximation for
constructing successive approximants of e(v) and f(v). The new P-approximants
are not only more effectual (larger overlaps) and more faithful (smaller
biases) than the standard Taylor approximants, but also converge faster and
monotonically. The presently available O(v/c)^5-accurate post-Newtonian results
can be used to construct P-approximate wave forms that provide overlaps with
the exact wave form larger than 96.5% implying that more than 90% of potential
events can be detected with the aid of P-approximants as opposed to a mere
10-15 % that would be detectable using standard post-Newtonian approximants.Comment: Latex ([prd,aps,eqsecnum,epsf]{revtex}), 40 pages including 12
encapsulated figures. (The paper, together with all the figures and tables is
available from ftp://carina.astro.cf.ac.uk/pub/incoming/sathya/dis97.uu
Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order
Gravitational waves generated by inspiralling compact binaries are
investigated to the second--post-Newtonian (2PN) approximation of general
relativity. Using a recently developed 2PN-accurate wave generation formalism,
we compute the gravitational waveform and associated energy loss rate from a
binary system of point-masses moving on a quasi-circular orbit. The crucial new
input is our computation of the 2PN-accurate ``source'' quadrupole moment of
the binary. Tails in both the waveform and energy loss rate at infinity are
explicitly computed. Gravitational radiation reaction effects on the orbital
frequency and phase of the binary are deduced from the energy loss. In the
limiting case of a very small mass ratio between the two bodies we recover the
results obtained by black hole perturbation methods. We find that finite mass
ratio effects are very significant as they increase the 2PN contribution to the
phase by up to 52\%. The results of this paper should be of use when
deciphering the signals observed by the future LIGO/VIRGO network of
gravitational-wave detectors.Comment: 43 pages, LaTeX-ReVTeX, no figures
Gravitational Wave Chirp Search: Economization of PN Matched Filter Bank via Cardinal Interpolation
The final inspiral phase in the evolution of a compact binary consisting of
black holes and/or neutron stars is among the most probable events that a
network of ground-based interferometric gravitational wave detectors is likely
to observe. Gravitational radiation emitted during this phase will have to be
dug out of noise by matched-filtering (correlating) the detector output with a
bank of several templates, making the computational resources required
quite demanding, though not formidable. We propose an interpolation method for
evaluating the correlation between template waveforms and the detector output
and show that the method is effective in substantially reducing the number of
templates required. Indeed, the number of templates needed could be a factor
smaller than required by the usual approach, when the minimal overlap
between the template bank and an arbitrary signal (the so-called {\it minimal
match}) is 0.97. The method is amenable to easy implementation, and the various
detector projects might benefit by adopting it to reduce the computational
costs of inspiraling neutron star and black hole binary search.Comment: scheduled for publicatin on Phys. Rev. D 6
Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
We derive the gravitational field and equations of motion of compact binary
systems up to the 5/2 post-Newtonian approximation of general relativity (where
radiation-reaction effects first appear). The approximate post-Newtonian
gravitational field might be used in the problem of initial conditions for the
numerical evolution of binary black-hole space-times. On the other hand we
recover the Damour-Deruelle 2.5PN equations of motion of compact binary
systems. Our method is based on an expression of the post-Newtonian metric
valid for general (continuous) fluids. We substitute into the fluid metric the
standard stress-energy tensor appropriate for a system of two point-like
particles. We remove systematically the infinite self-field of each particle by
means of the Hadamard partie finie regularization.Comment: 41 pages to appear in Physical Review
Design and implementation of a compliant robot with force feedback and strategy planning software
Force-feedback robotics techniques are being developed for automated precision assembly and servicing of NASA space flight equipment. Design and implementation of a prototype robot which provides compliance and monitors forces is in progress. Computer software to specify assembly steps and makes force feedback adjustments during assembly are coded and tested for three generically different precision mating problems. A model program demonstrates that a suitably autonomous robot can plan its own strategy
General relativistic dynamics of compact binaries at the third post-Newtonian order
The general relativistic corrections in the equations of motion and
associated energy of a binary system of point-like masses are derived at the
third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian
expansion of the metric in harmonic coordinates at the 3PN approximation. The
metric is parametrized by appropriate non-linear potentials, which are
evaluated in the case of two point-particles using a Lorentzian version of an
Hadamard regularization which has been defined in previous works.
Distributional forms and distributional derivatives constructed from this
regularization are employed systematically. The equations of motion of the
particles are geodesic-like with respect to the regularized metric. Crucial
contributions to the acceleration are associated with the non-distributivity of
the Hadamard regularization and the violation of the Leibniz rule by the
distributional derivative. The final equations of motion at the 3PN order are
invariant under global Lorentz transformations, and admit a conserved energy
(neglecting the radiation reaction force at the 2.5PN order). However, they are
not fully determined, as they depend on one arbitrary constant, which reflects
probably a physical incompleteness of the point-mass regularization. The
results of this paper should be useful when comparing theory to the
observations of gravitational waves from binary systems in future detectors
VIRGO and LIGO.Comment: 78 pages, submitted to Phys. Rev. D, with minor modification
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
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
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