8,409 research outputs found
Binary inspiral, gravitational radiation, and cosmology
Observations of binary inspiral in a single interferometric gravitational
wave detector can be cataloged according to signal-to-noise ratio and
chirp mass . The distribution of events in a catalog composed of
observations with greater than a threshold depends on the
Hubble expansion, deceleration parameter, and cosmological constant, as well as
the distribution of component masses in binary systems and evolutionary
effects. In this paper I find general expressions, valid in any homogeneous and
isotropic cosmological model, for the distribution with and of
cataloged events; I also evaluate these distributions explicitly for relevant
matter-dominated Friedmann-Robertson-Walker models and simple models of the
neutron star mass distribution. In matter dominated Friedmann-Robertson-Walker
cosmological models advanced LIGO detectors will observe binary neutron star
inspiral events with from distances not exceeding approximately
, corresponding to redshifts of (0.26) for
(), at an estimated rate of 1 per week. As the binary system mass
increases so does the distance it can be seen, up to a limit: in a matter
dominated Einstein-deSitter cosmological model with () that limit
is approximately (1.7) for binaries consisting of two
black holes. Cosmological tests based on catalogs of the
kind discussed here depend on the distribution of cataloged events with
and . The distributions found here will play a pivotal role in testing
cosmological models against our own universe and in constructing templates for
the detection of cosmological inspiraling binary neutron stars and black holes.Comment: REVTeX, 38 pages, 9 (encapsulated) postscript figures, uses epsf.st
Aperture synthesis for gravitational-wave data analysis: Deterministic Sources
Gravitational wave detectors now under construction are sensitive to the
phase of the incident gravitational waves. Correspondingly, the signals from
the different detectors can be combined, in the analysis, to simulate a single
detector of greater amplitude and directional sensitivity: in short, aperture
synthesis. Here we consider the problem of aperture synthesis in the special
case of a search for a source whose waveform is known in detail: \textit{e.g.,}
compact binary inspiral. We derive the likelihood function for joint output of
several detectors as a function of the parameters that describe the signal and
find the optimal matched filter for the detection of the known signal. Our
results allow for the presence of noise that is correlated between the several
detectors. While their derivation is specialized to the case of Gaussian noise
we show that the results obtained are, in fact, appropriate in a well-defined,
information-theoretic sense even when the noise is non-Gaussian in character.
The analysis described here stands in distinction to ``coincidence
analyses'', wherein the data from each of several detectors is studied in
isolation to produce a list of candidate events, which are then compared to
search for coincidences that might indicate common origin in a gravitational
wave signal. We compare these two analyses --- optimal filtering and
coincidence --- in a series of numerical examples, showing that the optimal
filtering analysis always yields a greater detection efficiency for given false
alarm rate, even when the detector noise is strongly non-Gaussian.Comment: 39 pages, 4 figures, submitted to Phys. Rev.
Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
Assuming that general relativity is the correct theory of gravity in the
strong field limit, can gravitational wave observations distinguish between
black hole and other compact object sources? Alternatively, can gravitational
wave observations provide a test of one of the fundamental predictions of
general relativity? Here we describe a definitive test of the hypothesis that
observations of damped, sinusoidal gravitational waves originated from a black
hole or, alternatively, that nature respects the general relativistic no-hair
theorem. For astrophysical black holes, which have a negligible charge-to-mass
ratio, the black hole quasi-normal mode spectrum is characterized entirely by
the black hole mass and angular momentum and is unique to black holes. In a
different theory of gravity, or if the observed radiation arises from a
different source (e.g., a neutron star, strange matter or boson star), the
spectrum will be inconsistent with that predicted for general relativistic
black holes. We give a statistical characterization of the consistency between
the noisy observation and the theoretical predictions of general relativity,
together with a numerical example.Comment: 19 pages, 7 figure
A Demonstration of LISA Laser Communication
Over the past few years questions have been raised concerning the use of
laser communications links between sciencecraft to transmit phase information
crucial to the reduction of laser frequency noise in the LISA science
measurement. The concern is that applying medium frequency phase modulations to
the laser carrier could compromise the phase stability of the LISA fringe
signal. We have modified the table-top interferometer presented in a previous
article by applying phase modulations to the laser beams in order to evaluate
the effects of such modulations on the LISA science fringe signal. We have
demonstrated that the phase resolution of the science signal is not degraded by
the presence of medium frequency phase modulations.Comment: minor corrections found in the CQG versio
Wetting and Minimal Surfaces
We study minimal surfaces which arise in wetting and capillarity phenomena.
Using conformal coordinates, we reduce the problem to a set of coupled boundary
equations for the contact line of the fluid surface, and then derive simple
diagrammatic rules to calculate the non-linear corrections to the Joanny-de
Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all
geometric length scales of the fluid container decouple from the
short-wavelength deformations of the contact line. This is illustrated by a
calculation of the linearized interaction between contact lines on two opposite
parallel walls. We present a simple algorithm to compute the minimal surface
and its energy based on these ideas. We also point out the intriguing
singularities that arise in the Legendre transformation from the pure Dirichlet
to the mixed Dirichlet-Neumann problem.Comment: 22 page
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
Performance of Newtonian filters in detecting gravitational waves from coalescing binaries
Coalescing binary systems are one of the most promising sources of
gravitational waves. The technique of matched filtering used in the detection
of gravitational waves from coalescing binaries relies on the construction of
accurate templates. Until recently filters modelled on the quadrupole or the
Newtonian approximation were deemed sufficient. Recently it was shown that
post-Newtonian effects contribute to a secular growth in the phase difference
between the actual signal and its corresponding Newtonian template. In this
paper we investigate the possibility of compensating for the phase difference
caused by the post-Newtonian terms by allowing for a shift in the Newtonian
filter parameters. We find that Newtonian filters perform adequately for the
purpose of detecting the presence of the signal for both the initial and the
advanced LIGO detectors.Comment: Revtex 9 pages + 6 figures ( Can be obtained by "anonymous" ftp from
144.16.31.1 in dir /pub/rbs. Submitted to Physical Review D. IUCAA 1
Testing Alternative Theories of Gravity using LISA
We investigate the possible bounds which could be placed on alternative
theories of gravity using gravitational wave detection from inspiralling
compact binaries with the proposed LISA space interferometer. Specifically, we
estimate lower bounds on the coupling parameter \omega of scalar-tensor
theories of the Brans-Dicke type and on the Compton wavelength of the graviton
\lambda_g in hypothetical massive graviton theories. In these theories,
modifications of the gravitational radiation damping formulae or of the
propagation of the waves translate into a change in the phase evolution of the
observed gravitational waveform. We obtain the bounds through the technique of
matched filtering, employing the LISA Sensitivity Curve Generator (SCG),
available online. For a neutron star inspiralling into a 10^3 M_sun black hole
in the Virgo Cluster, in a two-year integration, we find a lower bound \omega >
3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6.
The bound is independent of LISA arm length, but is inversely proportional to
the LISA position noise error. Lower bounds on the graviton Compton wavelength
ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year
observations of massive binary black hole inspirals at cosmological distances
(3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass
systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and
to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent
of these parameters because of the dominance of white-dwarf confusion noise in
the relevant part of the frequency spectrum. These bounds improve and extend
earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit
On the crosscorrelation between Gravitational Wave Detectors for detecting association with Gamma Ray Bursts
Crosscorrelation of the outputs of two Gravitational Wave (GW) detectors has
recently been proposed [1] as a method for detecting statistical association
between GWs and Gamma Ray Bursts (GRBs). Unfortunately, the method can be
effectively used only in the case of stationary noise. In this work a different
crosscorrelation algorithm is presented, which may effectively be applied also
in non-stationary conditions for the cumulative analysis of a large number of
GRBs. The value of the crosscorrelation at zero delay, which is the only one
expected to be correlated to any astrophysical signal, is compared with the
distribution of crosscorrelation of the same data for all non-zero delays
within the integration time interval. This background distribution is gaussian,
so the statistical significance of an experimentally observed excess would be
well-defined.
Computer simulations using real noise data of the cryogenic GW detectors
Explorer and Nautilus with superimposed delta-like signals were performed, to
test the effectiveness of the method, and theoretical estimates of its
sensitivity compared to the results of the simulation. The effectiveness of the
proposed algorithm is compared to that of other cumulative techniques, finding
that the algorithm is particularly effective in the case of non-gaussian noise
and of a large (100-1000s) and unpredictable delay between GWs and GRBs.Comment: 7 pages, 4 figures, 1 table. Submitted by Phys. Rev.
Maximum elastic deformations of relativistic stars
We present a method for calculating the maximum elastic quadrupolar
deformations of relativistic stars, generalizing the previous Newtonian,
Cowling approximation integral given by [G. Ushomirsky et al., Mon. Not. R.
Astron. Soc. 319, 902 (2000)]. (We also present a method for Newtonian gravity
with no Cowling approximation.) We apply these methods to the m = 2 quadrupoles
most relevant for gravitational radiation in three cases: crustal deformations,
deformations of crystalline cores of hadron-quark hybrid stars, and
deformations of entirely crystalline color superconducting quark stars. In all
cases, we find suppressions of the quadrupole due to relativity compared to the
Newtonian Cowling approximation, particularly for compact stars. For the crust
these suppressions are up to a factor ~6, for hybrid stars they are up to ~4,
and for solid quark stars they are at most ~2, with slight enhancements instead
for low mass stars. We also explore ranges of masses and equations of state
more than in previous work, and find that for some parameters the maximum
quadrupoles can still be very large. Even with the relativistic suppressions,
we find that 1.4 solar mass stars can sustain crustal quadrupoles of a few
times 10^39 g cm^2 for the SLy equation of state or close to 10^40 g cm^2 for
equations of state that produce less compact stars. Solid quark stars of 1.4
solar masses can sustain quadrupoles of around 10^44 g cm^2. Hybrid stars
typically do not have solid cores at 1.4 solar masses, but the most massive
ones (~2 solar masses) can sustain quadrupoles of a few times 10^41 g cm^2 for
typical microphysical parameters and a few times 10^42 g cm^2 for extreme ones.
All of these quadrupoles assume a breaking strain of 0.1 and can be divided by
10^45 g cm^2 to yield the fiducial "ellipticities" quoted elsewhere.Comment: 21 pages, 11 figures, version accepted by PRD, including the
corrected maximum hybrid star quadrupoles (from the erratum to the shear
modulus calculation) and the corrected binding energy computatio
- âŠ