2,364 research outputs found
Equation of motion for relativistic compact binaries with the strong field point particle limit : the second and half post-Newtonian order
We study the equation of motion appropriate to an inspiralling binary star
system whose constituent stars have strong internal gravity. We use the
post-Newtonian approximation with the strong field point particle limit by
which we can introduce into general relativity a notion of a point-like
particle with strong internal gravity without using Dirac delta distribution.
Besides this limit, to deal with strong internal gravity we express the
equation of motion in surface integral forms and calculate these integrals
explicitly. As a result we obtain the equation of motion for a binary of
compact bodies accurate through the second and half post-Newtonian (2.5 PN)
order. This equation is derived in the harmonic coordinate. Our resulting
equation perfectly agrees with Damour and Deruelle 2.5 PN equation of motion.
Hence it is found that the 2.5 PN equation of motion is applicable to a
relativistic compact binary.Comment: 48 pages, revtex, accepted for publication in Phys. Rev.
Rates of convergence for empirical spectral measures: a soft approach
Understanding the limiting behavior of eigenvalues of random matrices is the
central problem of random matrix theory. Classical limit results are known for
many models, and there has been significant recent progress in obtaining more
quantitative, non-asymptotic results. In this paper, we describe a systematic
approach to bounding rates of convergence and proving tail inequalities for the
empirical spectral measures of a wide variety of random matrix ensembles. We
illustrate the approach by proving asymptotically almost sure rates of
convergence of the empirical spectral measure in the following ensembles:
Wigner matrices, Wishart matrices, Haar-distributed matrices from the compact
classical groups, powers of Haar matrices, randomized sums and random
compressions of Hermitian matrices, a random matrix model for the Hamiltonians
of quantum spin glasses, and finally the complex Ginibre ensemble. Many of the
results appeared previously and are being collected and described here as
illustrations of the general method; however, some details (particularly in the
Wigner and Wishart cases) are new.
Our approach makes use of techniques from probability in Banach spaces, in
particular concentration of measure and bounds for suprema of stochastic
processes, in combination with more classical tools from matrix analysis,
approximation theory, and Fourier analysis. It is highly flexible, as evidenced
by the broad list of examples. It is moreover based largely on "soft" methods,
and involves little hard analysis
GMRT detection of HI 21 cm associated absorption towards the z=1.2 red quasar 3C 190
We report the GMRT detection of associated HI 21 cm-line absorption in the
z=1.1946 red quasar 3C 190. Most of the absorption is blue-shifted with respect
to the systemic redshift. The absorption, at 647.7 MHz, is broad and
complex, spanning a velocity width of 600 \kms. Since the core is
self-absorbed at this frequency, the absorption is most likely towards the
hotspots. Comparison of the radio and deep optical images reveal linear
filaments in the optical which overlap with the brighter radio jet towards the
south-west. We therefore suggest that most of the HI 21 cm-line absorption
could be occurring in the atomic gas shocked by the south-west jet.Comment: 8 pages, 1 fugure. To appear in Journal of Astrophysics and Astronom
Gravitational waves from merging compact binaries
Largely motivated by the development of highly sensitive gravitational-wave
detectors, our understanding of merging compact binaries and the gravitational
waves they generate has improved dramatically in recent years. Breakthroughs in
numerical relativity now allow us to model the coalescence of two black holes
with no approximations or simplifications. There has also been outstanding
progress in our analytical understanding of binaries. We review these
developments, examining merging binaries using black hole perturbation theory,
post-Newtonian expansions, and direct numerical integration of the field
equations. We summarize these approaches and what they have taught us about
gravitational waves from compact binaries. We place these results in the
context of gravitational-wave generating systems, analyzing the impact
gravitational wave emission has on their sources, as well as what we can learn
about them from direct gravitational-wave measurements.Comment: 90 pages, 12 figures. Invited review to appear in Annual Reviews of
Astronomy and Astrophysics. Further minor tweaks in response to reader
feedbac
Coherent Bayesian inference on compact binary inspirals using a network of interferometric gravitational wave detectors
Presented in this paper is a Markov chain Monte Carlo (MCMC) routine for
conducting coherent parameter estimation for interferometric gravitational wave
observations of an inspiral of binary compact objects using data from multiple
detectors. The MCMC technique uses data from several interferometers and infers
all nine of the parameters (ignoring spin) associated with the binary system,
including the distance to the source, the masses, and the location on the sky.
The Metropolis-algorithm utilises advanced MCMC techniques, such as importance
resampling and parallel tempering. The data is compared with time-domain
inspiral templates that are 2.5 post-Newtonian (PN) in phase and 2.0 PN in
amplitude. Our routine could be implemented as part of an inspiral detection
pipeline for a world wide network of detectors. Examples are given for
simulated signals and data as seen by the LIGO and Virgo detectors operating at
their design sensitivity.Comment: 10 pages, 4 figure
Indium joints for cryogenic gravitational wave detectors
A viable technique for the preparation of highly thermal conductive joints between sapphire components in gravitational wave detectors is presented. The mechanical loss of such a joint was determined to be as low as 2 Ă 10â3 at 20 K and 2 Ă 10â2 at 300 K. The thermal noise performance of a typical joint is compared to the requirements of the Japanese gravitational wave detector, KAGRA. It is shown that using such an indium joint in the suspension system allows it to operate with low thermal noise. Additionally, results on the maximum amount of heat which can be extracted via indium joints are presented. It is found that sapphire parts, joined by means of indium, are able to remove the residual heat load in the mirrors of KAGRA
Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests
We present our first successful numerical results of 3D general relativistic
simulations in which the Einstein equation as well as the hydrodynamic
equations are fully solved. This paper is especially devoted to simulations of
test problems such as spherical dust collapse, stability test of perturbed
spherical stars, and preservation of (approximate) equilibrium states of
rapidly rotating neutron star and/or corotating binary neutron stars. These
test simulations confirm that simulations of coalescing binary neutron stars
are feasible in a numerical relativity code. It is illustrated that using our
numerical code, simulations of these problems, in particular those of
corotating binary neutron stars, can be performed stably and fairly accurately
for a couple of dynamical timescales. These numerical results indicate that our
formulation for solving the Einstein field equation and hydrodynamic equations
are robust and make it possible to perform a realistic simulation of coalescing
binary neutron stars for a long time from the innermost circular orbit up to
formation of a black hole or neutron star.Comment: 36 pages, to be published in PRD 15, erase unnecessary figure
Computational Resources to Filter Gravitational Wave Data with P-approximant Templates
The prior knowledge of the gravitational waveform from compact binary systems
makes matched filtering an attractive detection strategy. This detection method
involves the filtering of the detector output with a set of theoretical
waveforms or templates. One of the most important factors in this strategy is
knowing how many templates are needed in order to reduce the loss of possible
signals. In this study we calculate the number of templates and computational
power needed for a one-step search for gravitational waves from inspiralling
binary systems. We build on previous works by firstly expanding the
post-Newtonian waveforms to 2.5-PN order and secondly, for the first time,
calculating the number of templates needed when using P-approximant waveforms.
The analysis is carried out for the four main first-generation interferometers,
LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the
computational cost of generating banks of templates for filtering GW data. We
carry out the calculations for two initial conditions. In the first case we
assume a minimum individual mass of and in the second, we assume
a minimum individual mass of . We find that, in general, we need
more P-approximant templates to carry out a search than if we use standard PN
templates. This increase varies according to the order of PN-approximation, but
can be as high as a factor of 3 and is explained by the smaller span of the
P-approximant templates as we go to higher masses. The promising outcome is
that for 2-PN templates the increase is small and is outweighed by the known
robustness of the 2-PN P-approximant templates.Comment: 17 pages, 8 figures, Submitted to Class.Quant.Gra
A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity
We propose a new numerical method to compute quasi-equilibrium sequences of
general relativistic irrotational binary neutron star systems. It is a good
approximation to assume that (1) the binary star system is irrotational, i.e.
the vorticity of the flow field inside component stars vanishes everywhere
(irrotational flow), and (2) the binary star system is in quasi-equilibrium,
for an inspiraling binary neutron star system just before the coalescence as a
result of gravitational wave emission. We can introduce the velocity potential
for such an irrotational flow field, which satisfies an elliptic partial
differential equation (PDE) with a Neumann type boundary condition at the
stellar surface. For a treatment of general relativistic gravity, we use the
Wilson--Mathews formulation, which assumes conformal flatness for spatial
components of metric. In this formulation, the basic equations are expressed by
a system of elliptic PDEs. We have developed a method to solve these PDEs with
appropriate boundary conditions. The method is based on the established
prescription for computing equilibrium states of rapidly rotating axisymmetric
neutron stars or Newtonian binary systems. We have checked the reliability of
our new code by comparing our results with those of other computations
available. We have also performed several convergence tests. By using this
code, we have obtained quasi-equilibrium sequences of irrotational binary star
systems with strong gravity as models for final states of real evolution of
binary neutron star systems just before coalescence. Analysis of our
quasi-equilibrium sequences of binary star systems shows that the systems may
not suffer from dynamical instability of the orbital motion and that the
maximum density does not increase as the binary separation decreases.Comment: 20 pages, 18 figures, more results of convergence tests are added,
revised version accepted for publication in PR
Gravitational wave astronomy
The first decade of the new millenium should see the first direct detections
of gravitational waves. This will be a milestone for fundamental physics and it
will open the new observational science of gravitational wave astronomy. But
gravitational waves already play an important role in the modeling of
astrophysical systems. I review here the present state of gravitational
radiation theory in relativity and astrophysics, and I then look at the
development of detector sensitivity over the next decade, both on the ground
(such as LIGO) and in space (LISA). I review the sources of gravitational waves
that are likely to play an important role in observations by first- and
second-generation interferometers, including the astrophysical information that
will come from these observations. The review covers some 10 decades of
gravitational wave frequency, from the high-frequency normal modes of neutron
stars down to the lowest frequencies observable from space. The discussion of
sources includes recent developments regarding binary black holes, spinning
neutron stars, and the stochastic background.Comment: 29 pages, 2 figures, as submitted for special millenium issue of
Classical and Quantum Gravit
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