Michele's wiki/blog

Authors: Christian Röver, Renate Meyer, Nelson Christensen

Date: Thu, 28 Sep 2006

Abstract: 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.

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Authors: F. Cavalier (LAL), M. Barsuglia (LAL), M.-A. Bizouard (LAL), V. Brisson (LAL), A.-C. Clapson (LAL), M. Davier (LAL), P. Hello (LAL), S. Kreckelbergh (LAL), N. Leroy (LAL), M. Varvella (LAL)

Date: Tue, 26 Sep 2006

Abstract: This paper deals with the reconstruction of the direction of a gravitational wave source using the detection made by a network of interferometric detectors, mainly the LIGO and Virgo detectors. We suppose that an event has been seen in coincidence using a filter applied on the three detector data streams. Using the arrival time (and its associated error) of the gravitational signal in each detector, the direction of the source in the sky is computed using a chiˆ2 minimization technique. For reasonably large signals (SNR>4.5 in all detectors), the mean angular error between the real location and the reconstructed one is about 1 degree. We also investigate the effect of the network geometry assuming the same angular response for all interferometric detectors. It appears that the reconstruction quality is not uniform over the sky and is degraded when the source approaches the plane defined by the three detectors. Adding at least one other detector to the LIGO-Virgo network reduces the blind regions and in the case of 6 detectors, a precision less than 1 degree on the source direction can be reached for 99% of the sky.

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Authors: Murray Gell-Mann (Santa Fe Institute), James Hartle (University of California Santa Barbara)

Date: Mon, 25 Sep 2006

Abstract: Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no non-trivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact: Quantum theory allows for various coarse-grained descriptions some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of ‘quasiclassical descriptions’ defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a ‘quasiclassical realm’ this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.

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Authors: Amber L. Stuver, Lee Samuel Finn

Date: Sun, 24 Sep 2006

Abstract: Physically motivated gravitational wave signals are needed in order to study the behaviour and efficacy of different data analysis methods seeking their detection. GravEn, short for Gravitational-wave Engine, is a MATLAB software package that simulates the sampled response of a gravitational wave detector to incident gravitational waves. Incident waves can be specified in a data file or chosen from among a group of pre-programmed types commonly used for establishing the detection efficiency of analysis methods used for LIGO data analysis. Every aspect of a desired signal can be specified, such as start time of the simulation (including inter-sample start times), wave amplitude, source orientation to line of sight, location of the source in the sky, etc. Supported interferometric detectors include LIGO, GEO, Virgo and TAMA.

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Authors: Theocharis A. Apostolatos, Thomas P. Sotiriou

Date: Thu, 21 Sep 2006

Abstract: The electrovacuum around a rotating massive body with electric charge density is described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). A small uncharged test particle orbiting around such a body moves on geodesics if gravitational radiation is ignored. The waves emitted by the small body carry information about the geometry of the central object, and hence, in principle, we can infer all its multipole moments. Due to its axisymmetry the source is characterized now by four families of scalar multipole moments: its mass moments $M_l$, its mass-current moments $S_l$, its electrical moments $E_l$ and its magnetic moments $H_l$, where $l=0,1,2,…$. Four measurable quantities, the energy emitted by gravitational waves per logarithmic interval of frequency, the precession of the periastron (assuming almost circular orbits), the precession of the orbital plane (assuming almost equatorial orbits), and the number of cycles emitted per logarithmic interval of frequency, are presented as power series of the newtonian orbital velocity of the test body. The power series coefficients are simple polynomials of the various moments.

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Authors: Naoki Seto

Date: Mon, 18 Sep 2006

Abstract: We discussed prospects for directly detecting circular polarization signal of gravitational wave background. We found it is generally difficult to probe the monopole mode of the signal due to broad directivity of gravitational wave detectors. But the dipole (l=1) and octupole (l=3) modes of the signal can be measured in a simple manner by combining outputs of two unaligned detectors, and we can dig them deeply under confusion and detector noises. Around f~0.1mHz LISA will provide ideal data streams to detect these anisotropic components whose magnitudes are as small as ~1 percent of the detector noise level in terms of the non-dimensional energy density \Omega_{GW}(f).

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Authors: Luca Baiotti, Roberto De Pietri, Gian Mario Manca, Luciano Rezzolla

Date: Mon, 18 Sep 2006

Abstract: We present accurate simulations of the dynamical barmode instability in full General Relativity focussing on two aspects which have not been investigated in detail in the past. Namely, on the persistence of the bar deformation once the instability has reached its saturation and on the precise determination of the threshold for the onset of the instability in terms of the parameter $\beta={T}/{|W|}$. We find that generic nonlinear mode-coupling effects appear during the development of the instability and these can severely limit the persistence of the bar deformation and eventually suppress the instability. In addition, we observe the dynamics of the instability to be strongly influenced by the value $\beta$ and on its separation from the critical value $\beta_c$ marking the onset of the instability. We discuss the impact these results have on the detection of gravitational waves from this process and provide evidence that the classical perturbative analysis of the barmode instability for Newtonian and incompressible Maclaurin spheroids remains qualitatively valid and accurate also in full General Relativity.

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Authors: Keisuke Taniguchi, Thomas W. Baumgarte, Joshua A. Faber, Stuart L. Shapiro

Date: Fri, 15 Sep 2006

Abstract: We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics, and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere (the apparent horizon). In this paper we focus on irrotational configurations, meaning that both the neutron star and the black hole are approximately nonspinning in an inertial frame. We present results for a binary with polytropic index n=1, mass ratio M_{irr}ˆ{BH}/M_{B}ˆ{NS}=5 and neutron star compaction M_{ADM,0}ˆ{NS}/R_0=0.0879, where M_{irr}ˆ{BH} is the irreducible mass of the black hole, M_{B}ˆ{NS} the neutron star baryon rest-mass, and M_{ADM,0}ˆ{NS} and R_0 the neutron star Arnowitt-Deser-Misner mass and areal radius in isolation, respectively. Our models represent valid solutions to Einstein's constraint equations and may therefore be employed as initial data for dynamical simulations of black hole-neutron star binaries.

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Authors: David Garfinkle (Editor)

Date: Wed, 13 Sep 2006

Abstract: Research Briefs:
Singularity Avoidance in Canonical Quantum Gravity, by Viqar Husain
What's New in LIGO, by David Shoemaker
Conference reports:
Scanning New Horizons: GR Beyond 4 dimensions, by Donald Marolf
Quantum Gravity in the Americas III, by Jorge Pullin
New Frontiers in Numerical Relativity, by Luciano Rezzolla
Teaching General Relativity to Undergraduates, by Greg Comer
Ninth Capra Meeting on Radiation Reaction, by Lior Burko

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Authors: Carlos F. Sopuerta (Penn State)

Date: Fri, 8 Sep 2006

Abstract: This is a brief report on time-domain numerical simulations of extreme-mass-ratio binaries based on finite element methods. We discuss a new technique for solving the perturbative equations describing a point-like object orbiting a non-rotating massive black hole and the prospects of using it for the evaluation of the gravitational self-force responsible of the inspiral of these binary systems. We also discuss the perspectives of transferring this technology to the more astrophysically relevant case of a central rotating massive black hole.

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Authors: Joan M. Centrella

Date: Wed, 6 Sep 2006

Abstract: A remarkable series of breakthroughs in numerical relativity modeling of black hole binary mergers has occurred over the past few years. This paper provides a general overview of these exciting developments, focusing on recent progress in merger simulations and calculations of the resulting gravitational waveforms.

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Authors: Scott A. Hughes

Date: Thu, 7 Sep 2006

Abstract: LISA is a planned space-based gravitational-wave (GW) detector that would be sensitive to waves from low-frequency sources, in the band of roughly $(0.03 - 0.1) {\rm mHz} \lesssim f \lesssim 0.1 {\rm Hz}$. This is expected to be an extremely rich chunk of the GW spectrum -- observing these waves will provide a unique view of dynamical processes in astrophysics. Here we give a quick survey of some key LISA sources and what GWs can uniquely teach us about these sources. Particularly noteworthy science which is highlighted here is the potential for LISA to track the moderate to high redshift evolution of black hole masses and spins through the measurement of GWs generated from massive black hole binaries (which in turn form by the merger of galaxies and protogalaxies). Measurement of these binary black hole waves has the potential to determine the masses and spins of the constituent black holes with percent-level accuracy or better, providing a unique high-precision probe of an aspect of early structure growth. This article is based on the ‘Astrophysics Tutorial’ talk given by the author at the Sixth International LISA Symposium.

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Authors: Fernando de Felice, Alberto Vecchiato, Maria Teresa Crosta, Mario G. Lattanzi, Beatrice Bucciarelli

Date: Mon, 4 Sep 2006

Abstract: Modern astrometry is based on angular measurements at the micro-arcsecond level. At this accuracy a fully general relativistic treatment of the data reduction is required. This paper concludes a series of articles dedicated to the problem of relativistic light propagation, presenting the final microarcsecond version of a relativistic astrometric model which enable us to trace back the light path to its emitting source throughout the non-stationary gravity field of the moving bodies in the Solar System. The previous model is used as test-bed for numerical comparisons to the present one. Here we also test different versions of the computer code implementing the model at different levels of complexity to start exploring the best trade-off between numerical efficiency and the micro-arcsecond accuracy needed to be reached.

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Authors: Philippe Grandclement (LUTH)

Date: Wed, 6 Sep 2006

Abstract: This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical foundation of the spectral approximation is first introduced, based on the Gauss quadratures. The two usual basis of Legendre and Chebyshev polynomials are then presented. The next section is devoted to one dimensional equation solvers using only one domain. Three different methods are described. Techniques using several domains are shown in the last section of this paper and their various merits discussed.

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Authors: Edward K. Porter

Date: Tue, 5 Sep 2006

Abstract: In this work we examine the Cauchy convergence of both post-Newtonian (T-approximant) and re-summed post-Newtonian (P-approximant) templates for the case of a test-mass orbiting a Kerr black hole along a circular equatorial orbit. The Cauchy criterion demands that the inner product between the $n$ and $n+1$ order approximation approaches unity, as we increase the order of approximation. In previous works, it has been shown that we achieve greater fitting factors and better parameter estimation using the P-approximant templates for both Schwarzschild and Kerr black holes. In this work, we show that the P-approximant templates also display a faster Cauchy convergence making them a superior template to the standard post-Newtonian templates.

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Authors: Edward K. Porter

Date: Tue, 5 Sep 2006

Abstract: We introduce a new method for modelling the gravitational wave flux function of a test-mass particle inspiralling into an intermediate mass Schwarzschild black hole which is based on Chebyshev polynomials of the first kind. It is believed that these Intermediate Mass Ratio Inspiral events (IMRI) are expected to be seen in both the ground and space based detectors. Starting with the post-Newtonian expansion from Black Hole Perturbation Theory, we introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a model with faster convergence than either post-Newtonian or Padé based methods. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. We find that at the last stable orbit, the error between the Chebyshev approximation and a numerically calculated flux is reduced, $< 1.8%$, at all orders of approximation. We also find that the templates constructed using the Chebyshev approximation give better fitting factors, in general $> 0.99$, and smaller errors, $< 1/10%$, in the estimation of the Chirp mass when compared to a fiducial exact waveform, constructed using the numerical flux and the exact expression for the orbital energy function, again at all orders of approximation. We also show that in the intermediate test-mass case, the new Chebyshev template is superior to both PN and Padé approximant templates, especially at lower orders of approximation.

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Authors: Alexander Stroeer, Jonathan Gair, Alberto Vecchio

Date: Mon, 4 Sep 2006

Abstract: We demonstrate the use of automatic Bayesian inference for the analysis of LISA data sets. In particular we describe a new automatic Reversible Jump Markov Chain Monte Carlo method to evaluate the posterior probability density functions of the a priori unknown number of parameters that describe the gravitational wave signals present in the data. We apply the algorithm to a simulated LISA data set containing overlapping signals from white dwarf binary systems (DWD) and to a separate data set containing a signal from an extreme mass ratio inspiral (EMRI). We demonstrate that the approach works well in both cases and can be regarded as a viable approach to tackle LISA data analysis challenges.

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Authors: Archana Pai

Date: Thu, 31 Aug 2006

Abstract: We revisit the directionally optimal data streams of LISA first introduced in Nayak etal. It was shown that by using appropriate choice of Time delay interferometric (TDI) combinations, a monochromatic fixed source in the barycentric frame can be optimally tracked in the LISA frame. In this work, we study the beaming properties of these optimal streams. We show that all the three streams V+, Vx and Vo with maximum, minimum and zero directional SNR respectively are highly beamed. We study in detail the frequency dependence of the beaming.

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Authors: Scott A. Hughes

Date: Thu, 31 Aug 2006

Abstract: The inspirals of ‘small’ ($1 - 100 M_\odot$) compact bodies through highly relativistic orbits of massive (several $\times 10ˆ5 M_\odot -$ several $\times 10ˆ6 M_\odot$) black holes are among the most anticipated sources for the LISA gravitational-wave antenna. The measurement of these waves is expected to map the spacetime of the larger body with high precision, allowing us to test in detail the hypothesis that black hole candidates are described by the Kerr metric of general relativity. In this article, we will briefly describe how these sources can be used to perform such a test. These proposed measurements are often described as ‘testing relativity’. This description is at best somewhat glib: Because -- at least to date -- all work related to these measurements assumes general relativity as the theoretical framework in which these tests are performed, the measurements cannot be said to ‘test relativity’ in a fundamental way. More accurately, they test the {\it nature of massive compact bodies within general relativity}. A surprising result for such a test could point to deviations from general relativity, and would provide an experimentally motivated direction in which to pursue tests of gravity theories beyond GR.

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