Michele's wiki/blog

Authors: Stephon Alexander, Nicolas Yunes

Date: Wed, 28 Mar 2007

Abstract: We study Chern-Simons (CS) gravity in the parameterized post-Newtonian (PPN) framework through weak-field solutions of the modified field equations for a perfect fluid source. We discover that CS gravity possesses the same PPN parameters as general relativity, except for the inclusion of a new term, proportional both to the CS coupling parameter and the curl of the PPN vector potentials. This new term encodes the key physical effect of CS gravity in the weak-field limit, leading to a modification of frame dragging and, thus, the Lense-Thirring contribution to gyroscopic precession. We provide a physical interpretation for the new term, as well as an estimate of the size of this effect relative to the general relativistic Lense-Thirring prediction. This correction to frame dragging might be used in experiments, such as Gravity Probe B and lunar ranging, to place bounds on the CS coupling parameter, as well as other intrinsic parameters of string theory.

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Authors: Massimo Giovannini

Date: Wed, 28 Mar 2007

Abstract: The aim of these lectures is to introduce some basic problems arising in gravitation and modern cosmology. All along the discussion the guiding theme is provided by the phenomenological and theoretical properties of the Cosmic Microwave Background (CMB). These lectures have been prepared for a regular Phd course of the University of Milan-Bicocca.

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Authors: Abraham Loeb (Harvard)

Date: Wed, 28 Mar 2007

Abstract: According to recent general-relativistic simulations, the coalescence of two spinning black holes (BHs) could lead to recoil speeds of the BH remnant of up to thousands of km/s as a result of the emission of gravitational radiation. Such speeds would enable the merger product to escape its host galaxy. Here we examine the circumstances resulting from a gas-rich galaxy merger under which the ejected BH would carry an accretion disk with it and be observable. As the initial BH binary emits gravitational radiation and its orbit tightens, a hole is opened around it in the disk which delays the consumption of gas prior to the eventual BH ejection. The punctured disk remains bound to the ejected BH within the region where the gas orbital velocity is larger than the ejection speed. For a ~10ˆ7 solar mass BH the ejected disk has a characteristic size of tens of thousands of Schwarzschild radii and an accretion lifetime of ~10ˆ7 years. During that time, the ejected BH could traverse a considerable distance and appear as an off-center quasar with a feedback trail along the path it left behind. A small fraction of all quasars could be associated with an escaping BH.

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Authors: J. Clark, I.S. Heng, M. Pitkin, G. Woan

Date: Wed, 28 Mar 2007

Abstract: The excitation of quadrupolar quasi-normal modes in a neutron star leads to the emission of a short, distinctive, burst of gravitational radiation in the form of a decaying sinusoid or ‘ring-down’. We present a Bayesian analysis method which incorporates relevant prior information about the source and known instrumental artifacts to conduct a robust search for the gravitational wave emission associated with pulsar glitches and soft $\gamma$-ray repeater flares. Instrumental transients are modelled as sine-Gaussian and their evidence, or marginal likelihood, is compared with that of Gaussian white noise and ring-downs via the ‘odds-ratio’. Tests using simulated data with a noise spectral density similar to the LIGO interferometer around 1 kHz yield 50% detection efficiency and 1% false alarm probability for ring-down signals with signal-to-noise ratio $\rho=5.5$. For a source at 15 kpc this requires an energy of $2.8\times 10ˆ{-5}M_{\astrosun}cˆ2$ to be emitted as gravitational waves.

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Authors: S. Pireaux (Observatoire de la Cote d'Azur, Department ARTEMIS, Grasse, France)

Date: Fri, 23 Mar 2007

Abstract: The LISA mission is a space interferometer aiming at the detection of gravitational waves in the [$10ˆ{-4}$,$10ˆ{-1}$] Hz frequency band. In order to reach the gravitational wave detection level, a Time Delay Interferometry (TDI) method must be applied to get rid of (most of) the laser frequency noise and optical bench noise. This TDI analysis is carried out in terms of the coordinate time corresponding to the Barycentric Coordinate Reference System (BCRS), TCB, whereas the data at each of the three LISA stations is recorded in terms of each station proper time. We provide here the required proper time versus BCRS time transformation. We show that the difference in rate of station proper time versus TCB is of the order of $5 10ˆ{-8}$. The difference between station proper times and TCB exhibits an oscillatory trend with a maximum amplitude of about $10ˆ{-3}$ s.

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Authors: Silvano Bonazzola (LUTH), Jos{é}-Luis Jaramillo (IAA-CSIC), Jerome Novak (LUTH)

Date: Fri, 23 Mar 2007

Abstract: We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The technique implements a fast spectral matching between two domains in relative rotation: an inner spherical domain, comoving with the sources and lying strictly inside the light cylinder, and an outer inertial spherical shell. Even though the emphasis is placed on spectral techniques, the matching is independent of the specific manner in which equations are solved inside each domain, and can be adapted to different schemes. We illustrate the strategy with some simple but representative examples.

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Authors: Florian Dubath, Jorge V. Rocha

Date: Wed, 21 Mar 2007

Abstract: We consider a population of small, high-velocity cosmic string loops. We assume the typical length of these loops is determined by the gravitational radiation scale and use the results of \cite{Polchinski:2007rg} which pointed out their highly relativistic nature. A study of the gravitational wave emission from such a population is carried out. The large Lorentz boost involved causes the lowest harmonics of the loops to fall within the frequency band of the LIGO detector. Due to this feature the gravitational waves emitted by such loops can be detected in a periodic search rather than in burst or stochastic analysis.
It is shown that, for interesting values of the string tension ($10ˆ{-10}\lsim G\mu\lsim 10ˆ{-8}$) the detector can observe loops at reasonably high redshifts and that detection is, in principle, possible. We compute the number of expected observations produced by such a process. For a 10 hour search we find that this number is of order $O(10ˆ{-4})$. This is a consequence of the low effective number density of the loops traveling along the line of sight. However, small probabilities of reconnection and longer observation times can improve the result.

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Authors: Michele Vallisneri

Date: Thu, 15 Mar 2007

Abstract: The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them.
Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond-Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.

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Authors: The LIGO Scientific Collaboration: B. Abbott, et al

Date: Fri, 9 Mar 2007

Abstract: We searched for an anisotropic background of gravitational waves using data from the LIGO S4 science run and a method that is optimized for point sources. This is appropriate if, for example, the gravitational wave background is dominated by a small number of distinct astrophysical sources. No signal was seen. Upper limit maps were produced assuming two different power laws for the source strain power spectrum. For an fˆ-3 power law and using the 50 Hz to 1.8 kHz band the upper limits on the source strain power spectrum vary between 1.2e-48 Hzˆ-1 (100 Hz/f)ˆ3 and 1.2e-47 Hzˆ-1 (100 Hz /f)ˆ3, depending on the position in the sky. Similarly, in the case of constant strain power spectrum, the upper limits vary between 8.5e-49 Hzˆ-1 and 6.1e-48 Hzˆ-1.
As a side product a limit on an isotropic background of gravitational waves was also obtained. All limits are at the 90% confidence level. Finally, as an application, we focused on the direction of Sco-X1, the closest low-mass X-ray binary. We compare the upper limit on strain amplitude obtained by this method to expectations based on the X-ray luminosity of Sco-X1.

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Authors: Emanuele Berti, Vitor Cardoso, Jose A. Gonzalez, Ulrich Sperhake, Mark Hannam, Sascha Husa, Bernd Bruegmann

Date: Thu, 8 Mar 2007

Abstract: We study the inspiral, merger and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and Post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the Post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the Post-Newtonian series to the numerical results is non-monotonic. To leading order the total energy emitted in the merger phase scales like etaˆ2 and the spin of the final black hole scales like eta, where eta=q/(1+q)ˆ2 is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross-correlating information from different multipoles we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.

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Authors: Mátyás Vasúth, Balázs Mikóczi, László Á. Gergely

Date: Thu, 8 Mar 2007

Abstract: We derive the rate of increase of the orbital frequency up to the second post-Newtonian order for inspiralling compact binaries with spin, mass quadrupole and magnetic dipole moments on eccentric orbits. We give this result in terms of orbital elements.

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Authors: Jonathan R Gair

Date: Tue, 6 Mar 2007

Abstract: The inspirals of compact objects into massive black holes are some of the most exciting of the potential sources of gravitational waves for the planned Laser Interferometer Space Antenna (LISA). Observations of such extreme mass ratio inspirals (EMRIs) will not only reveal to us the properties of black holes in the Universe, but will allow us to verify that the space-time structure around massive compact objects agrees with the predictions of relativity. Detection of EMRI signals via matched filtering and interpretation of the observations will require models of the gravitational waveforms. The extreme mass ratio allows accurate waveforms to be computed from black hole perturbation theory, but this is computationally expensive and has not yet been fully developed. Ongoing research to scope out LISA data analysis algorithms requires waveforms that can be generated quickly in large numbers. To fulfil this purpose, families of approximate, "kludge", EMRI waveforms have been developed that capture the main features of true EMRI waveforms, but that can also be generated for a comparatively small computational cost. In this proceedings article, we briefly outline one such waveform family (the "numerical kludge"), its accuracy and some possible ways in which it might be improved in the future. Although accurate parameter extraction will require use of perturbative waveforms, these approximate waveforms are sufficiently faithful to the true waveforms that they may be able to play a role in detection of EMRIs in the LISA data.

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Authors: Eric Gourgoulhon (LUTH, CNRS / Observatoire de Paris)

Date: Tue, 6 Mar 2007

Abstract: These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.

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Authors: Jonathan R Gair, Gareth Jones

Date: Tue, 6 Mar 2007

Abstract: The planned Laser Interferometer Space Antenna (LISA) will detect gravitational wave signals from a wide range of sources. However, disentangling individual signals from the source-dominated data stream is a challenging problem and the focus of much current research. The problems are particularly acute for detection of extreme mass ratio inspirals (EMRIs), for which the instantaneous signal amplitude is an order of magnitude below the level of the instrumental noise, and the parameter space of possible signals is too large to permit fully-coherent matched filtering. One possible approach is to attempt to identify sources in a time-frequency spectrogram of the LISA data. This is a computationally cheap method that may be useful as a first stage in a hierarchical analysis. Initial results, evaluated using a significantly simplified model of the LISA data stream, suggest that time-frequency techniques might be able to detect the nearest few tens of EMRI events. In this proceedings article, we briefly outline the methods that have so far been applied to the problem, initial results and possible future directions for the research.

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Authors: Luc Blanchet, L P Grishchuk, Gerhard Schaefer

Date: Tue, 6 Mar 2007

Abstract: This is an extended summary of the two parallel sessions held at MG11: PPN1 ‘Strong Gravity and Binaries’ (chaired by L.B. and L.G.) and PPN2 ‘Post-Newtonian Dynamics in Binary Objects’ (chaired by G.S.). The aims and contents of these sessions were close to each other and overlapping. It is natural to review both sessions in one joint contribution to the MG11 Proceedings. The summary places the delivered talks in a broader perspective of current studies in this area. One can find more details in individual contributions of the respective authors.

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Authors: Pranesh A. Sundararajan, Gaurav Khanna, Scott A. Hughes

Date: Mon, 5 Mar 2007

Abstract: We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.

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Authors: Chao Li, Geoffrey Lovelace

Date: Wed, 28 Feb 2007

Abstract: Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs)--binaries in which a stellar-mass object spirals into a massive black hole or other massive, compact body--are important sources of gravitational waves for LISA and LIGO, respectively. Thorne has speculated that the waves from EMRIs and IMRIs encode, in principle, all the details of (i) the central body's spacetime geometry (metric), (ii) the tidal coupling (energy and angular momentum exchange) between the central body and orbiting object, and (iii) the evolving orbital elements. Fintan Ryan has given a first partial proof that this speculation is correct: Restricting himself to nearly circular, nearly equatorial orbits and ignoring tidal coupling, Ryan proved that the central body's metric is encoded in the waves. In this paper we generalize Ryan's theorem. Retaining Ryan's restriction to nearly circular and nearly equatorial orbits, and dropping the assumption of no tidal coupling, we prove that Thorne's conjecture is nearly fully correct: the waves encode not only the central body's metric but also the evolving orbital elements and (in a sense slightly different from Thorne's conjecture) the evolving tidal coupling.

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