Bangalore Suryanarayana Sathyaprakash

Physics, astrophysics and cosmology with gravitational waves.

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Gravitational wave astronomy: In Anticipation of first sources to be detected

The first generation of long-baseline laser interferometric detectors of gravitational waves will start collecting data in 2001-2003. We carefully analyse their planned performance and compare it with the expected strengths of astrophysical sources. The scientific importance of the anticipated discovery of various gravitatinal wave signals and the reliability of theoretical predictions are taken into account in our analysis. We try to be conservative both in evaluating the theoretical uncertainties about a source and the prospects of its detection. After having considered many possible sources, we place our emphasis on (1) inspiraling binaries consisting of stellar mass black holes and (2) relic gravitational waves. We draw the conclusion that inspiraling binary black holes are likely to be detected first by the initial ground-based interferometers. We estimate that the initial interferometers will see 2-3 events per year from black hole binaries with component masses 10-15M_odot, with a signal-to-noise ratio of around 2-3, in each of a network of detectors consisting of GEO, VIRGO and the two LIGOs. It appears that other possible sources, including coalescing neutron stars, are unlikely to be detected by the initial instruments. We also argue that relic gravitational waves may be discovered by the space-based interferometers in the frequency interval 2x10^{-3}-10^{-2} Hz, at the signal-to-noise ratio level around 3.

Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors

The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v{sup 8}), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion, as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN waveform families in the context of initial and advanced gravitational-wave detectors. The waveforms employed in our analysis are those that are currently used by Initial LIGO/Virgo, that is, the time-domain PN models TaylorT1, TaylorT2, TaylorT3, the Fourier-domain representation TaylorF2 (or stationary phase approximant), and the effective-one-body model, and two more recent models, TaylorT4 and TaylorEt. For these models we examine their overlaps with one another for a number of different binaries at 2PN, 3PN, and 3.5PN orders to quantify their differences. We then study the overlaps of these families with the prototype effective-one-body family, currently used by Initial LIGO, calibrated to numerical-relativity simulations to help usmorexa0» decide whether there exist preferred families, in terms of detectability and computational cost, that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit M{sub crit}, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of M{sub crit} is found to be {approx}12M{sub {center_dot}} for Initial, Enhanced, and Advanced LIGO. From a purely computational point of view, we recommend that 3.5PN TaylorF2 be used below M{sub crit} and that the effective-one-body model calibrated to numerical-relativity simulations be used for total binary mass M>M{sub crit}.«xa0less

Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

Measuring the geometry and topology of large-scale structure using SURFGEN: methodology and preliminary results

Observations of the universe reveal that matter within it clusters on a variety of scales. On scales between 10 - 100 Mpc, the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions – voids. This paper, the first in a series, presents a new ansatz which can successfully be used to determine the morphological properties of the supercluster-void network. The ansatz is based on a surface modelling scheme (SURFGEN), developed explicitly for the purpose, which generates a triangulated surface from a discrete data set representing (say) the distribution of galaxies in real (or redshift) space. The triangulated surface describes, at progressively lower density thresholds, clusters of galaxies, superclusters of galaxies and voids. Four Minkowski functionals (MFs) – surface area, volume, extrinsic curvature and genus – describe the geometry and topology of the supercluster-void network. On a discretised and closed triangulated surface the MFs are determined using SURFGEN. Ratio’s of the Minkowski functionals provide us with an excellent diagnostic of three dimensional shapes of clusters, superclusters and voids. Minkowski functionals can be studied at different levels of the density contrast and therefore probe the morphology of large scale structure on a variety of length scales. Our method for determining the Minkowski functionals of a triangulated iso-density surface is tested against both simply and multiply connected eikonal surfaces such as triaxial ellipsoids and tori. The performance of our code is thereby evaluated using density distributions which are pancake-like, filamentary, ribbon-like and spherical. Remarkably, the first three Minkowski functionals are computed to better than 1% accuracy while the fourth (genus) is known exactly. SURFGEN also gives very accurate results when applied to Gaussian random fields. We apply SURFGEN to study morphology in three cosmological models, �CDM, �CDM and SCDM, at the present epoch. Geometrical properties of the supercluster-void network are found to be sensitive to the underlying

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M(circle dot). The choice of the lower frequency cutoff is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

Searching for gravitational waves from binary coalescence

We describe the implementation of a search for gravitational waves from compact binary coalescences in LIGO and Virgo data. This all-sky, all-time, multidetector search for binary coalescence has been used to search data taken in recent LIGO and Virgo runs. The search is built around a matched filter analysis of the data, augmented by numerous signal consistency tests designed to distinguish artifacts of non-Gaussian detector noise from potential detections. We demonstrate the search performance using Gaussian noise and data from the fifth LIGO science run and demonstrate that the signal consistency tests are capable of mitigating the effect of non-Gaussian noise and providing a sensitivity comparable to that achieved in Gaussian noise.

Gravitational wave data analysis

Table of Contensts.- 1: Sources of Gravitational Radiation.- Sources of Gravitational Radiation.- The Rate of Gravitational Collapse in the MilKy Way.- Gravitational Radiation from Rotating Stellar Core Collapse.- ReMarks on SN 1987a.- Coalescing Binaries to Post-Newtonian Order.- 2: Principles of Signal Processing.- A Review of the Statistical Theory of Signal Detection.- Radio Pulsar Search Techniques.- Sample Covariance Techniques in the Detection of Gravitational Waves.- 3: Quantum Limits on Detectors.- Parametric Transducers and Quantum Nondemolition in Bar Detectors.- Squeezed States of Light.- 4: Methods of Data Analysis in Gravitational Wave Detectors.- Round Table Discussion - Gravitational Wave Detectors.- Spacecraft Gravitational Wave Experiments.- Gravitational Wave Experiments with Resonant Antennas.- Gravitational Antenna Bandwidths and Cross Sections.- Comparison of Bars and Interferometers: Detection of Transient Gravitational Radiation.- Broadband Search Techniques for Periodic Sources of Gravitational Radiation.- Response of Michelson Interferometers to Linearly Polarized Gravitational Waves of Arbitrary Direction of Propagation.- Data Analysis as a Noise Diagnostic: Looking for Transients in Interferometers.- Data Acquisition and Analysis with the Glasgow Prototype Detector.- On the Analysis of Gravitational Wave Data.- GRAVNET, Multiple Antenna Coincidences and Antenna Patterns for Resonant Bar Antennas.- Coincidence Probabilities for networks of Laser Interferometric Detectors Observing Coalescing Compact Binaries.- Data Analysis Requirements of Networks of Detectors.- Round-Table on Data Exchange.

Evidence for Filamentarity in the Las Campanas Redshift Survey

We apply Shape—nders, statistical measures of ii shape ˇˇ constructed from two-dimensional partial Minkowski functionals, to study the degree of —lamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski functionals characterize the morphology of an object; these are its perimeter (L ), area (S), and genus. Out of L and S a single dimensionless Shape—nder sta- tistic, F, can be constructed (0 F 1). The statistic F acquires extreme values on a circle (F 0) and a —lament (F 1). Using F, we quantify the extent of —lamentarity in the LCRS by comparing our results with a Poisson distribution having similar geometrical properties and the same selection function as the survey. Our results unambiguously demonstrate that the LCRS displays a high degree of —lamen- tarity in both the northern and southern Galactic sections, in general agreement with the visual appear- ance of the catalog. It is well known that gravitational clustering from Gaussian initial conditions gives rise to the development of non-Gaussianity, re—ected in the formation of a network-like —lamentary structure on supercluster scales. Consequently, the fact that the smoothed LCRS catalog shows proper- ties consistent with those of a Gaussian random —eld,whereas the unsmoothed catalog demonstrates the presence of —lamentarity, lends strong support to the conjecture that the large-scale clustering of galaxies is driven by gravitational instability. Subject headings: galaxies: clusters: generallarge-scale structure of universemethods: statistical ¨ surveys