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Results are presented from high-precision computations of the orbital evolution and emitted gravitational waves for a stellar-mass object spiraling into a massive black hole in a slowly shrinking, circular, equatorial orbit. The focus of these computations is inspiral near the innermost stable circular orbit (isco)---more particularly, on orbits for which the angular velocity Omega is 0.03 < Omega/Omega_{isco} < 1. The computations are based on the Teukolsky-Sasaki-Nakamura formalism, and the results are tabulated in a set of functions that are of order unity and represent relativistic corrections to low-orbital-velocity formulas. These tables can form a foundation for future design studies for the LISA space-based gravitational-wave mission. A first survey of applications to LISA is presented: Signal to noise ratios S/N are computed and graphed as functions of the time-evolving gravitational-wave frequency for representative values of the hole's mass M and spin a and the inspiraling object's mass \mu, with the distance to Earth chosen to be r_o = 1 Gpc. These S/N's show a very strong dependence on the black-hole spin, as well as on M and \mu. A comparison with predicted event rates shows strong promise for detecting these waves, but not beyond about 1Gpc if the inspiraling object is a white dwarf or neutron star. This argues for a modest lowering of LISA's noise floor. A brief discussion is given of the prospects for extracting information from the observed waves, Comment: Physical Review D, in press; 21 pages, 9 figures, 10 tables it is present in the RevTeX file

We describe the design of a Kalman filter that identifies suspension violin modes in an interferometric gravitational wave detectors data channel. We demonstrate the filter's effectiveness by applying it to data taken on the LIGO~40M prototype., Comment: 7 pages, 2 embedded figures. To appear in proceedings of the Third Edoardo Amaldi Conference

Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an elliptic partial differential equation) for a black hole spacetime with angular momentum and for a black hole spacetime superposed with gravitational radiation. In PSC, an approximate solution, generally expressed as a sum over a set of orthogonal basis functions (e.g., Chebyshev polynomials), is substituted into the exact system of equations and the residual minimized. For systems with analytic solutions the approximate solutions converge upon the exact solution exponentially as the number of basis functions is increased. Consequently, PSC has a high computational efficiency: for solutions of even modest accuracy we find that PSC is substantially more efficient, as measured by either execution time or memory required, than finite differencing; furthermore, these savings increase rapidly with increasing accuracy. The solution provided by PSC is an analytic function given everywhere; consequently, no interpolation operators need to be defined to determine the function values at intermediate points and no special arrangements need to be made to evaluate the solution or its derivatives on the boundaries. Since the practice of numerical relativity by finite differencing has been, and continues to be, hampered by both high computational resource demands and the difficulty of formulating acceptable finite difference alternatives to the analytic boundary conditions, PSC should be further pursued as an alternative way of formulating the computational problem of finding numerical solutions to the field equations of general relativity., Comment: 15 pages, 5 figures, revtex, submitted to PRD

This paper has been withdrawn due to a crucial error in combining the two probability sectors represented in equations 13 and 14. Corrected, one can recover, in the limit of no background, the results of Allen et al. The general result that an analysis allowing for a background permits a substantial improvement of the limit still holds, though the presentation in the gr-qc/9907070 is flawed., Comment: Withdrawn

The goal of these lecture notes is to introduce the developing research area of gravitational-wave phenomenology. In more concrete terms, they are meant to provide an overview of gravitational-wave sources and an introduction to the interpretation of real gravitational wave detector data. They are, of course, limited in both regards. Either topic could be the subject of one or more books, and certainly more than the few lectures possible in a summer school. Nevertheless, it is possible to talk about the problems of data analysis and give something of their flavor, and do the same for gravitational wave sources that might be observed in the upcoming generation of sensitive detectors. These notes are an attempt to do just that., Comment: 85 pages, 13 figures. Uses ssi.sty macros (included). Written version of lectures given at XXVI SLAC Summer Institute on Particle Physics ``Gravity: From the Hubble Length to the Planck Length'', August 3-14, 1998

LIGO --- The Laser Interferometer Gravitational-Wave Observatory --- is one of several large projects being undertaken in the United States, Europe and Japan to detect gravitational radiation. The novelty and precision of these instruments is such that large volumes of data will be generated in an attempt to find a small number of weak signals, which can be identified only as subtle changes in the instrument output over time. In this paper, I discuss the how the nature of the LIGO experiment determines the size of the data archive that will be produced, how the nature of the analyses that must be used to search the LIGO data for signals determines the anticipated access patterns on the archive, and how the LIGO data analysis system is designed to cope with the problems of LIGO data analysis., Comment: 20 pages, 2 figures, uses elsart.sty macros (included); accepted for publication in Future Generation Computing Systems

If $\gamma$-ray bursts (GRBs) are accompanied by gravitational wave bursts (GWBs) the correlated output of two gravitational wave detectors evaluated in the moments just prior to a GRB will differ from that evaluated at times not associated with a GRB. We can test for this difference independently of any model of the GWB signal waveform. If we invoke a model for the GRB source population and GWB radiation spectral density we can find a confidence interval or upper limit on the root-mean-square GWB signal amplitude in the detector waveband. To illustrate we adopt a simple, physically motivated model and estimate that initial LIGO detector observations coincident with 1000 GRBs could lead us to exclude, with 95% confidence, associated GWBs with $h_{RMS} \gtrsim 1.7 \times 10^{-22}$. This result does not require the detector noise be Gaussian or that any inter-detector correlated noise be measured or measurable; it does not require advanced or a priori knowledge of the source waveform; and the limits obtained on the wave-strength improve with the number of observed GRBs., Comment: 4 pages, submitted to PRL

Data analysis is the application of probability and statistics to draw inference from observation. Is a signal present or absent? Is the source an inspiraling binary system or a supernova? At what point in the sky is the radiation incident from? In these notes I want to address how two different statistical methodologies --- Bayesian and Frequentist --- approach the problem of statistical inference, Comment: 12 pages, LaTeX, sprocl.sty, to appear in the Proceedings of the Second Eduardo Amaldi Meeting, 1-4 July 1997

When completed, the gravitational wave detectors now proposed or under construction will provide us with a perspective on the Universe fundamentally different from any we have come to know. With this new perspective comes the hope that new insights and understandings of Nature will emerge. The proposed acoustic detectors, with spherical geometries and operating at millikelvin temperatures, are particularly well-suited to study gravitational radiation in the 1--3 KHz band. In this brief report I review some sources of particular interest for these detectors., Comment: 11 pages, LaTeX type, sprocl.sty, to appear in the proceedings of OMNI-1: The first international workshop for an omnidirectional gravitational-wave observatory

The nature of binary black hole coalescence is the final, uncharted frontier of the relativistic Kepler problem. In the United States, binary black hole coalescence has been identified as a computational ``Grand Challenge'' whose solution is the object of a coordinated effort, just reaching its half-way point, by more than two-score researchers at nearly a dozen institutions. In this report I highlight what I see as the most serious problems standing between us and a general computational solution to the problem of binary black hole coalescence: * the computational burden associated of the problem based on reasonable extrapolations of present-day computing algorithms and near-term hardware developments; * some of the computational issues associated with those estimates, and how, through the use of different or more sophisticated computational algorithms we might reduce the expected burden; and * some of the physical problems associated with the development of a numerical solution of the field equations for a binary black hole system, with particular attention to work going on in, or in association with, the Grand Challenge., Comment: 20 pages (including two figures) LaTeX w/amssymb, amsbsy, epsf and sprocl (available from http://www.wspc.co.uk/wspc/index.html) macro packages. A written version of the plenary lecture by the same name delivered at GR14. To appear in proceedings of the GR14 conference

The LIGO Research Community (LRC) is an independent organization of researchers interested in the scientific opportunities created by the construction and operation of the Laser Interferometer Gravitational-wave Observatory (LIGO). Membership is open to all interested individuals, irrespective of any other affiliations (including affiliation with the LIGO project, VIRGO or other gravitational-wave detector projects). The LRC has begun a study project designed to {\em identify} the ways that an operating LIGO will affect the research environment in gravitational physics, {\em decide} what we want that environment to look like, and recommend (to LIGO and the NSF) the steps to be taken now to develop that environment in the future. Contributions from LRC members and from the broader gravitational physics research community are actively solicited., Comment: Revised to be compatible with older versions of LaTeX. 9 pages plain LaTeX; This report will also be available at LRC website linked to http://ligo.caltech.edu

Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio $\rho$ and chirp mass $\cal M$. The distribution of events in a catalog composed of observations with $\rho$ greater than a threshold $\rho_0$ 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 $\rho$ and $\cal M$ 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 $\rho>8$ from distances not exceeding approximately $2\,\text{Gpc}$, corresponding to redshifts of $0.48$ (0.26) for $h=0.8$ ($0.5$), 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 $h=0.8$ ($0.5$) that limit is approximately $z=2.7$ (1.7) for binaries consisting of two $10\,\text{M}_\odot$ black holes. Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with $\rho$ and $\cal M$. 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.sty

Gravitational radiation from a binary neutron star or black hole system leads to orbital decay and the eventual coalescence of the binary's components. During the last several minutes before the binary components coalesce, the radiation will enter the bandwidth of the United States Laser Inteferometer Gravitational-wave Observatory (LIGO) and the French/Italian VIRGO gravitational radiation detector. The combination of detector sensitivity, signal strength, and source density and distribution all point to binary inspiral as the most likely candidate for observation among all the anticipated sources of gravitational radiation for LIGO/VIRGO. Here I review briefly some of the questions that are posed to theorists by the impending observation of binary inspiral., Comment: 3 pages, LaTeX/SIAM Conference Series Macros