Gravitational Waves from a Compact Star in a Circular, Inspiral Orbit,

 in the Equatorial Plane of a Massive, Spinning Black Hole, as Observed by

 LISA

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Abstract

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

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Measures of abstinence in clinical trials: issues and recommendations.

John R Hughes, Josue P. Keely, Ray Niaura … (2003)

A workgroup formed by the Society for Research on Nicotine and Tobacco reviewed the literature on abstinence measures used in trials of smoking cessation interventions. We recommend that trials report multiple measures of abstinence. However, at a minimum we recommend that trial: (a) report prolonged abstinence (i.e., sustained abstinence after an initial period in which smoking is not counted as a failure) as the preferred measure, plus point prevalence as a secondary measure; (b) use 7 consecutive days of smoking or smoking on > or = 1 day of 2 consecutive weeks to define treatment failure; (c) include non-cigarette tobacco use, but not nicotine medications in definitions of failure; and (d) report results from survival analysis to describe outcomes more fully. Trials of smokers willing to set a quit date should tie all follow-ups to the quit date and report 6- and/or 12-month abstinence rates. For these trials, we recommend an initial 2-week grace period for prolonged abstinence definitions; however, the period may vary, depending on the presumed mechanism of the treatment. Trials of smokers who may not be currently trying to quit should tie follow-up to the initiation of the intervention and should report a prolonged abstinence measure of > or = 6-month duration and point prevalence rates at 6- and 12-month follow-ups. The grace period for these trials will depend on the time necessary for treatment dissemination, which will vary depending on the treatment, setting, and population. Trials that use short-term follow-ups ( or = 4 weeks. We again recommend a 2-week grace period; however, that period can vary.

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An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime

Theodore Quinn, Robert Wald (1996)

The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom'', which states that whenever two particles of the same charge \(e\) have the same magnitude of acceleration, the difference in their self-force is given by the ordinary Lorentz force of the difference in their (suitably compared) electromagnetic fields. We thereby derive an expression for the electromagnetic self-force which agrees with that of DeWitt and Brehme as corrected by Hobbs. Despite several important differences, our analysis of the gravitational self-force proceeds in close parallel with the electromagnetic case. In the gravitational case, our final expression for the (reduced order) equations of motion shows that the deviation from geodesic motion arises entirely from a ``tail term'', in agreement with recent results of Mino et al. Throughout the paper, we take the view that ``point particles'' do not make sense as fundamental objects, but that ``point particle equations of motion'' do make sense as means of encoding information about the motion of an extended body in the limit where not only the size but also the charge and mass of the body go to zero at a suitable rate. Plausibility arguments for the validity of our comparison axiom are given by considering the limiting behavior of the self-force on extended bodies.

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Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates

, (2010)

We discuss the extraction of information from detected binary black hole (BBH) coalescence gravitational waves, focusing on the merger phase that occurs after the gradual inspiral and before the ringdown. Our results are: (1) If numerical relativity simulations have not produced template merger waveforms before BBH detections by LIGO/VIRGO, one can band-pass filter the merger waves. For BBHs smaller than about 40 solar masses detected via their inspiral waves, the band pass filtering signal to noise ratio indicates that the merger waves should typically be just barely visible in the noise for initial and advanced LIGO interferometers. (2) We derive an optimized (maximum likelihood) method for extracting a best-fit merger waveform from the noisy detector output; one "perpendicularly projects" this output onto a function space (specified using wavelets) that incorporates our prior knowledge of the waveforms. An extension of the method allows one to extract the BBH's two independent waveforms from outputs of several interferometers. (3) If numerical relativists produce codes for generating merger templates but running the codes is too expensive to allow an extensive survey of the merger parameter space, then a coarse survey of this parameter space, to determine the ranges of the several key parameters and to explore several qualitative issues which we describe, would be useful for data analysis purposes. (4) A complete set of templates could be used to test the nonlinear dynamics of general relativity and to measure some of the binary parameters. We estimate the number of bits of information obtainable from the merger waves (about 10 to 60 for LIGO/VIRGO, up to 200 for LISA), estimate the information loss due to template numerical errors or sparseness in the template grid, and infer approximate requirements on template accuracy and spacing.