Binary inspiral, gravitational radiation, and cosmology

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.st

Higher order corrections to the Newtonian potential in the Randall-Sundrum model

The general formalism for calculating the Newtonian potential in fine-tuned or critical Randall-Sundrum braneworlds is outlined. It is based on using the full tensor structure of the graviton propagator. This approach avoids the brane-bending effect arising from calculating the potential for a point source. For a single brane, this gives a clear understanding of the disputed overall factor 4/3 entering the correction. The result can be written on a compact form which is evaluated to high accuracy for both short and large distances.Comment: 12 pages, LaTeX2e with RevTeX4, 3 postscript figures; Minor corrections, references update

Gravitational Waves from coalescing binaries: Estimation of parameters

The paper presents a statistical model which reproduces the results of Monte Carlo simulations to estimate the parameters of the gravitational wave signal from a coalesing binary system. The model however is quite general and would be useful in other parameter estimation problems.Comment: LaTeX with RevTeX macros, 4 figure

Gravitational Wave Hotspots: Ranking Potential Locations of Single-Source Gravitational Wave Emission

The steadily improving sensitivity of pulsar timing arrays (PTAs) suggests that gravitational waves (GWs) from supermassive black hole binary (SMBHB) systems in the nearby universe will be de- tectable sometime during the next decade. Currently, PTAs assume an equal probability of detection from every sky position, but as evidence grows for a non-isotropic distribution of sources, is there a most likely sky position for a detectable single source of GWs? In this paper, a collection of galactic catalogs is used to calculate various metrics related to the detectability of a single GW source resolv- able above a GW background, assuming that every galaxy has the same probability of containing a SMBHB. Our analyses of these data reveal small probabilities that one of these sources is currently in the PTA band, but as sensitivity is improved regions of consistent probability density are found in predictable locations, specifically around local galaxy clusters.Comment: 9 pages, 9 figures, accepted for submission in Ap

Orbital evolution of a test particle around a black hole: higher-order corrections

We study the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved perturbatively in the mass ratio (or the corresponding parameter in the scalar field toy model), using the self force, for quasi-circular orbits around a Schwarzschild black hole. This approach is applied for the scalar model. Higher-order corrections yield a phase shift which, if included, may make gravitational-wave astronomy potentially highly accurate.Comment: 4 pages, 3 Encapsulated PostScript figure

On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

Templates for stellar mass black holes falling into supermassive black holes

The spin modulated gravitational wave signals, which we shall call smirches, emitted by stellar mass black holes tumbling and inspiralling into massive black holes have extremely complicated shapes. Tracking these signals with the aid of pattern matching techniques, such as Wiener filtering, is likely to be computationally an impossible exercise. In this article we propose using a mixture of optimal and non-optimal methods to create a search hierarchy to ease the computational burden. Furthermore, by employing the method of principal components (also known as singular value decomposition) we explicitly demonstrate that the effective dimensionality of the search parameter space of smirches is likely to be just three or four, much smaller than what has hitherto been thought to be about nine or ten. This result, based on a limited study of the parameter space, should be confirmed by a more exhaustive study over the parameter space as well as Monte-Carlo simulations to test the predictions made in this paper.Comment: 12 pages, 4 Tables, 4th LISA symposium, submitted to CQ

Deconvolving the information from an imperfect spherical gravitational wave antenna

We have studied the effects of imperfections in spherical gravitational wave antenna on our ability to properly interpret the data it will produce. The results of a numerical simulation are reported that quantitatively describe the systematic errors resulting from imperfections in various components of the antenna. In addition, the results of measurements on a room-temperature prototype are presented that verify it is possible to accurately deconvolve the data in practice.Comment: 5 pages, 2 figures, to be published in Europhysics Letter

A First Comparison of SLOPE and Other LIGO Burst Event Trigger Generators

A number of different methods have been proposed to identify unanticipated burst sources of gravitational waves in data arising from LIGO and other gravitational wave detectors. When confronted with such a wide variety of methods one is moved to ask if they are all necessary, i.e. given detector data that is assumed to have no gravitational wave signals present, do they generally identify the same events with the same efficiency, or do they each 'see' different things in the detector? Here we consider three different methods, which have been used within the LIGO Scientific Collaboration as part of its search for unanticipated gravitational wave bursts. We find that each of these three different methods developed for identifying candidate gravitational wave burst sources are, in fact, attuned to significantly different features in detector data, suggesting that they may provide largely independent lists of candidate gravitational wave burst events.Comment: 10 Pages, 5 Figures, Presented at the 10th Gravitational Wave Data Analysis Workshop (GWDAW-10), 14-17 December 2005 at the University of Texas, Brownsvill