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

The Cosmological Constant and Advanced Gravitational Wave Detectors

Interferometric gravitational wave detectors could measure the frequency sweep of a binary inspiral [characterized by its chirp mass] to high accuracy. The observed chirp mass is the intrinsic chirp mass of the binary source multiplied by $(1+z)$, where $z$ is the redshift of the source. Assuming a non-zero cosmological constant, we compute the expected redshift distribution of observed events for an advanced LIGO detector. We find that the redshift distribution has a robust and sizable dependence on the cosmological constant; the data from advanced LIGO detectors could provide an independent measurement of the cosmological constant.Comment: 13 pages plus 5 figure, LaTeX. Revised and final version, to appear in Phys. Rev.

Rotochemical Heating of Neutron Stars: Rigorous Formalism with Electrostatic Potential Perturbations

The electrostatic potential that keeps approximate charge neutrality in neutron star matter is self-consistently introduced into the formalism for rotochemical heating presented in a previous paper by Fernandez and Reisenegger. Although the new formalism is more rigorous, we show that its observable consequences are indistinguishable from those of the previous one, leaving the conclusions of the previous paper unchanged.Comment: 14 pages, including 4 eps figures. Accepted for publication in The Astrophysical Journa

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

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

The R-Mode Oscillations in Relativistic Rotating Stars

The axial mode oscillations are examined for relativistic rotating stars with uniform angular velocity. Using the slow rotation formalism and the Cowling approximation, we have derived the equations governing the r-mode oscillations up to the second order with respect to the rotation. In the lowest order, the allowed range of the frequencies is determined, but corresponding spatial function is arbitrary. The spatial function can be decomposed in non-barotropic region by a set of functions associated with the differential equation of the second-order corrections. The equation however becomes singular in barotropic region, and a single function can be selected to describe the spatial perturbation of the lowest order. The frame dragging effect among the relativistic effects may be significant, as it results in rather broad spectrum of the r-mode frequency unlike in the Newtonian first-order calculation.Comment: 19 pages, 4 figures, AAS LaTeX, Accepted for publication in The Astrophysical Journa

Crustal Oscillations of Slowly Rotating Relativistic Stars

We study low-amplitude crustal oscillations of slowly rotating relativistic stars consisting of a central fluid core and an outer thin solid crust. We estimate the effect of rotation on the torsional toroidal modes and on the interfacial and shear spheroidal modes. The results compared against the Newtonian ones for wide range of neutron star models and equations of state.Comment: 15 page

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

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