A stochastic template placement algorithm for gravitational wave data analysis

This paper presents an algorithm for constructing matched-filter template banks in an arbitrary parameter space. The method places templates at random, then removes those which are "too close" together. The properties and optimality of stochastic template banks generated in this manner are investigated for some simple models. The effectiveness of these template banks for gravitational wave searches for binary inspiral waveforms is also examined. The properties of a stochastic template bank are then compared to the deterministically placed template banks that are currently used in gravitational wave data analysis.Comment: 14 pages, 11 figure

Compton Scattering by Static and Moving Media I. The Transfer Equation and Its Moments

Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first moments, in both the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in epsilon/m_e, T_e/m_e, and V, where epsilon is the photon energy, T_e and m_e are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second-order in V usually should be retained, because if the radiation energy density is sufficiently large compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second-order in V are at least as important as the effects described by the terms that are first-order in V, even when V is small. Our equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and the diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V^2 > 3 T_e/m_e.Comment: 31 pages, accepted for publication in The Astrophysical Journa

Energy Distribution in Melvin's Magnetic Universe

We use the energy-momentum complexes of Landau and Lifshitz and Papapetrou to obtain the energy distribution in Melvin's magnetic universe. For this space-time we find that these definitions of energy give the same and convincing results. The energy distribution obtained here is the same as we obtained earlier for the same space-time using the energy-momentum complex of Einstein. These results uphold the usefulness of the energy-momentum complexes.Comment: 8 pages, RevTex, no figure

Parametric resonant acceleration of particles by gravitational waves

We study the resonant interaction of charged particles with a gravitational wave propagating in the non-empty interstellar space in the presence of a uniform magnetic field. It is found that this interaction can be cast in the form of a parametric resonance problem which, besides the main resonance, allows for the existence of many secondary ones. Each of them is associated with a non-zero resonant width, depending on the amplitude of the wave and the energy density of the interstellar plasma. Numerical estimates of the particles' energisation and the ensuing damping of the wave are given.Comment: LaTeX file, 16 page

Gravitational Radiation from Rotational Instabilities in Compact Stellar Cores with Stiff Equations of State

We carry out 3-D numerical simulations of the dynamical instability in rapidly rotating stars initially modeled as polytropes with n = 1.5, 1.0, and 0.5. The calculations are done with a SPH code using Newtonian gravity, and the gravitational radiation is calculated in the quadrupole limit. All models develop the global m=2 bar mode, with mass and angular momentum being shed from the ends of the bar in two trailing spiral arms. The models then undergo successive episodes of core recontraction and spiral arm ejection, with the number of these episodes increasing as n decreases: this results in longer-lived gravitational wave signals for stiffer models. This instability may operate in a stellar core that has expended its nuclear fuel and is prevented from further collapse due to centrifugal forces. The actual values of the gravitational radiation amplitudes and frequencies depend sensitively on the radius of the star R_{eq} at which the instability develops.Comment: 39 pages, uses Latex 2.09. To be published in the Dec. 15, 1996 issue of Physical Review D. 21 figures (bitmapped). Originals available in compressed Postscript format at ftp://zonker.drexel.edu/papers/bars

General Relativistic versus Newtonian: a universality in radiation hydrodynamics

We compare Newtonian and general relativistic descriptions of the stationary accretion of self-gravitating fluids onto compact bodies. Spherical symmetry and thin gas approximation are assumed. Luminosity depends, amongst other factors, on the temperature and the contribution of gas to the total mass, in both -- general relativistic ($L_{GR}$) and Newtonian ($L_N$) -- models. We discover a remarkable universal behaviour for transonic flows: the ratio of respective luminosities $L_{GR}/L_N$ is independent of the fractional mass of the gas and depends on asymptotic temperature. It is close to 1 in the regime of low asymptotic temperatures and can grow by one order of magnitude for high temperatures. These conclusions are valid for a wide range of polytropic equations of state.Comment: 8 pages, 4 figure

Quantum Phase Shift in Chern-Simons Modified Gravity

Using a unified approach of optical-mechanical analogy in a semiclassical formula, we evaluate the effect of Chern-Simons modified gravity on the quantum phase shift of de Broglie waves in neutron interferometry. The phase shift calculated here reveals, in a single equation, a combination of effects coming from Newtonian gravity, inertial forces, Schwarzschild and Chern-Simons modified gravity. However the last two effects, though new, turn out to be too tiny to be observed, and hence only of academic interest at present. The approximations, wherever used, as well as the drawbacks of the non-dynamical approach are clearly indicated.Comment: 16 pages, minor errors corrected. Accepted for publication in Phys. Rev.

Gravitational Waves from the Dynamical Bar Instability in a Rapidly Rotating Star

A rapidly rotating, axisymmetric star can be dynamically unstable to an m=2 "bar" mode that transforms the star from a disk shape to an elongated bar. The fate of such a bar-shaped star is uncertain. Some previous numerical studies indicate that the bar is short lived, lasting for only a few bar-rotation periods, while other studies suggest that the bar is relatively long lived. This paper contains the results of a numerical simulation of a rapidly rotating gamma=5/3 fluid star. The simulation shows that the bar shape is long lived: once the bar is established, the star retains this shape for more than 10 bar-rotation periods, through the end of the simulation. The results are consistent with the conjecture that a star will retain its bar shape indefinitely on a dynamical time scale, as long as its rotation rate exceeds the threshold for secular bar instability. The results are described in terms of a low density neutron star, but can be scaled to represent, for example, a burned-out stellar core that is prevented from complete collapse by centrifugal forces. Estimates for the gravitational-wave signal indicate that a dynamically unstable neutron star in our galaxy can be detected easily by the first generation of ground based gravitational-wave detectors. The signal for an unstable neutron star in the Virgo cluster might be seen by the planned advanced detectors. The Newtonian/quadrupole approximation is used throughout this work.Comment: Expanded version to be published in Phys. Rev. D: 13 pages, REVTeX, 13 figures, 9 TeX input file

Field of a Radiation Distributuion

General relativistic spherically symmetric matter field with a vanishing stress energy scalar is analyzed. Procedure for generating exact solutions of the field equations for such matter distributions is given. It is further pointed out that all such type I spherically symmetric fields with distinct eignvalues in the radial two space can be treated as a mixture of isotropic and directed radiations. Various classes of exact solutions are given. Junction conditions for such a matter field to the possible exterior solutions are also discussed.Comment: Latex file, 13 pages, no figures. Accepted for publication in Phys. Rev.

Laser Interferometric Detectors of Gravitational Waves

A laser interferometric detector of gravitational waves is studied and a complete solution (to first order in the metric perturbation) of the coupled Einstein-Maxwell equations with appropriate boundary conditions for the light beams is determined. The phase shift, the light deflection and the rotation of the polarization axis induced by gravitational waves are computed. The results are compared with previous literature, and are shown to hold also for detectors which are large in comparison with the gravitational wavelength.Comment: 13 pages, LaTe