Gravitational Frequencies Research Articles

Beating the Spin-Down Limit on Gravitational Wave Emission from the Crab Pulsar

We present direct upper limits on gravitational wave emission from the Crab pulsar using data from the first nine months of the fifth science run of the Laser Interferometer Gravitational-wave Observatory (LIGO). These limits are based on two searches. In the first we assume that the gravitational wave emission follows the observed radio timing, giving an upper limit on gravitational wave emission that beats indirect limits inferred from the spin-down and braking index of the pulsar and the energetics of the nebula. In the second we allow for a small mismatch between the gravitational and radio signal frequencies and interpret our results in the context of two possible gravitational wave emission mechanisms.

Exact gravitational quasinormal frequencies of topological black holes

We compute the exact gravitational quasinormal frequencies for massless topological black holes in $d$-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies.

Gravitational radiation from rotational instabilites 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.

Gravitational lens frequencies and the cosmological constant: an examination of amplification bias and galaxy formation redshift

Previous investigations into the gravitational lens frequencies in quasar samples suggested that observations do not favor cosmological models with a large value of the cosmological constant. However, this conclusion depends critically on assumptions about the degree of amplification bias and the constant comoving number density of galaxies. We examine amplification bias selection effects under the condition that the darker image must be brighter than the limiting magnitude in the sample and show that the amplification bias selection effects are about five times smaller than the previous estimate. We also estimate the survey depth which is required for the darker image to recover the conventional estimates. This revision makes a cosmological model with a large cosmological constant consistent with observations of gravitational lenses. We also find that, when a model of the distribution of the galaxy formation redshifts is used, the lensing frequency is 15–45 percent lower than for the case of constant number density of galaxies.

Gravitational lensing frequencies: galaxy cross-sections and selection effects

Four issues - (1) the best currently available data on the galaxy velocity-dispersion distribution, (2) the effects of finite core radii potential ellipticity on lensing cross sections, (3) the predicted distribution of lens image separations compared to observational angular resolutions, and (4) the preferential inclusion of lens systems in flux limited samples - are considered in order to facilitate more realistic predictions of multiple image galaxy-quasar lensing frequencies. It is found that (1) the SIS lensing parameter F equals 0.047 +/-0.019 with almost 90 percent contributed by E and S0 galaxies, (2) observed E and S0 core radii are remarkably small, yielding a factor of less than about 2 reduction in total lensing cross sections, (3) 50 percent of galaxy-quasar lenses have image separations greater than about 1.3 arcsec, and (4) amplification bias factors are large and must be carefully taken into account. It is concluded that flat universe models excessively dominated by the cosmological constant are not favored by the small observed galaxy-quasar lensing rate.

An analytic representation for the quasi-normal modes of Kerr black holes

The gravitational quasi-normal frequencies of both stationary and rotating black holes are calculated by constructing exact eigensolutions to the radiative boundary-value problem of Chandrasekhar and Detweiler. The method is that employed by Jaffé in his determination of the electronic spectra of the hydrogen molecule ion in 1934, and analytic representations of the quasi-normal mode wavefunctions are presented here for the first time. Numerical solution of Jaffé’s characteristic equation indicates that for each l -pole there is an infinite number of damped Schwarzschild quasi-normal modes. The real parts of the corresponding frequencies are bounded, but the imaginary parts are not. Figures are presented that illustrate the trajectories the five least-damped of these frequencies trace in the complex frequency plane as the angular momentum of the black hole increases from zero to near the Kerr limit of maximum angular momentum per unit mass, a = M , where there is a coalescence of the more highly damped frequencies to the purely real value of the critical frequency for superradiant scattering.