Stabilization of a Fabry-Perot interferometer using a suspension-point interferometer

A suspension-point interferometer (SPI) is an auxiliary interferometer for active vibration isolation, implemented at the suspension points of the mirrors of an interferometric gravitational wave detector. We constructed a prototype Fabry-Perot interferometer equipped with an SPI and observed vibration isolation in both the spectrum and transfer function. The noise spectrum of the main interferometer was reduced by 40 dB below 1 Hz. Transfer function measurements showed that the SPI also produced good vibration suppression above 1 Hz. These results indicate that SPI can improve both the sensitivity and the stability of the interferometer.Comment: 14 pages, 8 figures; added discussion; to be published in Physics Letters

Second Order Quasi-Normal Mode of the Schwarzschild Black Hole

We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second order Zerilli equation by implementing the modified Leaver's continued fraction method. The second order QNM frequencies are found to be twice the first order ones, and the GW amplitude is up to $\sim 10$ that of the first order for the binary BH mergers. Since the second order QNMs always exist, we can use their detections (i) to test the nonlinearity of general relativity, in particular the no-hair theorem, (ii) to remove fake events in the data analysis of QNM GWs and (iii) to measure the distance to the BH.Comment: 23 pages, no figur

Operational status of TAMA300 with the seismic attenuation system (SAS)

TAMA300 has been upgraded to improve the sensitivity at low frequencies after the last observation run in 2004. To avoid the noise caused by seismic activities, we installed a new seismic isolation system —- the TAMA seismic attenuation system (SAS). Four SAS towers for the test-mass mirrors were sequentially installed from 2005 to 2006. The recycled Fabry–Perot Michelson interferometer was successfully locked with the SAS. We confirmed the reduction of both length and angular fluctuations at frequencies higher than 1 Hz owing to the SAS

Accuracy and effectualness of closed-form, frequency-domain waveforms for non-spinning black hole binaries

The coalescences of binary black hole (BBH) systems, here taken to be non-spinning, are among the most promising sources for gravitational wave (GW) ground-based detectors, such as LIGO and Virgo. To detect the GW signals emitted by BBHs, and measure the parameters of the source, one needs to have in hand a bank of GW templates that are both effectual (for detection), and accurate (for measurement). We study the effectualness and the accuracy of the two types of parametrized banks of templates that are directly defined in the frequency-domain by means of closed-form expressions, namely 'post-Newtonian' (PN) and 'phenomenological' models. In absence of knowledge of the exact waveforms, our study assumes as fiducial, target waveforms the ones generated by the most accurate version of the effective one body (EOB) formalism. We find that, for initial GW detectors the use, at each point of parameter space, of the best closed-form template (among PN and phenomenological models) leads to an effectualness >97% over the entire mass range and >99% in an important fraction of parameter space; however, when considering advanced detectors, both of the closed-form frequency-domain models fail to be effectual enough in significant domains of the two-dimensional [total mass and mass ratio] parameter space. Moreover, we find that, both for initial and advanced detectors, the two closed-form frequency-domain models fail to satisfy the minimal required accuracy standard in a very large domain of the two-dimensional parameter space. In addition, a side result of our study is the determination, as a function of the mass ratio, of the maximum frequency at which a frequency-domain PN waveform can be 'joined' onto a NR-calibrated EOB waveform without undue loss of accuracy.Comment: 29 pages, 8 figures, 1 table. Accepted for publication in Phys. Rev.

Optical vernier technique for in-situ measurement of the length of long Fabry-Perot cavities

We propose a method for in-situ measurement of the length of kilometer size Fabry-Perot cavities in laser gravitational wave detectors. The method is based on the vernier, which occurs naturally when the laser incident on the cavity has a sideband. By changing the length of the cavity over several wavelengths we obtain a set of carrier resonances alternating with sideband resonances. From the measurement of the separation between the carrier and a sideband resonance we determine the length of the cavity. We apply the technique to the measurement of the length of a Fabry-Perot cavity in the Caltech 40m Interferometer and discuss the accuracy of the technique.Comment: LaTeX 2e, 12 pages, 4 figure

Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors

The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v^8), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN waveform families in the context of initial and advanced gravitational-wave detectors. The waveforms employed in our analysis are those that are currently used by Initial LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the Fourier-domain representation TaylorF2. We examine the overlaps of these models with one another and with the prototype effective one-body model (calibrated to numerical relativity simulations, as currently used by initial LIGO) for a number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their differences and to help us decide whether there exist preferred families that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit M_crit, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial, Enhanced and Advanced LIGO. From a purely computational point of view we recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to numerical relativity simulations be used for total binary mass M > Mcrit.Comment: 27 pages, 8 figures, 4 tables, submitted to PR

Optimal combination of signals from co-located gravitational wave interferometers for use in searches for a stochastic background

This article derives an optimal (i.e., unbiased, minimum variance) estimator for the pseudo-detector strain for a pair of co-located gravitational wave interferometers (such as the pair of LIGO interferometers at its Hanford Observatory), allowing for possible instrumental correlations between the two detectors. The technique is robust and does not involve any assumptions or approximations regarding the relative strength of gravitational wave signals in the detector pair with respect to other sources of correlated instrumental or environmental noise. An expression is given for the effective power spectral density of the combined noise in the pseudo-detector. This can then be introduced into the standard optimal Wiener filter used to cross-correlate detector data streams in order to obtain an optimal estimate of the stochastic gravitational wave background. In addition, a dual to the optimal estimate of strain is derived. This dual is constructed to contain no gravitational wave signature and can thus be used as on "off-source" measurement to test algorithms used in the "on-source" observation.Comment: 14 pages, 4 figures, submitted to Physical Review D Resubmitted after editing paper in response to referee comments. Removed appendices A, B and edited text accordingly. Improved legibility of figures. Corrected several references. Corrected reference to science run number (S1 vs. S2) in text and figure caption

Very high quality factor measured in annealed fused silica

We present the results of quality factor measurements for rod samples made of fused silica. To decrease the dissipation we annealed our samples. The highest quality factor that we observed was $Q=(2.03\pm0.01)\times10^8$ for a mode at 384 Hz. This is the highest published value of $Q$ in fused silica measured to date.Comment: 8 pages, 2 figure

Data analysis of gravitational-wave signals from spinning neutron stars. II. Accuracy of estimation of parameters

We examine the accuracy of estimation of parameters of the gravitational-wave signals from spinning neutron stars that can be achieved from observations by Earth-based laser interferometers. We consider a model of the signal consisting of two narrowband components and including both phase and amplitude modulation. We calculate approximate values of the rms errors of the parameter estimators using the Fisher information matrix. We carry out extensive Monte Carlo simulations and obtain cumulative distribution functions of rms errors of astrophysically interesting parameters: amplitude of the signal, wobble angle, position of the source in the sky, frequency, and spindown coefficients. We consider both all-sky searches and directed searches. We also examine the possibility of determination of neutron star proper motion. We perform simulations for all laser-interferometric detectors that are currently under construction and for several possible lengths of the observation time and sizes of the parameter space. We find that observations of continuous gravitational-wave signals from neutron stars by laser-interferometric detectors will provide a very accurate information about their astrophysical properties. We derive several simplified models of the signal that can be used in the theoretical investigations of the data analysis schemes independently of the physical mechanisms generating the gravitational-wave signal.Comment: LaTeX, 34 pages, 15 figures, submitted to Phys. Rev.