Optimal detection of burst events in gravitational wave interferometric observatories

We consider the problem of detecting a burst signal of unknown shape. We introduce a statistic which generalizes the excess power statistic proposed by Flanagan and Hughes and extended by Anderson et al. The statistic we propose is shown to be optimal for arbitrary noise spectral characteristic, under the two hypotheses that the noise is Gaussian, and that the prior for the signal is uniform. The statistic derivation is based on the assumption that a signal affects only affects N samples in the data stream, but that no other information is a priori available, and that the value of the signal at each sample can be arbitrary. We show that the proposed statistic can be implemented combining standard time-series analysis tools which can be efficiently implemented, and the resulting computational cost is still compatible with an on-line analysis of interferometric data. We generalize this version of an excess power statistic to the multiple detector case, also including the effect of correlated noise. We give full details about the implementation of the algorithm, both for the single and the multiple detector case, and we discuss exact and approximate forms, depending on the specific characteristics of the noise and on the assumed length of the burst event. As a example, we show what would be the sensitivity of the network of interferometers to a delta-function burst.Comment: 21 pages, 5 figures in 3 groups. Submitted for publication to Phys.Rev.D. A Mathematica notebook is available at http://www.ligo.caltech.edu/~avicere/nda/burst/Burst.nb which allows to reproduce the numerical results of the pape

Testing Scalar-Tensor Gravity Using Space Gravitational-Wave Interferometers

We calculate the bounds which could be placed on scalar-tensor theories of gravity of the Jordan, Fierz, Brans and Dicke type by measurements of gravitational waveforms from neutron stars (NS) spiralling into massive black holes (MBH) using LISA, the proposed space laser interferometric observatory. Such observations may yield significantly more stringent bounds on the Brans-Dicke coupling parameter \omega than are achievable from solar system or binary pulsar measurements. For NS-MBH inspirals, dipole gravitational radiation modifies the inspiral and generates an additional contribution to the phase evolution of the emitted gravitational waveform. Bounds on \omega can therefore be found by using the technique of matched filtering. We compute the Fisher information matrix for a waveform accurate to second post-Newtonian order, including the effect of dipole radiation, filtered using a currently modeled noise curve for LISA, and determine the bounds on \omega for several different NS-MBH canonical systems. For example, observations of a 1.4 solar mass NS inspiralling to a 1000 solar mass MBH with a signal-to-noise ratio of 10 could yield a bound of \omega > 240,000, substantially greater than the current experimental bound of \omega > 3000.Comment: 18 pages, 4 figures, 1 table; to be submitted to Phys. Rev.

Observational constraints on the neutron star mass distribution

Radio observations of neutron star binary pulsar systems have constrained strongly the masses of eight neutron stars. Assuming neutron star masses are uniformly distributed between lower and upper bounds $m_l$ and $m_u$, the observations determine with 95\% confidence that $1.01 < m_l/\text{M}_\odot < 1.34$ and $1.43 < m_u/\text{M}_\odot < 1.64$. These limits give observational support to neutron star formation scenarios that suggest that masses should fall predominantly in the range $1.3<m/\text{M}_\odot<1.6$, and will also be important in the interpretation of binary inspiral observations by the Laser Interferometer Gravitational-wave Observatory.Comment: Postscript, 4 pages, NU-GR-

Filtering post-Newtonian gravitational waves from coalescing binaries

Gravitational waves from inspiralling binaries are expected to be detected using a data analysis technique known as {\it matched filtering.} This technique is applicable whenever the form of the signal is known accurately. Though we know the form of the signal precisely, we will not know {\it a priori} its parameters. Hence it is essential to filter the raw output through a host of search templates each corresponding to different values of the parameters. The number of search templates needed in detecting the Newtonian waveform characterized by three independent parameters is itself several thousands. With the inclusion of post-Newtonian corrections the inspiral waveform will have four independent parameters and this, it was thought, would lead to an increase in the number of filters by several orders of magnitude---an unfavorable feature since it would drastically slow down data analysis. In this paper I show that by a judicious choice of signal parameters we can work, even when the first post-Newtonian corrections are included, with as many number of parameters as in the Newtonian case. In other words I demonstrate that the effective dimensionality of the signal parameter space does not change when first post-Newtonian corrections are taken into account.Comment: 5 pages, revtex, 2 figures available upon reques

Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion

A particle of mass $\mu$ moves on a circular orbit around a nonrotating black hole of mass $M$. Under the assumption $\mu \ll M$ the gravitational waves emitted by such a binary system can be calculated exactly numerically using black-hole perturbation theory. If, further, the particle is slowly moving, then the waves can be calculated approximately analytically, and expressed in the form of a post-Newtonian expansion. We determine the accuracy of this expansion in a quantitative way by calculating the reduction in signal-to-noise ratio incurred when matched filtering the exact signal with a nonoptimal, post-Newtonian filter.Comment: 5 pages, ReVTeX, 1 figure. A typographical error was discovered in the computer code used to generate the results presented in the paper. The corrected results are presented in an Erratum, which also incorporates new results, obtained using the recently improved post-Newtonian calculations of Tanaka, Tagoshi, and Sasak

Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters

The paper deals with issues pertaining the detection of gravitational waves from coalescing binaries. We introduce the application of differential geometry to the problem of optimal detection of the `chirp signal'. We have also carried out extensive Monte Carlo simulations to understand the errors in the estimation of parameters of the binary system. We find that the errors are much more than those predicted by the covariance matrix even at a high SNR of 10-15. We also introduce the idea of using the instant of coalescence rather than the time of arrival to determine the direction to the source.Comment: 28 pages, REVTEX, 12 figures (bundled via uufiles command along with this paper) submitted to Phys. Rev.

LISA, binary stars, and the mass of the graviton

We extend and improve earlier estimates of the ability of the proposed LISA (Laser Interferometer Space Antenna) gravitational wave detector to place upper bounds on the graviton mass, m_g, by comparing the arrival times of gravitational and electromagnetic signals from binary star systems. We show that the best possible limit on m_g obtainable this way is ~ 50 times better than the current limit set by Solar System measurements. Among currently known, well-understood binaries, 4U1820-30 is the best for this purpose; LISA observations of 4U1820-30 should yield a limit ~ 3-4 times better than the present Solar System bound. AM CVn-type binaries offer the prospect of improving the limit by a factor of 10, if such systems can be better understood by the time of the LISA mission. We briefly discuss the likelihood that radio and optical searches during the next decade will yield binaries that more closely approach the best possible case.Comment: ReVTeX 4, 6 pages, 1 figure, submitted to Phys Rev

Measuring black-hole parameters and testing general relativity using gravitational-wave data from space-based interferometers

Among the expected sources of gravitational waves for the Laser Interferometer Space Antenna (LISA) is the capture of solar-mass compact stars by massive black holes residing in galactic centers. We construct a simple model for such a capture, in which the compact star moves freely on a circular orbit in the equatorial plane of the massive black hole. We consider the gravitational waves emitted during the late stages of orbital evolution, shortly before the orbiting mass reaches the innermost stable circular orbit. We construct a simple model for the gravitational-wave signal, in which the phasing of the waves plays the dominant role. The signal's behavior depends on a number of parameters, including $\mu$, the mass of the orbiting star, $M$, the mass of the central black hole, and $J$, the black hole's angular momentum. We calculate, using our simplified model, and in the limit of large signal-to-noise ratio, the accuracy with which these quantities can be estimated during a gravitational-wave measurement. Our simplified model also suggests a method for experimentally testing the strong-field predictions of general relativity.Comment: ReVTeX, 16 pages, 5 postscript figure

Gravitational waves from inspiralling compact binaries: Parameter estimation using second-post-Newtonian waveforms

The parameters of inspiralling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. Using a recently calculated formula, accurate to second post-Newtonian (2PN) order [order $(v/c)^4$, where $v$ is the orbital velocity], for the frequency sweep ($dF/dt$) induced by gravitational radiation damping, we study the statistical errors in the determination of such source parameters as the ``chirp mass'' $\cal M$, reduced mass $\mu$, and spin parameters $\beta$ and $\sigma$ (related to spin-orbit and spin-spin effects, respectively). We find that previous results using template phasing accurate to 1.5PN order actually underestimated the errors in $\cal M$, $\mu$, and $\beta$. For two inspiralling neutron stars, the measurement errors increase by less than 16 percent.Comment: 14 pages, ReVTe

Effects of finite arm-length of LISA on analysis of gravitational waves from MBH binaries

Response of an interferometer becomes complicated for gravitational wave shorter than the arm-length of the detector, as nature of wave appears strongly. We have studied how parameter estimation for merging massive black hole binaries are affected by this complicated effect in the case of LISA. It is shown that three dimensional positions of some binaries might be determined much better than the past estimations that use the long wave approximation. For equal mass binaries this improvement is most prominent at \sim 10^5\sol.Comment: 10 pages, 3 figures, to appear in Phys.Rev.