The information content of gravitational wave harmonics in compact binary inspiral

The nonlinear aspect of gravitational wave generation that produces power at harmonics of the orbital frequency, above the fundamental quadrupole frequency, is examined to see what information about the source is contained in these higher harmonics. We use an order (4/2) post-Newtonian expansion of the gravitational wave waveform of a binary system to model the signal seen in a spaceborne gravitational wave detector such as the proposed LISA detector. Covariance studies are then performed to determine the ultimate accuracy to be expected when the parameters of the source are fit to the received signal. We find three areas where the higher harmonics contribute crucial information that breaks degeneracies in the model and allows otherwise badly-correlated parameters to be separated and determined. First, we find that the position of a coalescing massive black hole binary in an ecliptic plane detector, such as OMEGA, is well-determined with the help of these harmonics. Second, we find that the individual masses of the stars in a chirping neutron star binary can be separated because of the mass dependence of the harmonic contributions to the wave. Finally, we note that supermassive black hole binaries, whose frequencies are too low to be seen in the detector sensitivity window for long, may still have their masses, distances, and positions determined since the information content of the higher harmonics compensates for the information lost when the orbit-induced modulation of the signal does not last long enough to be apparent in the data.Comment: 13 pages, 5 figure

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.

Angular Resolution of the LISA Gravitational Wave Detector

We calculate the angular resolution of the planned LISA detector, a space-based laser interferometer for measuring low-frequency gravitational waves from galactic and extragalactic sources. LISA is not a pointed instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will measure simultaneously both polarization components of incoming gravitational waves, so the data will consist of two time series. All physical properties of the source, including its position, must be extracted from these time series. LISA's angular resolution is therefore not a fixed quantity, but rather depends on the type of signal and on how much other information must be extracted. Information about the source position will be encoded in the measured signal in three ways: 1) through the relative amplitudes and phases of the two polarization components, 2) through the periodic Doppler shift imposed on the signal by the detector's motion around the Sun, and 3) through the further modulation of the signal caused by the detector's time-varying orientation. We derive the basic formulae required to calculate the LISA's angular resolution $\Delta \Omega_S$ for a given source. We then evaluate $\Delta \Omega_S$ for two sources of particular interest: monchromatic sources and mergers of supermassive black holes. For these two types of sources, we calculate (in the high signal-to-noise approximation) the full variance-covariance matrix, which gives the accuracy to which all source parameters can be measured. Since our results on LISA's angular resolution depend mainly on gross features of the detector geometry, orbit, and noise curve, we expect these results to be fairly insensitive to modest changes in detector design that may occur between now and launch. We also expect that our calculations could be easily modified to apply to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil

LISA data analysis I: Doppler demodulation

The orbital motion of the Laser Interferometer Space Antenna (LISA) produces amplitude, phase and frequency modulation of a gravitational wave signal. The modulations have the effect of spreading a monochromatic gravitational wave signal across a range of frequencies. The modulations encode useful information about the source location and orientation, but they also have the deleterious affect of spreading a signal across a wide bandwidth, thereby reducing the strength of the signal relative to the instrument noise. We describe a simple method for removing the dominant, Doppler, component of the signal modulation. The demodulation reassembles the power from a monochromatic source into a narrow spike, and provides a quick way to determine the sky locations and frequencies of the brightest gravitational wave sources.Comment: 5 pages, 7 figures. References and new comments adde

RHIC Physics with the Parton Cascade Model

We present an analysis of the net-baryon number rapidity distribution and of direct photon emission in the framework of the Parton Cascade Model.Comment: 4 pages 4 figures included, proceedings of QM 200

Gravitational Wave Chirp Search: Economization of PN Matched Filter Bank via Cardinal Interpolation

The final inspiral phase in the evolution of a compact binary consisting of black holes and/or neutron stars is among the most probable events that a network of ground-based interferometric gravitational wave detectors is likely to observe. Gravitational radiation emitted during this phase will have to be dug out of noise by matched-filtering (correlating) the detector output with a bank of several $10^5$ templates, making the computational resources required quite demanding, though not formidable. We propose an interpolation method for evaluating the correlation between template waveforms and the detector output and show that the method is effective in substantially reducing the number of templates required. Indeed, the number of templates needed could be a factor $\sim 4$ smaller than required by the usual approach, when the minimal overlap between the template bank and an arbitrary signal (the so-called {\it minimal match}) is 0.97. The method is amenable to easy implementation, and the various detector projects might benefit by adopting it to reduce the computational costs of inspiraling neutron star and black hole binary search.Comment: scheduled for publicatin on Phys. Rev. D 6

LISA data analysis: The monochromatic binary detection and initial guess problems

We consider the detection and initial guess problems for the LISA gravitational wave detector. The detection problem is the problem of how to determine if there is a signal present in instrumental data and how to identify it. Because of the Doppler and plane-precession spreading of the spectral power of the LISA signal, the usual power spectrum approach to detection will have difficulty identifying sources. A better method must be found. The initial guess problem involves how to generate {\it a priori} values for the parameters of a parameter-estimation problem that are close enough to the final values for a linear least-squares estimator to converge to the correct result. A useful approach to simultaneously solving the detection and initial guess problems for LISA is to divide the sky into many pixels and to demodulate the Doppler spreading for each set of pixel coordinates. The demodulated power spectra may then be searched for spectral features. We demonstrate that the procedure works well as a first step in the search for gravitational waves from monochromatic binaries.Comment: 8 pages, 8 figure

Time-frequency detection of Gravitational Waves

We present a time-frequency method to detect gravitational wave signals in interferometric data. This robust method can detect signals from poorly modeled and unmodeled sources. We evaluate the method on simulated data containing noise and signal components. The noise component approximates initial LIGO interferometer noise. The signal components have the time and frequency characteristics postulated by Flanagan and Hughes for binary black hole coalescence. The signals correspond to binaries with total masses between $45 M_\odot$ to $70 M_\odot$ and with (optimal filter) signal-to-noise ratios of 7 to 12. The method is implementable in real time, and achieves a coincident false alarm rate for two detectors $\approx$ 1 per 475 years. At this false alarm rate, the single detector false dismissal rate for our signal model is as low as 5.3% at an SNR of 10. We expect to obtain similar or better detection rates with this method for any signal of similar power that satisfies certain adiabaticity criteria. Because optimal filtering requires knowledge of the signal waveform to high precision, we argue that this method is likely to detect signals that are undetectable by optimal filtering, which is at present the best developed detection method for transient sources of gravitational waves.Comment: 24 pages, 5 figures, uses REVTE

Gravitational waves from inspiraling compact binaries: Second post-Newtonian waveforms as search templates

We ascertain the effectiveness of the second post-Newtonian approximation to the gravitational waves emitted during the adiabatic inspiral of a compact binary system as templates for signal searches with kilometer-scale interferometric detectors. The reference signal is obtained by solving the Teukolsky equation for a small mass moving on a circular orbit around a large nonrotating black hole. Fitting factors computed from this signal and these templates, for various types of binary systems, are all above the 90% mark. According to Apostolatos' criterion, second post-Newtonian waveforms should make acceptably effective search templates.Comment: LaTeX, one eps figure. Hires and color versions are available from http://jovian.physics.uoguelph.ca/~droz/uni/papers/search.htm