Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities

TL;DR

This paper develops the full statistical framework for detecting a stochastic gravitational-wave background with a network of laser interferometers. It derives the optimal cross-correlation filter, captures the impact of detector geometry through the overlap reduction function, and provides explicit SNR and Omega_gw sensitivity formulas, including extensions to nonstationary noise and multi-detector networks. The authors implement a computer simulation to validate the theory and supply detailed numerical data for major detectors, highlighting practical sensitivities and guiding detector design and data analysis. The work lays out a rigorous frequentist approach to detection, parameter estimation, and multi-detector synthesis, with clear implications for current and future gravitational-wave experiments.

Abstract

We analyze the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. Starting with basic assumptions about the statistical properties of a stochastic gravity-wave background, we derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation of the outputs of two gravity-wave detectors. Sensitivity levels required for detection are then calculated. Issues related to: (i) calculating the signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii) performing the data analysis in the presence of nonstationary detector noise, (iii) combining data from multiple detector pairs to increase the sensitivity of a stochastic background search, (iv) correlating the outputs of 4 or more detectors, and (v) allowing for the possibility of correlated noise in the outputs of two detectors are discussed. We briefly describe a computer simulation which mimics the generation and detection of a simulated stochastic gravity-wave signal in the presence of simulated detector noise. Numerous graphs and tables of numerical data for the five major interferometers (LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. The treatment given in this paper should be accessible to both theorists involved in data analysis and experimentalists involved in detector design and data acquisition.

Figures (30)

• Figure 1: A log-log plot of the predicted noise power spectra for the initial and advanced LIGO detectors. The data for these noise power spectra were taken from the published design goals science92.
• Figure 2: The overlap reduction function $\gamma(f)$ for the Hanford, WA and Livingston, LA LIGO detector pair. (The horizontal axis of the left-hand graph is linear, while that of the right-hand graph is $\rm log_{10}$.) The overlap reduction function has its first zero at 64 Hz, as explained in the text. It falls off rapidly at higher frequencies.
• Figure 3: The surface of the earth ($15^\circ<{\rm latitude}< 75^\circ$, $-130^\circ <{\rm longitude}<20^\circ$) including the LIGO detectors in Hanford, WA (L1) and Livingston, LA (L2), the VIRGO detector (V) in Pisa, Italy, and the GEO-600 (G) detector in Hanover, Germany. The perpendicular arms of the LIGO detectors are also illustrated (though not to scale). A plane gravitational wave passing by the earth is indicated by successive minimum, zero, and maximum of the wave. As this wave passes by the pair of LIGO detectors, it excites the two in coincidence at the moment shown, since both detectors are driven negative by the wave. During the time when the zero is between L1 and L2, the two detectors respond in anti-coincidence. Provided that the wavelength of the incident gravitational wave is larger than twice the separation ($d=3001$ km) between the detectors, the two detectors are driven in coincidence more of the time than in anti-coincidence.
• Figure 4: Optimal filter functions $\tilde{Q}(f)$ for the initial and advanced LIGO detector pairs, for a stochastic background having a constant frequency spectrum $\Omega_{\rm gw}(f) =\Omega_0$. Both filters are normalized to have maximum magnitude equal to unity.
• Figure 5: Optimal filter functions $Q(t-t')$ for the initial and advanced LIGO detector pairs, for a stochastic background having a constant frequency spectrum $\Omega_{\rm gw}(f) =\Omega_0$. Both filters are normalized to have maximum magnitude equal to unity.