Excess power statistic for detection of burst sources of gravitational radiation

We examine the properties of an excess power method to detect gravitational waves in interferometric detector data. This method is designed to detect short-duration (≲0.5 s) burst signals of unknown waveform, such as those from supernovae or black hole mergers. If only the bursts’ duration and frequency band are known, the method is an optimal detection strategy in both Bayesian and frequentist senses. It consists of summing the data power over the known time interval and frequency band of the burst. If the detector noise is stationary and Gaussian, this sum is distributed as a χ² (non-central χ²) deviate in the absence (presence) of a signal. One can use these distributions to compute frequentist detection thresholds for the measured power. We derive the method from Bayesian analyses and show how to compute Bayesian thresholds. More generically, when only upper and/or lower bounds on the bursts duration and frequency band are known, one must search for excess power in all concordant durations and bands. Two search schemes are presented and their computational efficiencies are compared. We find that given reasonable constraints on the effective duration and bandwidth of signals, the excess power search can be performed on a single workstation. Furthermore, the method can be almost as efficient as matched filtering when a large template bank is required: for Gaussian noise the excess power method can detect a source to a distance at least half of the distance detectable by matched filtering if the product of duration and bandwidth of the signals is ≲100, and to a much greater fraction of the distance when the size of the matched filter bank is large. Finally, we derive generalizations of the method to a network of several interferometers under the assumption of Gaussian noise. However, further work is required to determine the efficiency of the method in the realistic context of a detector network with non-Gaussian noise.