Detecting a Non-gaussian Stochastic Background of Gravitational Radiation

Consider a large collection of similar gravitational wave sources. If we cannot resolve the individual signals produced by these sources and know only their statistical properties, the signals form a stochastic background. We group stochastic backgrounds into the following two classes: those for which the individual sources have (i) average redshift z ≫ 1 and (ii) average redshift z ∼ 1. Typically in case (i) the number of individual sources is large enough that the duration of events is long compared to the time between events, and then the central limit theorem enforces Gaussianity of the background. However, for some sources in case (ii) the anticipated number of individual sources might be small enough that this argument breaks down and a non-Gaussian stochastic background might be expected. Examples of (ii) are supernovae, binary inspirals, and young neutron stars. Well developed data analysis methods exist for detecting Gaussian backgrounds. Here we derive a data analysis method for a non-Gaussian background under idealized assumptions; further work is needed to obtain realistic detection methods. Assume a pair of co-located, aligned detectors with outputs hi = n k i + s k (i = 1, 2) of uncorrelated Gaussian noise ni and possibly a stochastic background signal s. Here i labels the detectors and k with 1 ≤ k ≤ N labels the time samples of the detector output. We assume the following probability distribution for the stochastic background signal: