Cross-correlation method for intermediate-duration gravitational wave searches associated with gamma-ray bursts

Several models of gamma-ray burst progenitors suggest that the gamma-ray event may be followed by gravitational wave signals of $10^3$-$10^4$ seconds duration (possibly accompanying the so-called X-ray afterglow "plateaus"). We term these signals "intermediate-duration" because they are shorter than continuous wave signals but longer than signals traditionally considered as gravitational wave bursts, and are difficult to detect with most burst and continuous wave methods. The cross-correlation technique proposed by [S. Dhurandhar et al., Phys. Rev. D 77, 082001 (2008)], which so far has been used only on continuous wave signals, in principle unifies both burst and continuous wave (as well as matched filtering and stochastic background) methods, reducing them to different choices of which data to correlate on which time scales. Here we perform the first tuning of this cross-correlation technique to intermediate-duration signals. We derive theoretical estimates of sensitivity in Gaussian noise in different limits of the cross-correlation formalism, and compare them to the performance of a prototype search code on simulated Gaussian-noise data. We estimate that the code is likely able to detect \emph{some} classes of intermediate-duration signals (such as the ones described in [A. Corsi \& P. M\'esz\'aros, Astrophys. J., 702, 1171 (2009)]) from sources located at astrophysically-relevant distances of several tens of Mpc.