Detecting an association between gamma ray and gravitational wave bursts

If $\gamma$-ray bursts (GRBs) are accompanied by gravitational wave bursts (GWBs) the correlated output of two gravitational wave detectors evaluated in the moments just prior to a GRB will differ from that evaluated at other times. We can test for this difference without prior knowledge of either the GWB wave form or the detector noise spectrum. With a model for the GRB source population and GWB spectrum we can put a limit on the in-band rms GWB signal amplitude. Laser-Interferometer Gravitational Wave Observatory I detector observations coincident with 1000 GRB observations could lead us to exclude with 95% confidence associated GWBs with $h_{\mathrm{RMS}}\gtrsim 1.7\times {10}^{-22}.$