Bounding the Time Delay between High-energy Neutrinos and Gravitational-wave Transients from Gamma-ray Bursts

We derive a conservative coincidence time window for joint searches of gravita-tional-wave (GW) transients and high-energy neutrinos (HENs, with energies above 100GeV), emitted by gamma-ray bursts (GRBs). The last are among the most interesting astrophysical sources for coincident detections with current and near-future detectors. We take into account a broad range of emission mechanisms. We take the upper limit of GRB durations as the 95% quantile of the T90's of GRBs observed by BATSE, obtaining a GRB duration upper limit of ~150s. Using published results on high-energy (>100MeV) photon light curves for 8 GRBs detected by Fermi LAT, we verify that most high-energy photons are expected to be observed within the first ~150s of the GRB. Taking into account the breakout-time of the relativistic jet produced by the central engine, we allow GW and HEN emission to begin up to 100s before the onset of observable gamma photon production. Using published precursor time differences, we calculate a time upper bound for precursor activity, obtaining that 95% of precursors occur within ~250s prior to the onset of the GRB. Taking the above different processes into account, we arrive at a time window of tHEN - tGW ~ [-500s,+500s]. Considering the above processes, an upper bound can also be determined for the expected time window of GW and/or HEN signals coincident with a detected GRB, tGW - tGRB ~ tHEN - tGRB ~ [-350s,+150s]