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].
