We present the results of searches for high-energy muon neutrinos from 41 gamma-ray bursts ( GRBs ) in the northern sky with the IceCube detector in its 22-string configuration active in 2007/2008 .
The searches cover both the prompt and a possible precursor emission as well as a model-independent , wide time window of -1 h to +3 h around each GRB .
In contrast to previous searches with a large GRB population , we do not utilize a standard Waxman–Bahcall GRB flux for the prompt emission but calculate individual neutrino spectra for all 41 GRBs from the burst parameters measured by satellites .
For all three time windows the best estimate for the number of signal events is zero .
Therefore , we place 90 % CL upper limits on the fluence from the prompt phase of 3.7 \times 10 ^ { -3 } \mathrm { erg } \mathrm { cm } ^ { -2 } ( 72 TeV – 6.5 PeV ) and on the fluence from the precursor phase of 2.3 \times 10 ^ { -3 } \mathrm { erg } \mathrm { cm } ^ { -2 } ( 2.2 TeV – 55 TeV ) , where the quoted energy ranges contain 90 % of the expected signal events in the detector .
The 90 % CL upper limit for the wide time window is 2.7 \times 10 ^ { -3 } \mathrm { erg } \mathrm { cm } ^ { -2 } ( 3 TeV – 2.8 PeV ) assuming an E ^ { -2 } flux .