To date, no neutrinos with energies in or above the GeV range have been identified from astrophysical objects. The aim of the two analyses described in this dissertation is to observe high-energy muon neutrinos from Gamma Ray Bursts (GRBs). GRBs are distant sources, which were discovered by satellites recording their flashes of high-energy electromagnetic radiation. In some cases, the gamma-ray flashes are followed by lower energy radiation. GRBs are observed to have a well localized position and a short duration. This allows us to reduce the background in searching the data of the AMANDA/IceCube detector for a possible signal. As no detection of those highly energetic neutrinos has succeeded so far, we aim to analyze our data in a rather unbiased way and limit the dependence on theoretical modelling of the GRB engine. To this end we filter the data using parameters which depend only weakly on the neutrino energy spectrum (unlike a previous analysis in Achterberg et al. (2007)). Besides this, we allow for a possible time di erence between the arrival time of the prompt photon emission and the neutrino signal: our analyses are sensitive to signals arriving within one hour of the satellite trigger time (whereas previous analyses followed an approach which is only sensitive for signals within ten minutes centered around the arrival of the prompt -s (Achterberg et al. 2008)). The two separate analyses presented here di er in one important aspect: in the analysis of the specific burst GRB080319B we analyze the data of one single GRB event for the presence of neutrinos from this GRB. The central assumption is that this ”brightest GRB observed to date” might produce a high-energy neutrino flux which is significantly higher than the average GRB neutrino flux. (This approach was also followed in the analysis of the data of GRB030329 (Stamatikos & et al. 2005).) The second analysis we present is based on stacking the data of multiple GRBs (with average properties) to cope with low fluxes. The directional and timing information of the GRBs used in our analyses is taken from these sources. As we do not use complex spectral information and the required resolution on time and location is moderate, we can incorporate the information of various experiments. Most of the GRBs in our sample were observed by the Swift satellite, others by Fermi, Integral, SuperAgile or IPN (the InterPlanetary Network). In chapter 2 we briefly outline the leading GRB models and discuss to what extent our analyses depend on model assumptions. In chapter 3 we give the characteristics of our detector. Subsequently in chapter 4 we provide all details on how we calibrate the detector and process the data. The method we will use to assess the significance of our observations is outlined in chapter 5. The details of the analyses themselves are given in chapters 6 and 7. We discuss the results in chapter 8
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