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Appendix A: GRB selection

The table of the Swift satellite⁷ contains data from the three on-board instruments BAT (gamma rays), XRT (X-rays), and UVOT (ultraviolet), ordered with increasing position-measurement accuracy from arcminutes to sub-arcseconds. The information provides BAT spectral measurements in the energy range from 15 to 150keV. The Swift BAT2 Catalogue (Sakamoto et al. 2011)⁸ provides re-analysed Swift data, so the spectral information therein is considered to be more accurate. The Fermi GBM Burst Catalogue⁹ (Goldstein et al. 2012; Paciesas et al. 2012) supplies the best spectral information in the energy range from 10keV to 1MeV: the peak flux spectrum and the spectrum averaged over the burst duration (which is eventually used for the neutrino spectrum calculation) is fitted with four different spectral functions. The angular resolution is of the order of degrees. The IceCube Collaboration also provides a table with GRB parameters¹⁰ (Aguilar 2011), which is created by parsing the Gamma-ray Coordinates Network (GCN) notices¹¹. This table is used to fill up missing parameter values for GRBs that have been found in at least one of the other tables.

When merging the information on the GRB parameters, we assigned priorities to the measured values according to their considered accuracy. The priorities of parameters are shown in Table A.1 in square brackets, as well as the percentage of how often information was obtained from each source.

When a parameter could not be measured, standard values as given in Table A.2 were used to calculate the spectra. The form of the photon spectrum is determined by the spectral indices α and β with the break energy ϵ_peak giving their transition. The isotropic luminosity L_iso can be calculated from the redshift z and the total measured fluence in gamma rays ℱ (given in the energy range from E_min to E_max) via with the luminosity distance d_L. In case of unknown redshift z, we took the default value of L_iso. T₉₀ is the time in which 90% of the fluence is emitted. The other parameters such as the jet Lorentz boost factor Γ, the fraction of jet energy in electrons ϵ_e and in the magnetic field ϵ_B, the ratio of energy in electrons and protons f_e, the average fraction of proton energy transferred to a pion ⟨ x_p → π ⟩ and the variability of the gamma-ray light curve t_var are not present in the tables and hence were taken as default. The standard values are the same as given in Aguilar (2011), with some differences to the IC 22 (Abbasi et al. 2010) default values: z = 2.0, Γ = 300, L_iso = 10⁵¹ergs^-1. Baerwald et al. (2012) give a very elaborate overview about the NeuCosmA spectra changing with the input parameters.

The parameters of the extraordinarily strong GRB 110918 are presented in Table A.3.

The time window of the search, T_search, for emission from each burst is delineated by the start and stop times as measured by the satellites or, when these are not provided in the catalogues, as T₉₀ ± 30%. Additionally, we accounted for the detector’s data acquisition uncertainty (0.4s), the satellite time given in integer seconds (1s), and the light propagation from a satellite through Earth to the detector (0.5s) by adding another ± 2s to the search-time window.

Appendix B: Background estimation

We estimated the background event rate for each GRB separately. First, the time-averaged reconstructed event rate in the data from late 2007 to 2011 from the direction of the GRB was estimated. Either the rate averaged over all data-taking runs at the GRB’s position (θ,φ)_GRB was used, or – if resulting in a higher rate – the mean of the corresponding time-averaged rates within a 10° cone around this position. This establishes a conservative background estimate, accounting for non-uniformity of the background in the vicinity of the GRB’s position.

To take into account the varying efficiency of the detector with time, this average rate was then scaled by a correction factor c_i for each data-taking run i of ~2.5 h. Each c_i was calculated by the ratio of the total number of events (in all directions) in the corresponding run n_i to the average total number of events for the respective run duration t_i (see Eq. (B.1)). As n_i may be very small for short runs, the 90% C.L. upper limit was used instead. Additionally, factors for specific run periods c_period were applied taking into account differences between longer phases of similar run conditions. These values were obtained by fitting the background rate in certain periods separately. This approach assumes that the total number of events – dominated mostly by downgoing atmospheric muons – is proportional to the number of upgoing events. To test this assumption, we determined the measured and estimated rates of upgoing events in longer time periods of a few days, excluding data-taking runs in which GRBs occurred. The measured rate was always found to be μ_meas < 1.5  μ_est, thus we conservatively increased the estimate by 50%. Consequently, the expected number of background events in coincidence with each GRB search-time window T_search was calculated via (B.1)with , where j includes all data-taking runs.

© ESO, 2013