We present the results for a search of high-energy muon neutrinos with the IceCube detector in coincidence with the Crab nebula flare reported on September 2010 by various experiments. Due to the unusual flaring state of the otherwise steady source we performed a prompt analysis of the 79-string configuration data to search for neutrinos that might be emitted along with the observed gamma-rays. We performed two different and complementary data selections of neutrino events in the time window of 10 days around the flare. One event selection is optimized for discovery of E^-2 neutrino spectrum typical of 1st order Fermi acceleration. A similar event selection has also been applied to the 40-string data to derive the time-integrated limits to the neutrino emission from the Crab. The other event selection was optimized for discovery of neutrino spectra with softer spectral index and TeV energy cut-offs as observed for various galactic sources in gamma-rays. The 90% CL best upper limits on the Crab flux during the 10 day flare are 4.73 x 10^-11 cm-2 s-1 TeV-1 for an E^-2 neutrino spectrum and 2.50 x 10^-10 cm-2 s-1 TeV-1 for a softer neutrino spectra of E-2.7, as indicated by Fermi measurements during the flare. IceCube has also set a time-integrated limit on the neutrino emission of the Crab using 375.5 days of livetime of the 40-string configuration data. This limit is compared to existing models of neutrino production from the Crab and its impact on astrophysical parameters is discussed. The most optimistic predictions of some models are already rejected by the IceCube neutrino telescope with more than 90% CL.
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