Observations of the Crab Nebula with H.E.S.S

The Crab nebula was observed with the H.E.S.S. stereoscopic Cherenkov-telescope array between October 2003 and January 2005 for a total of 22.9 hours (after data quality selection). Observations were made with three operational telescopes in late 2003 and with the complete 4 telescope array in January - February 2004 and October 2004 - January 2005. The observations are discussed and used as an example to detail the flux and spectral analysis procedures of H.E.S.S., and to evaluate the systematic uncertainties in H.E.S.S. flux measurements. The flux and spectrum of gamma-rays from the source are calculated on run-by-run and monthly time-scales, and a correction is applied for long-term variations in the detector sensitivity. Comparisons of the measured flux and spectrum over the observation period, along with the results from a number of different analysis procedures are used to estimate systematic uncertainties in the measurements. The energy spectrum is found to follow a power law with an exponential cutoff, with photon index $\Gamma = 2.39 \pm 0.03\stat$ and cutoff energy $E_{c} = (14.3 \pm 2.1\stat) \textrm{TeV}$ between 440 GeV and 40 TeV. The observed integral flux above 1 TeV is $(2.26 \pm 0.08\stat) \times 10^{-11} cm^{-2} s^{-1}$. The estimated systematic error on the flux measurement is estimated to be 20%, while the estimated systematic error on the spectral slope is 0.1.