Observations of the Crab nebula with HESS

Context.The Crab nebula was observed with the HESS stereoscopic Cherenkov-telescope array between October 2003 and January 2005 for a total of 22.9 h (after data quality selection). This period of time partly overlapped with the commissioning phase of the experiment; 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. Aims.Observations of the Crab nebula are discussed and used as an example to detail the flux and spectral analysis procedures of HESS. The results are used to evaluate the systematic uncertainties in HESS flux measurements. Methods.The Crab nebula data are analysed using standard HESS analysis procedures, which are described in detail. 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. Results.The data, taken at a range of zenith angles between $45^{\circ}$ and $65^{\circ}$, show a clear signal with over 7500 excess events. The energy spectrum is found to follow a power law with an exponential cutoff, with photon index $\Gamma = 2.39$ $\pm$ $0.03_{{\rm {stat}}}$ and cutoff energy $E_{\rm c} = (14.3 \pm 2.1_{{\rm {stat}}})~{\rm TeV}$ between 440 GeV and 40 TeV. The observed integral flux above 1 TeV is $(2.26 \pm 0.08_{{\rm {stat}}}) \times 10^{-11}~{{\rm cm}^{-2}~{\rm s}^{-1}}$. 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.