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 γ-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• and 65• , 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 Γ = 2.39 ± 0.03 stat and cutoff energy E c = (14.3 ± 2.1 stat ) TeV between 440 GeV and 40 TeV. The observed integral flux above 1 TeV is (2.26 ± 0.08 stat ) × 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.

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Observations of the Sagittarius dwarf spheroidal (Sgr dSph) galaxy were carried out with the H.E.S.S. array of four imaging air Cherenkov telescopes in June 2006. A total of 11 hours of high quality data are available after data selection. There is no evidence for a very high energy γ-ray signal above the energy threshold at the target position. A 95% C.L. flux limit of 3.6 × 10 −12 cm −2 s −1 above 250 GeV has been derived. Constraints on the velocity-weighted cross section σv are calculated in the framework of Dark Matter particle annihilation using realistic models for the Dark Matter halo profile of Sagittarius dwarf galaxy. Two different models have been investigated encompassing a large class of halo types. A 95% C.L. exclusion limit on σv of the order of 2 × 10 −25 cm 3 s −1 is obtained for a core profile in the 100 GeV -1 TeV neutralino mass range.

The detection of fast variations of the tera–electron volt (TeV) (10 12 eV) γ-ray flux, on time scales of days, from the nearby radio galaxy M87 is reported. These variations are about 10 times as fast as those observed in any other wave band and imply a very compact emission region with a dimension similar to the Schwarzschild radius of the central black hole. We thus can exclude several other sites and processes of the γ-ray production. The observations confirm that TeV γ rays are emitted by extragalactic sources other than blazars, where jets are not relativistically beamed toward the observer.