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The Crab supernova remnant has been observed regularly with the stereoscopic system of 5 imaging air Cherenkov telescopes that was part of the High Energy Gamma Ray Astronomy (HEGRA) experiment. In total, close to 400 hours of useful data have been collected from 1997 until 2002. The spectrum extends up to energies of 80 TeV and is well matched by model calculations in the framework of inverse Compton scattering of various seed photons in the nebula including for the first time a recently detected compact emission region at mm-wavelengths. The observed indications for a gradual steepening of the energy spectrum in data is expected in the inverse Compton emission model.The average magnetic field in the emitting volume is determined to be $(161.6\pm0.8mathrm{stat}\pm18_\mathrm{sys}) \mu$G. The presence of protons in the nebula is not required to explain the observed flux and upper limits on the injected power of protons are calculated being as low as 20 % of the total spin down luminosity for bulk Lorentz factors of the wind in the range of $10^4-10^6$.The position and size of the emission region have been studied over a wide range of energies. The position is shifted by 13\arcsec to the west of the pulsar with a systematic uncertainty of 25\arcsec. No significant shift in the position with energy is observed. The size of the emission region is constrained to be less than 2\arcmin at energies between 1 and 10 TeV. Above 30 TeV the size is constrained to be less than 3\arcmin.No indications for pulsed emission has been found and upper limits in differential bins of energy have been calculated reaching typically 1-3 % of the unpulsed component., Comment: 53 pages, 12 figures. Accepted for publication in Astrophysical Journal

In this paper we present the results of simultaneous observations of the TeV blazar Markarian 421 (Mrk 421) at X-ray and TeV Gamma-ray energies with the Rossi X-Ray Timing Explorer (RXTE) and the stereoscopic Cherenkov Telescope system of the HEGRA (High Energy Gamma Ray Astronomy) experiment, respectively. The source was monitored from February 2nd to February 16th and from May 3rd to May 8th, 2000. We discuss in detail the temporal and spectral properties of the source. Remarkably, the TeV observations of February 7th/8th showed statistically significant evidence for substantial TeV flux variability on 30 min time scale. We show the results of modeling the data with a time dependent homogeneous Synchrotron Self-Compton (SSC) model. The X-ray and TeV gamma-ray emission strengths and energy spectra together with the rapid flux variability strongly suggest that the emission volume is approaching the observer with a Doppler factor of 50 or higher. The different flux variability time scales observed at X-rays and TeV Gamma-rays indicate that a more detailed analysis will require inhomogeneous models with several emission zones.

During 1997, the BL Lac object Mkn 501 went into an extraordinary state of high X-ray and TeV gamma-ray activity, lasting more than 6 months. In this paper we report on the TeV emission characteristics of the source in the subsequent years of 1998 and 1999 as measured with the Stereoscopic Cherenkov Telescope System of HEGRA (La Palma, Canary Islands). Our observations reveal a 1998-1999 mean emission level at 1 TeV of 1/3 of the flux of the Crab Nebula, a factor of 10 lower than during the year of 1997. A dataset of 122 observations hours with the HEGRA telescope system makes it possible to assess for the first time the Mkn 501 TeV energy spectrum for a mean flux level substantially below that of the Crab Nebula with reasonable statistical accuracy. Excluding the data of a strong flare, we find evidence that the 1998--1999 low-flux spectrum is substantially softer (by 0.44+-0.1(stat) in spectral index) than the 1997 time averaged spectrum. The 500 GeV to 10 TeV energy spectrum can well be described by a power law model with exponential cutoff: dN/dE ~ E^(-alpha) exp(-E/E0) with alpha=2.31+-0.22(stat), and E0=5.1 (-2.3+7.8)(stat) TeV. Within statistical accuracy, also a pure power law model gives an acceptable fit to the data: dN/dE ~ E^(-Gamma) with Gamma=2.76+-0.08(stat). After presenting the 1998-1999 TeV characteristics of the source we discuss the implications of the results., Accepted for publication in The Astrophysical Journal, Part 1, on August 4th, 2000