The Crab Nebula as a standard candle in very high-energy astrophysics

The continuum high-energy gamma-ray emission between 1 GeV and 10(5) GeV from the Crab Nebula has been measured for the first time in overlapping energy bands by the Fermi large-area telescope (Fermi/LAT) below approximate to 100 GeV and by ground-based imaging air Cherenkov telescopes (IACTs) above approximate to 60 GeV. To follow up on the phenomenological approach suggested by Hillas et al. (1998), the broad band spectral and spatial measurement (from radio to low-energy gamma-rays <1 GeV) is used to extract the shape of the electron spectrum. While this model per construction provides an excellent description of the data at energies <1 GeV, the predicted inverse Compton component matches the combined Fermi/LAT and IACT measurements remarkably well after including all relevant seed photon fields and fitting the average magnetic field to B = (124 +/- 6 (stat.)(-6)(+15) (sys.)) mu G. The close match of the resulting broad band inverse Compton component with the combined Fermi/LAT and IACTs data is used to derive instrument specific energy-calibration factors. These factors can be used to combine data from Fermi/LAT and IACTs without suffering from systematic uncertainties on the common energy scale. As a first application of the cross calibration, we derive an upper limit to the diffuse gamma-ray emission between 250 GeV and 1 TeV based upon the combined measurements of Fermi/LAT and the H. E. S. S. ground-based Cherenkov telescopes. Finally, the predictions of the magneto-hydrodynamic flow model of Kennel & Coroniti (1984) are compared to the measured SED.