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

The continuum high-energy gamma-ray emission between 1 GeV and 100 TeV from the Crab Nebula has been measured for the first time in overlapping energy bands by the Fermi large-area telescope (Fermi/LAT) below ~ 100 GeV and by ground-based imaging air Cherenkov telescopes (IACTs) above ~ 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.) +15 / -6 (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.