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 \approx 100 GeV and by ground-based imaging air Cherenkov telescopes ( IACTs ) above \approx 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 = \left ( 124 { } \pm 6 \mathrm { ( stat . ) } { } ^ { +15 } _ { -6 } \mathrm { ( sys . ) } \right ) % \mu \mathrm { 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 .