The Spectrum of TeV Gamma Rays from the Crab Nebula

The spectrum of gamma rays from the Crab Nebula has been measured in the energy range 500 GeV-8 TeV at the Whipple Observatory by the atmospheric Cerenkov technique. Two methods of analysis that were used to derive spectra, in order to reduce the chance of calibration errors, gave good agreement, as did analysis of observations made with changed equipment several years apart. It is concluded that stable and reliable energy spectra can now be made in the TeV range. The spectrum can be represented in this energy range by the power-law fit, J = (3.20 +/- 0.17 +/- 0.6) x 10(-7) x (E/1 TeV)(-2.49+/-0.06+/-0.04) m(-2) s(-1) TeV-1, or by the following form, which extends much better to the GeV domain: J = (3.25 +/- 0.14 +/- 0.6) x 10(-7)E(-2.44+/-0.06+/-0.04-0.151 log10 E) m(-2) s(-1) TeV-1 (E in TeV). The integral flux above 1 TeV is (2.1 +/- 0.2 +/- 0.3) x 10(-7) m(-2) s(-1). Using the complete spectrum of the Crab Nebula, the spectrum of relativistic electrons is deduced, and the spectrum of the inverse Compton emission that they would generate is in good agreement with the observed gamma-ray flux from 1 GeV to many TeV, if the magnetic field in the region where these scattered photons originate (essentially the X-ray-emitting region, around 0.4 pc from the pulsar) is similar to 16 nT (160 mu G), in reasonable agreement with the held deduced by Aharonian & Atoyan. If the same field strength were present throughout the nebula, there would be no clear need for an additional radiation source in the GeV domain such as has recently been suggested; the results give an indication that the magnetic field is well below the often-assumed equipartition strength (35-60 nT). Further accurate gamma-ray spectral measurements over the range from 1 GeV to tens of TeV have the potential to probe the growth in the magnetic field in the inner region of the nebula.