Compton scattering and the gamma-ray power-law spectrum in Markarian 421

The nearest BL Lac object, Mrk 421, has a gamma-ray spectrum which is approximately flat in EF-sub E from E less than about 50 MeV to E greater than about 1 TeV. Inverse Compton scattering can explain this smooth spectrum, despite the structure in the Klein-Nishina cross section, if the injected electron distribution function is proportional to gamma exp -2, where gamma is the electron Lorentz factor. When this is the case, the structure imprinted on the steady state electron distribution function by the structure in the Klein-Nishina cross section is almost exactly compensated in the radiated spectrum. Because particle acceleration in strong shocks injects particles with this distribution function, this shape injection function is in fact quite plausible. Other blazars may be explained by the same model if the cutoff below TeV energies observed in other objects is due to pair production on the cosmological IR background, as suggested by Stecker et al. (1992).