The gamma-ray spectrum of Geminga and the inverse Compton model of pulsar high energy emission

We reanalyze the Fermi spectra of the Geminga and Vela pulsars. We find that the spectrum of Geminga above the break is exceptionally well approximated by a simple power law without the exponential cut-off, making Geminga's spectrum similar to that of Crab. Vela's broadband gamma-ray spectrum is equally well fit with both the exponential cut-off and the double power law shapes. In the broadband double power-law fits, for a typical Fermi spectrum of a bright \gamma-ray pulsar, most of the errors accumulate due to the arbitrary parametrization of the spectral roll-off. In addition, a power law with an exponential cut-off gives an acceptable fit for the underlying double power-law spectrum for a very broad range of parameters, making such fitting procedures insensitive to the underlying Fermi photon spectrum. Our results have important implications for the mechanism of pulsar high energy emission. A number of observed properties of \gamma-ray pulsars, i.e., the broken power law spectra without exponential cut-offs and stretching in case of Crab beyond the maximal curvature limit, spectral breaks close to or exceeding the maximal breaks due to curvature emission, a Crab patterns of relative intensities of the leading and trailing pulses repeated in the X-ray and \gamma-ray regions, all point to the inverse Compton origin of the high energy emission from majority of pulsars.