High energy tails of pulsar gamma-ray emission

We perform spectral analyses of four bright $\gamma$-ray pulsars: PSR J0007+7303, Vela, Geminga and PSR J2021+3651 concentrating on the high-energy tails, defined as emission above 10\,GeV. The two competing models of pulsar $\gamma$-ray emission predict qualitatively different spectra well above the break energy: curvature emission predicts an exponential cut-off in the spectra, while the inverse-Compton scattering mechanism favors a power-law. We perform fits to the phase-averaged spectral energy distributions for each of the four pulsars. We find that in all cases both models fit the data equally well---the present data set does not allow any firm claim to be made about the shape of the spectra above 10\,GeV. In no case is the power-law fit or exponential cut-off fit significantly preferred over the other. The Crab pulsar remains the only known pulsar in which the power-law fit is clearly preferred over the exponential cut-off.