Non-thermal emission from relativistic MHD simulations of pulsar wind nebulae: from synchrotron to inverse Compton

Aims. We develop a set of diagnostic tools for synchrotron-emitting sources, presented in a previous paper, to include a computation of inverse-Compton radiation from the same relativistic particles that give rise to the synchrotron emission. For the first time, we then study the gamma-ray emission properties of Pulsar Wind Nebulae, in the context of the axisymmetric jet-torus scenario. Methods. We evolve the relativistic MHD equations and the maximum energy of the emitting particles, including adiabatic and synchrotron losses along streamlines. The particle energy distribution function is split into two components: one corresponds to radio-emitting electrons, which are interpreted to be a relic population that is born at the outburst of the supernova, and the other is associated with a wind population that is continuously accelerated at the termination shock and emits up to the gamma-ray band. The inverse Compton emissivity is calculated using the general Klein-Nishina differential cross-section and three different photon targets for the relativistic particles are considered: the nebular synchrotron photons, photons associated with the far-infrared thermal excess, and the cosmic microwave background. Results. When the method is applied to the simulations that match the optical and X-ray morphology of the Crab Nebula, the overall synchrotron spectrum can only be fitted assuming an excess of injected particles and a steeper power law (E(-2.7)) with respect to previous models. The resulting TeV emission has then the correct shape but is in excess of the data. This is related to the magnetic-field structure in the nebula, derived using simulations: in particular, the field is strongly compressed close to the termination shock, but with a lower than expected volume average. The jet-torus structure is also found to be visible clearly in high-resolution gamma-ray synthetic maps. We present a preliminary exploration of time variability in X- and gamma-rays. We find variations with timescales of about 2 years in both bands. The variability observed originates in the strongly time-dependent MHD motions inside the nebula.