We develop a simple one-zone model of the steady-state Crab nebula spectrum encompassing both the radio/soft X-ray and the GeV/multi-TeV observations. By solving the transport equation for GeV-TeV electrons injected at the wind termination shock as a log-parabola momentum distribution and evolved via energy losses, we determine analytically the resulting differential energy spectrum of photons. We find an impressive agreement with the observed spectrum of synchrotron emission, and the synchrotron self-Compton component reproduces the previously unexplained broad 200-GeV peak that matches the Fermi/Large Area Telescope (LAT) data beyond 1 GeV with the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) data. We determine the parameters of the single log-parabola electron injection distribution, in contrast with multiple broken power-law electron spectra proposed in the literature. The resulting photon differential spectrum provides a natural interpretation of the deviation from power law customarily fitted with empirical multiple broken power laws. Our model can be applied to the radio-to-multi-TeV spectrum of a variety of astrophysical outflows, including pulsar wind nebulae and supernova remnants, as well as to interplanetary shocks.Key words: acceleration of particles -shock waves -cosmic rays -ISM: supernova remnants.
I N T RO D U C T I O NCurrent theoretical models of the overall spectral energy distribution (SED) of the Crab nebula fail in reproducing both the peak in the very high energy (hereafter VHE) range and the radio/X-ray data with a single and physically justified population of accelerated particles. The photon differential spectrum from ground-based observatories, i. is consistent with a log-parabola distribution in the range ∼50 GeV up to 100 TeV. However, the joint photon differential spectrum matching the VHE observations of MAGIC (0.05-30 TeV) with the Fermi/LAT spectrum in the range 1-200 GeV exhibits a broad and flat peak that is fit (Aleksić et al. 2015) by a modified log-parabola with an additional ad hoc free parameter. Such a VHE spectrum cannot originate from an electron-positron spectrum evolved from the standard power-law distribution of shock-accelerated energetic particles; however, no attempt has been reported so far to reconstruct the electron-positron source spectrum.The VHE emission of the Crab nebula is usually modelled with inverse Compton (hereafter IC) radiation from a non-thermal population of electron-positron pairs via scattering of three possible E-mail: ffrasche@lpl.arizona.edu (FF); marpohl@uni-potsdam.de (MP) photon targets: synchrotron radiation emitted by the same electronpositron population within the nebula (synchrotron self-Compton) in the spectral range from the optical to X-rays, thermal far-infrared radiation (typically associated with dust) and cosmic microwave background (CMB) radiation. A variety of radiation processes proposed to explain the broad-band spectrum of the Crab pulsar wind nebula (PWN) seems to fail in matching the VHE emission with th...