We construct a turbulent model of the Crab Nebulas non-thermal emission. The present model resolves a number of long-standing problems of the Kennel-Coroniti (1984) model: (i) the sigma problem; (ii) the hard spectrum of radio electrons; (iii) the high peak energy of gamma-ray flares; (iv) and the spacial evolution of the infrared (IR) emission. The Nebula contains two populations of injected particles: Component-I accelerated at the wind termination shock via Fermi-I mechanism, and Component-II accelerated in reconnecting turbulence in highly magnetized ($sigma$ $gg 1$) plasma in the central part of the Crab Nebula. The reconnecting turbulence Component-II extends from radio to gamma rays: it accelerate radio electrons with a hard spectrum, destroy the large scale magnetic flux (and thus resolves the sigma-problem), and occasionally produces gamma-ray flares (from the largest scale reconnection events). The model reproduces the broad-band spectrum of the Crab Nebula, from low-frequency synchrotron emission in radio to inverse-Compton emission at TeV energies, as well as spatially resolved evolution of the spectral indices in IR and optical bands.
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