We construct a turbulent model of the Crab Nebula’s nonthermal emission. The present model resolves a number of long-standing problems of the Kennel–Coroniti model: (i) the sigma problem, (ii) the hard spectrum of radio electrons, (iii) the high peak energy of gamma-ray flares, (iv) and the spatial evolution of the infrared (IR) emission. The Nebula contains two populations of injected particles: Component-I, accelerated at the wind termination shock via the Fermi-I mechanism; and Component-II, accelerated in reconnecting turbulence in highly magnetized (σ ≫ 1) plasma in the central part of the Crab Nebula. The reconnecting turbulence in Component-II extends from radio to gamma-rays: it accelerates radio electrons with a hard spectrum, destroys 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 broadband spectrum of the Crab Nebula, from low-frequency synchrotron emission in radio to inverse-Compton emission at TeV energies, as well as the spatially resolved evolution of the spectral indices in the IR and optical bands.

We have developed a model of early X-ray afterglows of gamma-ray bursts originating from the reverse shock (RS) propagating through ultrarelativistic, highly magnetized pulsar-like winds produced by long-lasting central engines. We first performed fluid and magnetohydrodynamic numerical simulations of relativistic double explosions. We demonstrate that even for constant properties of the wind a variety of temporal behaviors can be produced, depending on the energy of the initial explosion and the wind power, the delay time for the switch-on of the wind, and the magnetization of the wind. X-ray emission of the highly magnetized RS occurs in the fast-cooling regime—this ensures high radiative efficiency and allows fast intensity variations. We demonstrate that (i) RS emission naturally produces light curves, showing power-law temporal evolution with various temporal indices; (ii) mild wind power, of the order of ∼1046 erg s−1 (equivalent isotropic), can reproduce the afterglows’ plateau phase; (iii) termination of the wind can produce sudden steep decays; and (iv) short-duration afterglow flares are due to mild variations in the wind luminosity, with small total injected energy.

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Afterglows of gamma-ray bursts often show flares, plateaus, and sudden intensity drops: these temporal features are difficult to explain as coming from the forward shock. We calculate radiative properties of early GRB afterglows with the dominant contribution from the reverse shock (RS) propagating in an ultra-relativistic (pulsarlike) wind produced by the long-lasting central engine. RS emission occurs in the fast cooling regime -this ensures high radiative efficiency and allows fast intensity variations. We demonstrate that: (i) mild wind power, of the order of ∼ 10 46 erg s −1 , can reproduce the afterglows' plateau phase; (ii) termination of the wind can produce sudden steep decays; (iii) mild variations in the wind luminosity can produce short-duration afterglow flares.