Magnetic energy dissipation and origin of non-thermal spectra in radiatively efficient relativistic sources

Abstract

The dissipation of turbulent magnetic fields is an appealing scenario to explain the origin of non-thermal particles in high-energy astrophysical sources. However, it has been suggested that the particle distribution may effectively thermalise when the radiative (synchrotron and/or Inverse Compton) losses are severe. Inspired by recent PIC simulations of relativistic turbulence, which show that electrons are impulsively heated in intermittent current sheets by a strong electric field aligned with the local magnetic field, we instead argue that in plasmas where the particle number density is dominated by the pairs (electron-positron and electron-positron-ion plasmas): (i) as an effect of fast cooling and of different injection times, the electron energy distribution is ${\rm d}n_e/{\rm d}γ\proptoγ^{-2}$ for $γ\lesssimγ_{\rm heat}$ (the Lorentz factor $γ_{\rm heat}$ being close to the equipartition value), while the distribution steepens at higher energies; (ii) since the time scales for the turbulent fields to decay and for the photons to escape are of the same order, the magnetic and the radiation energy densities in the dissipation region are comparable; (iii) if the mass energy of the plasma is dominated by the ion component, the pairs with a Lorentz factor smaller than a critical one (of the order of the proton-to-electron mass ratio) become isotropic, while the pitch angle remains small otherwise. The outlined scenario is consistent with the typical conditions required to reproduce the Spectral Energy Distribution of blazars, and allows one to estimate the magnetisation of the emission site. Finally, we show that turbulence within the Crab Nebula may power the observed gamma-ray flares if the pulsar wind is nearly charge-separated at high latitudes.