Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks

In this concise review of the recent developments in relativistic shock theory in the Universe we restrict ourselves to shocks that do not exhibit quantum effects. On the other hand, emphasis is given to the formation of shocks under both non-magnetised and magnetised conditions. We only briefly discuss particle acceleration in relativistic shocks where much of the results are still preliminary. Analytical theory is rather limited in predicting the real shock structure. Kinetic instability theory is briefed including its predictions and limitations. A recent self-similar relativistic shock theory is described which predicts the average long-term shock behaviour to be magnetised and to cause reasonable power-law distributions for energetic particles. The main focus in this review is on numerical experiments on highly relativistic shocks in (i) pair and (ii) electron-nucleon plasmas and their limitations. These simulations do not validate all predictions of analytic and self-similar theory and so far they do not solve the injection problem and the self-modification by self-generated cosmic rays. The main results of the numerical experiments discussed in this review are: (i) a confirmation of shock evolution in non-magnetised relativistic plasma in 3D due to either the lepton-Weibel instability (in pair plasmas) or to the ion-Weibel instability; (ii) the sensitive dependence of shock formation on upstream magnetisation which causes suppression of Weibel modes for large upstream magnetisation ratios sigma > 10(-3); (iii) the sensitive dependence of particle dynamics on the upstream magnetic inclination angle theta(Bn), where particles of theta(Bn) > 34 degrees cannot escape upstream, leading to the distinction between 'subluminal' and 'superluminal' shocks; (iv) particles in ultra-relativistic shocks can hardly overturn the shock and escape to upstream; they may oscillate around the shock ramp for a long time, so to speak 'surfing it' and thereby becoming accelerated by a kind of SDA; (v) these particles form a power-law tail on the downstream distribution; their limitations are pointed out; (vi) recently developed methods permit the calculation of the radiation spectra emitted by the downstream high-energy particles; (vii) the Weibel-generated downstream magnetic fields form large-amplitude vortices which could be advected by the downstream flow to large distances from the shock and possibly contribute to an extended strong field region; (viii) if cosmic rays are included, Bell-like modes can generate upstream magnetic turbulence at short and, by diffusive re-coupling, also long wavelengths in nearly parallel magnetic field shocks; (ix) advection of such large-amplitude waves should cause periodic reformation of the quasi-parallel shock and eject large-amplitude magnetic field vortices downstream where they contribute to turbulence and to maintaining an extended region of large magnetic fields.