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

Abstract

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 σ > 10 −3 ; (iii) the sensitive dependence of particle dynamics on the upstream magnetic inclination angle θ Bn , where particles of θ Bn > 34 • cannot escape upstream, leading to the distinction between 'sub-luminal' and 'super-luminal' 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 2 A M Bykov and R A Treumann 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.

Particle Acceleration in Two Converging Shocks∗

“…The Weibel-generated downstream magnetic fields form largeamplitude vortices which could be convected by the downstream flow to large distances from the shock and possibly contribute to an extended strong field region. If CRs are included, the non-resonant models can generate upstream magnetic turbulence at short and long wavelengths in nearly parallel magnetic field shocks (Bykov & Treumann 2011). The scattering process is usually modeled by some dependence of the mean free path of the particles on the momentum in most particle simulation cases.…”

Nonthermal particles and photons in starburst regions and superbubbles

“…A distinctive feature of collisionless shocks in extended astrophysical flows is their ability to transfer a sizeable fraction of mechanical power of the flow to non-thermal particles and fluctuating magnetic fields by means of the first order Fermi acceleration mechanism called the diffusive shock acceleration (see, e.g., Bell 1978, Axford 1981, Drury 1983, Blandford and Eichler 1987, Berezhko and Krymskiȋ 1988, Jones and Ellison 1991, Malkov and Drury 2001, Treumann 2009, Bykov and Treumann 2011, Schure et al 2012, Blasi 2013). The high efficiency of particle acceleration which may be well above 10% as deduced, in particular, from observations of young supernova remnants (see, e.g., Vink 2012, Helder et al 2012, Blasi 2013 implies strong coupling between the accelerated particle population and the shock structure.…”

The differential cosmic ray energy flux in the light of an ultrarelativistic generalized Lorentzian thermodynamics

“…The accepted interpretation of the cosmic ray flux spectra (cf., e.g., Schlickeiser 2002) and their "knee" and "ankle" sections is in terms of superposition of acceleration spectra of the various known chemical particle components generated in AGNs, stars, supernovae and shocks (Balogh and Treumann 2013;Bykov and Treumann 2011). These particles undergo many acceleration cycles in diffusive Fermi acceleration of the various heavy charged known elemental nucleons in turbulent magnetic fields (Schlickeiser 2002) being smallangle scattered and slowly pushed up in energy until reaching the quasi-equilibrium state in the generalized Lorentzian thermodynamics.…”

“…It involves distributed magnetic fields and many of such magnetic scattering centers located within a large spatial volume. It has by now been sufficiently well developed being in its ultimate completion phase while including a variety of anomalous processes, for instance astrophysical turbulence where the turbulent mechanical energy is ultimately dissipated in electric current filaments (Treumann and Baumjohann 2015) on leptonic scales by spontaneous collisionless reconnection and as well by ultrarelativistic collisionless shock waves (Bykov and Treumann 2011), which generates the necessary diffusivities in energy and momentum space.…”