Ultrarelativistic particle acceleration in collisionless shock waves

AbstractWe discuss recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is either pure electrons and positrons or primarily electrons and positrons with an admixture of heavy ions. Particle-in-cell simulation techniques as well as analytic theory have been used to show that such shocks in pure pair plasmas are fully thermalized—the downstream particle spectra are relativistic Maxwellians at the temperature expected from the jump conditions. On the other hand, shocks containing heavy ions which are a minority constituent by number but which carry most of the energy density in the upstream medium do put ~20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) ∝ E−2, where N(E)dE is the number of particles with energy between E and E + dE.The mechanism of thermalization and particle acceleration is found to be synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front. The synchrotron maser modes radiated by the heavy ions are absorbed by the pairs at their (relativistic) cyclotron frequencies, allowing the maximum energy achievable by the pairs to be γ±m±c2 = mic2γ1/Zi, where γ1 is the Lorentz factor of the upstream flow and Zi, is the atomic number of the ions. The shock’s spatial structure is shown to contain a series of “overshoots” in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value.This shock model is applied to an interpretation of the structure of the inner regions of the Crab Nebula, in particular to the “wisps,” surface brightness enhancements near the pulsar. We argue that these surface brightness enhancements are the regions of magnetic overshoot, which appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar’s wind in the Crab Nebula is spatially resolved, and allows one to measure γ1, and a number of other properties of the pulsar’s wind. We also discuss applications of the shock theory to the termination shocks of the winds from rotation-powered pulsars embedded in compact binaries. We show that this model adequately accounts for (and indeed predicted) the recently discovered X-ray flux from PSR 1957+20, and we discuss several other applications to other examples of these systems.Subject headings: acceleration of particles — ISM: individual (Crab Nebula) — relativity — shock waves

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