Pulsars as gamma ray sources: Nebular shocks and magnetospheric gaps

Abstract

I summarize the results of 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 primarily electrons and positrons with an admixture of heavy ions. Shocks which contain heavy ions that are a minority constituent by number but which carry most of the energy density in the upstream medium put ∼ 20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) α E ^-2, where N(E)dE is the number of particles with energy between E and E+dE. 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, provides the mechanism of thermalization and non-thermal particle acceleration. The maximum energy achievable by the pairs is γ _± m _± c ² = m _i c ² γ ₁/Z _i, where γ ₁ is the Lorentz factor of the upstream flow and Z _i is the atomic number of the ions. The shock's spatial structure contains 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. These overshoots provide a new interpretation of the structure of the inner regions of the Crab Nebula, in particular of the “wisps”, surface brightness enhancements near the pulsar. The wisps 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 γ ₁ ∼ 4 × 10⁶, the upstream magnetic field B ₁ to be ∼ 3 × 10^-5 Gauss, as well as to show that the total ion flow is ∼ 3 × 10³⁴ elementary charges/sec, in good agreement with the total current flow predicted by the early Goldreich and Julian (1969) model. The total pair outflow is shown to be about 5 × 10³⁷ pairs per second, in good agreement with the particle flux required to explain the nebular X—ray source.

The energetics of particle acceleration within the magnetospheres of rotation powered pulsars and the consequences for pulsed gamma ray emission are also briefly discussed. The gamma ray luminosity above 100 MeV is shown to scale in proportion to Ė ^1/2 _R , as is in accord with some of the simplest ideas about “polar cap” models. Models based on acceleration in the outer magnetosphere are also briefly discussed.