Emission Mechanisms in High Energy Pulsars: From Gamma Rays to Infrared

Abstract

We present a model for the gamma-ray emission of pulsars in terms of curvature radiation by highly relativistic particles. It is shown that the injection of power-law primary particles from an outer gap and subsequent cooling by curvature radiation losses reproduces the high energy spectrum and the luminosity of pulsars. As a result a spectral break is to be expected at a photon energy of $\sim 1\thinspace{\rm GeV}$. This value does not depend on the surface magnetic field strength or on the period of the neutron star, but only involves a geometric factor. The predicted change of the spectral index by 1 explains in particular the spectral shape of PSR B1706--44. We find that according to this model the luminosity of pulsars in the high energy band varies according to $L_γ\propto B_0/P^{5/3}$, which is in good agreement with the observations. A model for the infrared, optical and soft X-ray emission of pulsar is also presented. It is based on anisotropic synchrotron emission by relativistic particles in an outer gap scenario with a single energy distribution $N(γ)\propto γ^{-2}$. It is shown that this synchrotron model is able to reproduce the spectral shape between the infrared and soft X-rays and also the corresponding luminosities for the Crab pulsar. In particular, the long standing problem of the rapid spectral decline towards infrared frequencies is understandable as emission at very small pitch angles from low energy particles with $γ\ga 10$. It is also shown that the scaling of the synchrotron model explains the observed correlation between the X-ray luminosity and the spin-down luminosity of the neutron star $L_{\rm x} \sim 10^{-3} {\dot E}$.