Electron energy losses near pulsar polar caps: a Monte Carlo approach

Abstract

We use Monte Carlo approach to study the energetics of electrons accelerated in a pulsar polar gap. As energy-loss mechanisms we consider magnetic Compton scattering of thermal X-ray photons and curvature radiation. The results are compared with previous calculations which assumed that changes of electron energy occurred smoothly according to approximations for the average energy loss rate due to the Compton scattering. We confirm a general dependence of efficiency of electron energy losses due to inverse Compton mechanism on the temperature and size of a thermal polar cap and on the pulsar magnetic field. However, we show that trajectories of electrons in energy-altitude space as calculated in the smooth way do not always coincide with averaged Monte Carlo behaviour. In particular, for pulsars with high magnetic field strength ($B_{pc} > 3\times 10^{12}$ G) and low thermal polar cap temperatures ($T < 5\times 10^6$ K) final electron Lorentz factors computed with the two methods may differ by a few orders of magnitude. We discuss consequences for particular objects with identified thermal X-ray spectral components like Geminga, Vela, and PSR B1055-52.