Pulsar Polar Cap Heating and Surface Thermal X-ray Emission

We investigate the production of electron-positron pairs by inverse Compton scattered (ICS) photons above a pulsar polar cap (PC) and calculate surface heating by returning positrons. This paper is a continuation of our self-consistent treatment of acceleration, pair dynamics, and electric field screening above pulsar PCs. We calculate the altitude of the inverse Compton pair-formation fronts, the flux of returning positrons, and present the heating efficiencies and X-ray luminosities. We revise pulsar death lines implying cessation of pair formation, and present them in surface magnetic field-period space. We find that virtually all known radio pulsars are capable of producing pairs by resonant and nonresonant ICS photons radiated by particles accelerated above the PC in a pure star-centered dipole field, so that our ICS pair death line coincides with empirical radio pulsar death. Our calculations show that ICS pairs are able to screen the accelerating electric field only for high PC surface temperatures and magnetic fields. We argue that such screening at ICS pair fronts occurs locally, slowing but not turning off acceleration of particles until screening can occur at a curvature radiation (CR) pair front at higher altitude. In the case where no screening occurs above the PC surface, we anticipate that the pulsar gamma-ray luminosity will be a substantial fraction of its spin-down luminosity. The X-ray luminosity resulting from PC heating by ICS pair fronts is significantly lower than the PC heating luminosity from CR pair fronts, which dominates for most pulsars. PC heating from ICS pair fronts is highest in millisecond pulsars, which cannot produce CR pairs, and may account for observed thermal X-ray components in the spectra of these old pulsars.