Pulsar polar cap heating and surface thermal X-ray emission. I. Curvature radiation pair fronts

We investigate the effect of pulsar polar cap (PC) heating produced by posi trons returning from the upper pair formation front. Our calculations are b ased on a self-consistent treatment of the pair dynamics and the effect of electric field screening by the returning positrons. We calculate the resul tant X-ray luminosities and discuss the dependence of the PC heating effici encies on pulsar parameters, such as characteristic spin-down age, spin per iod, and surface magnetic field strength. In this study we concentrate on t he regime where the pairs are produced in a magnetic field by curvature pho tons emitted by accelerating electrons. Our theoretical results are not in conflict with the available observational X-ray data and suggest that the e ffect of PC heating should significantly contribute to the thermal X-ray fl uxes from middle-aged and old pulsars. The implications for current and fut ure X-ray observations of pulsars are briefly outlined.