Particle Acceleration Zones above Pulsar Polar Caps: Electron and Positron Pair Formation Fronts

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Abstract
We investigate self-consistent particle acceleration near a pulsar polar cap (PC) by the electrostatic field due to the effect of inertial frame dragging. Test particles gain energy from the electric field parallel to the open magnetic field lines and lose energy by both curvature radiation (CR) and resonant and nonresonant inverse Compton scattering (ICS) with soft thermal X-rays from the neutron star (NS) surface. Gamma rays radiated by electrons accelerated from the stellar surface produce pairs in the strong magnetic field, which screen the electric field beyond a pair formation front (PFF). Some of the created positrons can be accelerated back toward the surface and produce γ-rays and pairs that create another PFF above the surface. We find that ICS photons control PFF formation near the surface, but because of the different angles at which the electron and positron scatter the soft photons, positron-initiated cascades develop above the surface and may screen the accelerating electric field. Stable acceleration from the NS surface is therefore not possible in the presence of dominant ICS energy losses. However, we find that stable acceleration zones may occur at some distance above the surface, where CR dominates the electron and positron energy losses and there is up-down symmetry between the electron and positron PFFs. We examine the dependence of CR-controlled acceleration zone voltage, width, and height above the surface on parameters of the pulsar and its soft X-ray emission. For most pulsars, we find that acceleration will start at a height of 0.5-1 stellar radii above the NS surface.
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