2002ApJ...576..366H

We investigate the conditions required for the production of electron-positron pairs above a pulsar polar cap (PC) and the influence of pair production on the energetics of the primary particle acceleration. Assuming space charge-limited flow acceleration including the inertial frame-dragging effect, we allow both one-photon and two-photon pair production by either curvature radiation (CR) photons or photons resulting from inverse Compton scattering of thermal photons from the PC by primary electrons. We find that while only the younger pulsars can produce pairs through CR, nearly all known radio pulsars are capable of producing pairs through nonresonant inverse Compton scatterings. The effect of the neutron star equations of state on the pair death lines is explored. We show that pair production is facilitated in more compact stars and more massive stars. Therefore, accretion of mass by pulsars in binary systems may allow pair production in most of the millisecond pulsar population. We also find that two-photon pair production may be important in millisecond pulsars if their surface temperatures are above ≃three million kelvins. Pulsars that produce pairs through CR will have their primary acceleration limited by the effect of screening of the electric field. In this regime, the high-energy luminosity should follow an L_HE∝E{dot}^1/2_rot dependence. The acceleration voltage drop in pulsars that produce pairs only through inverse Compton emission will not be limited by electric field screening. In this regime, the high-energy luminosity should follow an L_HE∝E{dot}_rot dependence. Thus, older pulsars will have significantly lower γ-ray luminosity.