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We investigate the conditions required for the production ofelectron-positron pairs above a pulsar polar cap (PC) and the influence of pairproduction on the energetics of the primary particle acceleration. Assumingspace-charge limited flow acceleration including the inertial frame-draggingeffect, we allow both one-photon and two-photon pair production by eithercurvature radiation (CR) photons or photons resulting from inverse-Comptonscattering of thermal photons from the PC by primary electrons. We find that,while only the younger pulsars can produce pairs through CR, nearly all knownradio pulsars are capable of producing pairs through non-resonantinverse-Compton scatterings. The effect of the neutron star equations of stateon the pair death lines is explored. We show that pair production isfacilitated in more compact stars and more massive stars. Therefore accretionof mass by pulsars in binary systems may allow pair production in most of themillisecond pulsar population. We also find that two-photon pair production maybe important in millisecond pulsars if their surface temperatures are aboveabout three million degrees K. Pulsars that produce pairs through CR will havetheir primary acceleration limited by the effect of screening of the electricfield. In this regime, the high-energy luminosity should follow a $L_{HE}\propto \dot E_{rot}^{1/2}$ dependence. The acceleration voltage drop inpulsars that produce pairs only through inverse-Compton emission will not belimited by electric field screening. In this regime, the high-energy luminosityshould follow a $L_{HE} \propto \dot E_{rot}$ dependence. Thus, older pulsarswill have significantly lower gamma-ray luminosity.Comment: 22 pages, 4 figures, accepted for publication in Astrophysical  Journa

Regimes of Pulsar Pair Formation and Particle Energetics