Pair multiplicities and pulsar death

Through a simple model of particle acceleration and pair creation above the polar caps of rotation-powered pulsars, we calculate the height of the pair formation front (PFF) and the dominant photon emission mechanism for the pulsars in the Princeton catalog. We find that for most low- and moderate-field pulsars, the height of the PFF and the final Lorentz factor of the primary beam is set by nonresonant inverse Compton scattering (NRICS), in the Klein-Nishina limit. NRICS is capable of creating pairs over a wide range of pulsar parameters without invoking a magnetic field more complicated than a centered dipole, although we still require a reduced radius of curvature for most millisecond pulsars. For short-period pulsars, the dominant process is curvature radiation, while for extremely high field pulsars, it is resonant inverse Compton scattering (RICS). The dividing point between NRICS dominance and curvature dominance is very temperature dependent; large numbers of pulsars dominated by NRICS at a stellar temperature of 10(6) K are dominated by curvature at 10(5) K. Our principle result is a new determination of the theoretical pulsar death line. Proper inclusion of ICS allows us to reach the conclusion that all known radio pulsars are consistent with pair creation above their polar caps, assuming steady acceleration of a space charge-limited particle beam. We identify a new region of the P-(P) over dot diagram where slow pulsars with narrow radiation beams should be found in sufficiently large surveys. We also show that the injection rate of electrons and positrons into the Crab Nebula inferred from the polar cap pair creation model at the present epoch (10(39) electrons and positrons s(-1)) suffices to explain the nebular X-ray and gamma -ray emission, the best empirical measure of the instantaneous particle-loss rate from any pulsar, but that the contemporary injection rate is about a factor of 5 below the rate averaged over the nebula's history required to explain the nebular radio emission (assuming that the nebular radio source is homogeneous). It is not clear whether this discrepancy can be resolved by evolutionary effects and by better treatment of nebular inhomogeneity or is an indication of another particle source in the pulsar's magnetosphere.