Pair Multiplicities and Pulsar Death

Abstract

Through a simple model of particle acceleration and pair creation above the polar caps of rotationpowered 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 Ðnd that for most low-and moderateÐeld pulsars, the height of the PFF and the Ðnal 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 Ðeld 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 Ðeld 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 106 K are dominated by curvature at 105 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 chargeÈlimited particle beam. We identify a new region of the diagram where P-P0 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 (1039 electrons and positrons s~1) suffices to explain the nebular X-ray and c-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 nebulaÏs 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 e †ects and by better treatment of nebular inhomogeneity or is an indication of another particle source in the pulsarÏs magnetosphere.

Electrodynamics of Magnetars. III. Pair Creation Processes in an Ultrastrong Magnetic Field and Particle Heating in a Dynamic Magnetosphere

“…As a result of the conversion of the scattered photons to pairs, macroscopic electric fields are screened rapidly enough that the electrons and positrons in the inner magnetosphere do not reach the energies that are required for gamma-ray emission by curvature radiation. The surface gap model investigated by Hibschman & Arons (2001a, 2001b and by Thompson (2008) has this property, as does the more dynamic circuit model described in this paper.…”

“…This process has been discussed extensively in the context of radio pulsars, by Kardashev et al (1984), Daugherty & Harding (1989), Chang (1995), Sturner 1995, and Hibschman & Arons (2001a, 2001b. As a result of the conversion of the scattered photons to pairs, macroscopic electric fields are screened rapidly enough that the electrons and positrons in the inner magnetosphere do not reach the energies that are required for gamma-ray emission by curvature radiation.…”

The coughing pulsar magnetosphere

“…Models of particle acceleration and pair creation above the polar cap of rotation-powered pulsars yield potential drops near the surface of the star of the order of 10 12 Volts (e.g. Hibschman & Arons 2001;Arons, personal communication), and therefore, in general, Ω F < Ω.…”

Wave Modes in the Magnetospheres of Pulsars and Magnetars

“…In the polar-cap region of a pulsar, primary particles may be accelerated to very high energy (γ ∼ 10 6 − 10 7 ) by a field-aligned electric field. The bulk of the plasma produced in an electromagnetic cascade may have lower energies, γ ∼ 10 2 − 10 4 , with multiplicity factor η ∼ 10 2 − 10 5 (e.g., Dangherty & Harding 1982;Hibschman & Arons 2001). Kunzl et al (1998) argued that too high a density of secondary particles in the magnetosphere is in contradiction to the observed low-frequency emission from radio pulsars, implying η < ∼ 100.…”