Pulsars with Strong Magnetic Fields: Polar Gaps, Bound Pair Creation and Nonthermal Luminosities

Modifications to polar-gap models for pulsars are discussed for the case where the surface magnetic field, BS, of the neutron star is strong. For B ∼ 4× 10 T, the curvature γ-quanta emitted tangentially to the curved force lines of the magnetic field are captured near the threshold of bound pair creation and are channelled along the magnetic field as bound electron-positron pairs (positronium). The stability of such bound pairs against ionization by the parallel electric field, E‖, in the polar cap, and against photoionization is discussed. Unlike free pairs, bound pairs do not screen E‖ near the neutron star. As a consequence, the energy flux in highly relativistic particles and high-frequency (X-ray and/or γ-ray) radiation from the polar gaps can be much greater than in the absence of positronium formation. We discuss this enhancement for (a) Arons-type models, in which particles flow freely from the surface, and find any enhancement to be modest, and (b) Ruderman-Sutherland-type models, in which particles are tightly bound to the surface, and find that the enhancement can be substantial. In the latter case we argue for a selfconsistent, time-independent model in which partial screening of E‖ maintains it close to the threshold value for field ionization of the bound pairs, and in which a reverse flux of accelerated particles maintains the polar cap at a temperature such that thermionic emission supplies the particles needed for this screening. This model applies only in a restricted range of periods, P2 < P < P1, and it implies an energy flux in high-energy particles that can correspond to a substantial fraction of the spin-down power of the pulsar. Nonthermal, high-frequency radiation has been observed from six radio pulsars and Geminga is usually included as a seventh case. The nonthermal luminosity can be higher than can be explained in terms of conventional polar-gap and outer-gap models. The selfconsistent polar-gap model proposed here alleviates this difficulty, provided the magnetic field satisfies B ∼ 4×108 T (which is so for five of these pulsars, and plausibly for the other two if a modest nondipolar component is assumed), and the surface temperature (in the absence of heating by the reverse flux) satisfies TS ∼ 10 6 K, so that thermionic emission from the surface is unimportant. It is argued that sufficient power is available to explain the observed high-frequency radiation of most of these pulsars. However, the Crab and PSR 0540–69 have periods P < P2, and we suggest that an outer-gap model is more appropriate for these.