A Model of Pulsars

The model comprises a rotating neutron star (R 106 cm) with a strong magnetic field (B 1012 gauss). Magnetic-field lines which reach the light cylinder are open field lines which connect to the surface of the star at the "polar caps." Each polar cap contains two zones, an electron polar zone (EPZ) and a proton polar zone (PPZ) from which electrons and protons, respectively, stream from the star. Acceleration of each stream is effected close to the surface of the star. Primary electrons in the EPZ follow magnetic-field lines; this acceleration leads to -radiation. It is found that, if the period T is less than 1 sec, these -rays annihilate to produce electron-positron pairs. Steady flow is then impossible, but flow comprising a sequence of charge sheets seems possible. These charge sheets produce radio emission. This may explain why most pulsars have periods shorter than 1 sec. If the sheets are thin, the spectrum varies as -5/3 and provides a good fit to the luminosity spectrum of CP 1919. If the sheet has a rectangular current distribution, the spectrum varies as p '1/3 and provides a good fit to the radio luminosity spectrum of the Crab pulsar. In each EPZ of the Crab pulsar, -ray emission and pair creation combine in a cascade. The resulting flux of electrons and positrons from the star is of order 1041 . The secondary electrons and positrons radiate by the synchrotron mechanism to yield a -1I2 spectrum, but the radiation is self-absorbed in the X-ray part of the spectrum and cannot explain the optical radiation from the Crab pulsar. The Crab pulsar spins rapidly enough for pair production to occur at the PPZs also, apparently out to several times R. In consequence, synchrotron radiation from the electron-positron flux is self-absorbed at much lower frequencies. It seems that the optical and X-ray radiation from the Crab pulsar can be understood quantitatively in this way. The optical, X-ray, and -ray flux expected from this model of the Crab pulsar can be reconciled with observation if the rotation axis, dipole axis, and line of sight are so related that we receive radiation from both PPZs but no radiation from the EPZs.