Pulsar birth line, appearance line and death line

Abstract

In this paper, the sparking condition of pulsar inner gap is reinvestigated concerning the inverse Compton scattering (ICS) process of the outgoing high energy particles with the thermal photons in the neutron star vicinity. To study B - γ process of pair production, the dominant incident photon frequency is adopted to be the frequency at which the brightness is the maximum for a black-body radiation, and the absorption effects due to electric fields are also taken into account. Three boundary lines are obtained in Ṗ-P diagram: (a)the birth line, above which the perpendicular components of the outgoing photon energies with respect to the magnetic field direction are not large enough to cause pair production cascade; (b)the appearance line, below which the perpendicular magnetic fields with respect to the direction of the γ-rays are not strong enough to cause B - γ pair production process; (c)the death line, below which the potential across the gap is not large enough to cause gap breakdown. In the three above-mentioned regions, a pair production avalanche can not be formed, so that no neutron star can be observed as a radio pulsar. The region enclosed by these lines is the only region of observed pulsars. All these are in good agreement with the observations.