Vacuum Gaps in Pulsars and PSR J2144−3933

In this paper we revisit the radio pulsar death line problem within the framework of curvature radiation and/or the inverse Compton scattering-induced vacuum gap model above neutron star polar caps. Our special interest is in the recently detected pulsar PSR J2144-3933 with extremal period 8.5 s, which lies far beyond conventional death lines. We argue that the formation of vacuum gaps requires a complicated multipolar surface magnetic field, with a strength B s typically much higher than the surface dipolar component B d and a radii of curvature much smaller than the neutron star radius R = 10 6 cm. Such a multipolar surface field is also consistent with death lines including the extremal pulsar PSR J2144-3933. Since vacuum gap models produce sparks, our paper naturally supports the spark related models of subpulse drift phenomenon as well as the spark-associated models of coherent pulsar radio emission.