2002A&A...388..235G

We propose a vacuum gap (VG) model which can be applied uniformly for normal and high-magnetic-field pulsars. The model requires a strong and non-dipolar surface magnetic field near the pulsar polar cap. We assume that the actual surface magnetic field B_s in pulsars results from the superposition of a global dipole field B_d and a crust-anchored small scale magnetic anomaly B_m. We provide a numerical formalism for modelling such structures of the surface magnetic field and explore it within the framework of the VG model, which requires strong surface fields B_s>10¹³G. Thus, in order to increase the resultant surface field to values exceeding 10¹³G, in low magnetic field pulsars with B_d≪10¹³G it is required that B_m≫B_d, with the same polarities (orientations) of B_d and B_m. However, if the polarities are opposite, the resultant surface field can be lower than the dipolar surface component inferred from the pulsar spin-down. We propose that high-magnetic-field pulsars (HBPs) with the inferred global dipole field B_d exceeding the so-called photon splitting threshold B_cr∼4x10¹³G, can generate observable radio emission ``against the odds'', provided that the surface dipolar magnetic field B_d is reduced below B_cr by the magnetic anomaly B_m of the right strength and polarity. We find that effective reduction is possible if the values of B_d and B_m are of the same order of magnitude, which would be expected in HBPs with B_d>B_cr. The proposed VG model of radio emission from HBPs, in which pair production occurs directly above the polar cap, is an alternative to the recently proposed lengthened space-charge-limited-flow (SCLF) model, in which the pair formation front is located at relatively high altitudes, where the dipole field is degraded below B_cr. Our model allows high B_d radio-loud pulsars not only just above B_cr but even above 2x10¹⁴G, which is the upper limit for HBPs within the lengthened SCLF model.