Modelling of the surface magnetic field in neutron stars: Application to radio pulsars

¹ Institute of Astronomy, University of Zielona Góra, Lubuska 2, 65-265, Zielona Góra, Poland
² Center for Plasma Astrophysics, Abastumani Astrophysical Observatory, Al.Kazbegi ave. 2a, Tbilisi 380060, Georgia
³ Max-Planck Institute for Radioastronomy, Auf dem Hügel 69, 53121 Bonn, Germany

Corresponding author: J. A. Gil, jag@astro.ca.wsp.zgora.pl

Received: 27 November 2001
Accepted: 25 March 2002

Abstract

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  G. Thus, in order to increase the resultant surface field to values exceeding 10¹³ G, in low magnetic field pulsars with  G it is required that , 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  G, 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 . 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  G, which is the upper limit for HBPs within the lengthened SCLF model.