An investigation of magnetic field distortions in accretion discs around neutron stars

II. Analysis of the toroidal field component

¹ Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, PR China
e-mail: luca.naso@gmail.com
² SISSA and INFN, via Bonomea 265, 34136 Trieste, Italy
³ Department of Physics (Astrophysics), University of Oxford, Keble Road, Oxford OX1 3RH, UK

Received: 14 December 2010
Accepted: 4 April 2011

Abstract

Millisecond pulsars are believed to be old pulsars spun up by a surrounding accretion disc. Magnetic fields are thought to play a leading role in this, both by determining the location of the inner edge of the disc and by exerting an additional torque on the star (as a result of the interaction between the stellar magnetic field and the disc plasma motion, which creates a toroidal component B_φ). In some well-known analytic models, developed in the 1980s, the B_φ profile was taken to be proportional to the relative angular velocity between the disc plasma and the neutron star, multiplied by a vertical dipolar field. The present work stands in the line of improving those models, suggesting a new profile for B. In a previous paper, we discussed the poloidal component of the magnetic field and here we consider the toroidal component, again making the kinematic approximation and looking for steady solutions of the induction equation for axisymmetric models. The poloidal magnetic field is not assumed to be dipolar and the poloidal velocity field is not taken to be zero everywhere. We also do not use the thin disc approximation to simplify the induction equation but instead solve it numerically in full 2D. The profile obtained in the earlier analytic models is shown to have very limited validity and a more general semi-analytic solution is proposed.