An investigation of magnetic field distortions in accretion discs around neutron stars - II. Analysis of the toroidal field component

TL;DR

This paper develops a new model for the toroidal magnetic field component in accretion discs around neutron stars, improving upon previous analytic models by solving the induction equation numerically in full 2D.

Contribution

It introduces a more general semi-analytic solution for the toroidal magnetic field, moving beyond the limited assumptions of earlier models.

Findings

The new B_phi profile differs significantly from previous analytic models.

Numerical solutions reveal complex magnetic field structures in accretion discs.

The model does not assume a dipolar poloidal field or zero poloidal velocity.

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_phi). In some well-known analytic models, developed in the 1980s, the B_phi 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.