Magnetic field structure and torque in accretion discs around millisecond pulsars

Abstract

Millisecond pulsars are rather weakly-magnetized neutron stars which are thought to have been spun up by disc accretion, with magnetic linkage between the star and the disc playing a key role. Their spin history depends sensitively on details of the magnetic field structure, but idealized models from the 1980s and 1990s are still commonly used for calculating the magnetic field components. This paper is the third in a series presenting results from a step-by-step analysis which we are making of the problem, starting with very simple models and then progressively including additional features one at a time, with the aim of gaining new insights into the mechanisms involved. In our first two papers, the magnetic field structure in the disc was calculated for a standard Shakura and Sunyaev model, by solving the magnetic induction equation numerically in the stationary limit within the kinematic approximation; here we consider a more general velocity field in the disc, including backflow. We find that the profiles of the poloidal and toroidal components of the magnetic field are fairly similar in the two cases but that they can be very different from those in the models mentioned above, giving important consequences for the torque exerted on the central object. In particular we find that, contrary to what is usually thought, some regions of the disc outward of the co-rotation point (rotating more slowly than the neutron star) may nevertheless contribute to spinning up the neutron star on account of the detailed structure of the magnetic field in those parts of disc.