The interaction of a magnetic neutron star with an accretion disc

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Abstract
The interaction of a magnetic neutron star with an accretion disc is considered, in the axisymmetric case. Stellar poloidal field penetrates the disc and acts as a source of toroidal field, generated by material shears. For typical neutron star magnetic moments the back reaction of the field on the main part of the disc is small. However, in the inner parts of the disc magnetic stresses become comparable to material stresses and the angular velocity of matter tends towards that of the star. Magnetic field solutions are found for two forms of diffusion coefficient and for two angular velocity distributions. These solutions are used to derive the magnetic torque on the star as a function of its rotation rate. Magnetic and accretion torques are compared and expressions are found for the time evolution of the stellar angular velocity and the equilibrium period at which the torques cancel. If this period is to lie in the slow rotator regime, in which accretion along field lines can occur, an upper limit is placed on the diffusion coefficient of the disc.

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