Non-local effects in the mean-field disc dynamo: II – numerical and asymptotic solutions

Abstract

The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, Q(r) in the disc plane at a distance r from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local effects act similarly to an enhanced magnetic diffusion. This leads to a wider radial distribution of the eigensolution and faster propagation of magnetic fronts, compared to solutions with the radial surface field neglected. Another result of non-local effects is a slowly decaying algebraic tail of the eigenfunctions outside the dynamo active region, , which is shown to persist in non-linear solutions where α-quenching is included. The non-local nature of the solutions can affect the radial profile of the regular magnetic field in spiral galaxies and accretion discs at large distances from the centre.