Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions

Details Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions

2003-09-24

arxiv.org/abs/astro-ph/0309667v2

Astronomy and Astrophysics

Astrophysics

Revised version, as accepted; Geophys. Astrophys. Fluid Dynam

Scientific paper

10.1080/03091920410001700797

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, $Q(r)\sim r^{-4}$, which is shown to persist in nonlinear solutions where $\alpha$-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.

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