Global magnetic patterns in the Milky Way and the Andromeda nebula.

A non-linear, thin-disc galactic dynamo model based on α-quenching is proposed. Assuming that the mean helicity depends on the magnetic field strength averaged across the disc, we derive a universal form of non-linearity in the radial dynamo equation. We apply our model to the Milky Way and the Andromeda nebula to study the origin of reversals, along the radius, of the regular magnetic field, and to obtain constraints on the geometrical shape and thickness of the magnetoionic layer. The reversals are shown to be a relic inherited from the structure of the seed field, which can survive provided that the dynamo is strong enough. The dynamo efficiency increases with the half- thickness of the magnetoionic layer, h, for moderate values of the latter. The presence of the reversal between the Orion and Sagittarius spiral arms in the Galaxy and of the magnetic ring in M31 can be used to obtain certain bounds on h. For the galactocentric distance r = 10 kpc, we obtain 350 <~ h <~ 1500 pc in the Galaxy and 350 <~ h <~ 450 pc in M31 if the seed field for the dynamo is produced within the galaxies by interstellar turbulence. The quasi-stationary number of the reversals and their positions are controlled by the radial profiles of the rotation velocity, disc thickness and gas density. All extra reversals in the seed field are rapidly washed out by magnetic diffusion. It is shown that the thickness of the magnetoionic disc must increase monotonically with the galactocentric distance in M31, unlike the H I layer thickness that remains constant at moderate r.