Evolving galactic dynamos and fits to the reversing rotation measures in the halo of NGC 4631

Rotation measure (RM) synthesis maps of NGC 4631 show remarkable sign reversals with distance from the minor axis in the northern halo of the galaxy on kpc scales. To explain this new phenomenon, we solve the dynamo equations under the assumption of scale invariance and search for rotating logarithmic spiral solutions. Solutions for velocity fields representing accretion onto the disk, outflow from the disk, and rotation-only in the disk are found that produce RM with reversing signs viewed edge-on. Model RM maps are created for a variety of input parameters using a Faraday screen and are scaled to the same amplitude as the observational maps. Residual images are then made and compared to find a best fit. Solutions for rotation-only, i.e. relative to a pattern uniform rotation, did in general, not fit the observations of NGC 4631 well. However, outflow models did provide a reasonable fit to the magnetic field. The best results for the specific region that was modelled in the northern halo are found with accretion. Since there is abundant evidence for both winds and accretion in NGC 4631, this modelling technique has the potential to distinguish between the dominant flows in galaxies.