Exact axially symmetric galactic dynamos

TL;DR

This paper presents exact, scale-invariant solutions for axially symmetric galactic dynamos, including analytic and special function solutions, demonstrating phenomena like X-shaped magnetic fields and spiral arms without additional mechanisms.

Contribution

It introduces new self-similar, zero-resistivity dynamo solutions that are exact and demonstrate observed galactic magnetic structures and behaviors.

Findings

Exact self-similar solutions for galactic dynamos.

Demonstration of X-shaped magnetic fields and spiral arms.

Prediction of reversing rotation measures in galaxy halos.

Abstract

We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy halos (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.