Exact spirally symmetric galactic dynamos

TL;DR

This paper develops exact, time-dependent models of spiral galactic magnetic fields using hypergeometric functions, expanding previous scale-invariant solutions to more realistic, infinitely conducting media.

Contribution

It introduces exact, time-dependent spiral magnetic mode solutions in galactic dynamos, extending prior scale-invariant models to include hypergeometric function descriptions.

Findings

Recovered magnetic disc spirals and X-type poloidal fields.

Matched recent rotation measure observations in galactic halos.

Provided exact solutions without previous approximations.

Abstract

This paper extends the results of an earlier paper on scale invariant galactic spiral magnetic modes to time dependent, scale invariant, spirals. The examples given are all exact in that they may be described in terms of hypergeometric functions. We restrict the discussion to an infinitely conducting medium in order to avoid earlier approximation, which limited the solutions to cones lying within about twenty degrees to the plane. The magnetic disc spirals, `X type" poloidal fields, and the recent discovery of rotation measure screens in edge-on galactic halos were all recovered in such solutions.