Exact axially symmetric galactic dynamos
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 scaleinvariant solutions with zero resistivity that are selfsimilar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is selfsimilar 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) Xshaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANGES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 2018
 DOI:
 10.1093/mnras/sty256
 arXiv:
 arXiv:1801.08637
 Bibcode:
 2018MNRAS.476..635H
 Keywords:

 dynamo;
 galaxies: haloes;
 galaxies: magnetic fields;
 galaxies: spiral;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 23 doublespaced pages, 5 figures, accepted to MNRAS 23 Jan, 2018