A magnetohydrodynamical theorem for steady axisymmetric systems with implications to ring galaxies

A magnetohydrodynamical theorem can be deduced for steady axisymmetric magnetized systems in situations which are usually accepted as representative in interstellar plasmas. It shows that for particular conditions detailed below, magnetic fields have either the direction of the symmetry axis of the system or have field lines encircling this axis of symmetry, but intermediate directions are excluded. Ring galaxies are probably of the second type, which would be important in explaining ring patterns. Our galaxy itself would be of this second type slightly separated from steady state, and the magnetic field radial distribution compatible with the gas content is estimated. The implication of this theorem in actual galaxies is difficult to analyze and gives rise to rather speculative discussions.