Galactic spiral patterns and dynamo action I: A new twist on magnetic
  arms
  We generalise the theory of mean-field galactic dynamos by allowing for
temporal non-locality in the mean electromotive force (emf). This arises in
random flows due to a finite response time of the mean emf to changes in the
mean magnetic field, and leads to the telegraph equation for the mean field.
The resulting dynamo model also includes the nonlinear dynamo effects arising
from magnetic helicity balance. Within this framework, coherent large-scale
magnetic spiral arms superimposed on the dominant axially symmetric magnetic
structure are considered. A non-axisymmetric forcing of the mean-field dynamo
by a spiral pattern (either stationary or transient) is invoked, with the aim
of explaining the phenomenon of magnetic arms. For a stationary dynamo forcing
by a rigidly rotating material spiral, we find corotating non-axisymmetric
magnetic modes enslaved to the axisymmetric modes and strongly peaked around
the corotation radius. For a forcing by transient material arms wound up by the
galactic differential rotation, the magnetic spiral is able to adjust to the
winding so that it resembles the material spiral at all times. There are
profound effects associated with the temporal non-locality, i.e. finite `dynamo
relaxation time'. For the case of a rigidly rotating spiral, a finite
relaxation time causes each magnetic arm to mostly lag the corresponding
material arm with respect to the rotation. For a transient material spiral that
winds up, the finite dynamo relaxation time leads to a large, negative (in the
sense of the rotation) phase shift between the magnetic and material arms,
similar to that observed in NGC 6946 and other galaxies. We confirm that
sufficiently strong random seed fields can lead to global reversals of the
regular field along the radius whose long-term survival depends on specific
features of a given galaxy.
