  The origin and evolution of cosmic magnetic fields as well as the influence
of the magnetic fields on the evolution of galaxies are unknown. Though not
without challenges, the dynamo theory can explain the large-scale coherent
magnetic fields which govern galaxies, but observational evidence for the
theory is so far very scarce. Putting together the available data of
non-interacting, non-cluster galaxies with known large-scale magnetic fields,
we find a tight correlation between the integrated polarized flux density,
S(PI), and the rotation speed, v(rot), of galaxies. This leads to an almost
linear correlation between the large-scale magnetic field B and v(rot),
assuming that the number of cosmic ray electrons is proportional to the star
formation rate, and a super-linear correlation assuming equipartition between
magnetic fields and cosmic rays. This correlation cannot be attributed to an
active linear alpha-Omega dynamo, as no correlation holds with global shear or
angular speed. It indicates instead a coupling between the large-scale magnetic
field and the dynamical mass of the galaxies, B ~ M^(0.25-0.4). Hence, faster
rotating and/or more massive galaxies have stronger large-scale magnetic
fields. The observed B-v(rot) correlation shows that the anisotropic turbulent
magnetic field dominates B in fast rotating galaxies as the turbulent magnetic
field, coupled with gas, is enhanced and ordered due to the strong gas
compression and/or local shear in these systems. This study supports an
stationary condition for the large-scale magnetic field as long as the
dynamical mass of galaxies is constant.
