Magnetized Turbulent Dynamos in Protogalaxies

The prevailing theory for the origin of cosmic magnetic fields is that theyhave been amplified to their present values by the turbulent dynamo inductiveaction in the protogalactic and galactic medium. Up to now, in calculation ofthe turbulent dynamo, it has been customary to assume that there is no backreaction of the magnetic field on the turbulence, as long as the magneticenergy is less than the turbulent kinetic energy. This assumption leads to thekinematic dynamo theory. However, the applicability of this theory toprotogalaxies is rather limited. The reason is that in protogalaxies thetemperature is very high, and the viscosity is dominated by magnetized ions. Asthe magnetic field strength grows in time, the ion cyclotron time becomesshorter than the ion collision time, and the plasma becomes stronglymagnetized. As a result, the ion viscosity becomes the Braginskii viscosity.Thus, in protogalaxies the back reaction sets in much earlier, at fieldstrengths much lower than those which correspond to field-turbulence energyequipartition, and the turbulent dynamo becomes what we call the magnetizedturbulent dynamo. In this paper we lay the theoretical groundwork for themagnetized turbulent dynamo. In particular, we predict that the magnetic energygrowth rate in the magnetized dynamo theory is up to ten time larger than thatin the kinematic dynamo theory. We also briefly discuss how the Braginskiiviscosity can aid the development of the inverse cascade of magnetic energyafter the energy equipartition is reached.Comment: accepted to ApJ, 35 pages, 3 figure