The Protogalactic Origin for Cosmic Magnetic Fields 7

It is demonstrated that strong magnetic elds are produced from a zero initial magnetic eld during the pregalactic era, when galaxies are rst forming. Their development proceeds in three phases. In the rst phase, weak magnetic elds are created by the Biermann battery mechanism, acting in shocked parts of the intergalactic medium where caustics form and intersect. In the second phase, these weak magnetic elds are ampliied to strong magnetic elds by the Kolmogoroo turbulence endemic to gravitational structure formation of galaxies. During this second phase, the magnetic elds reach saturation with the turbulent power, but they are coherent only on the scale of the smallest eddy. In the third phase, the magnetic eld strength increases to equipartition with the turbulent energy, and the coherence length of the magnetic elds increases to the scale of the largest turbulent eddy, comparable to the scale of the entire galaxy. The resulting magnetic eld represents a galactic magnetic eld of primordial origin. No further dynamo action is necessary, after the galaxy forms, to explain the origin of magnetic elds. However, the magnetic eld may be altered by dynamo action once the galaxy and the galactic disk have formed. It is rst shown by direct numerical simulations, that thermoelectric currentsassociated with the Biermann battery, build the eld up from zero to 10 ?21 G in the regions about to collapse into galaxies, by z 3. For weak elds, in the absence of dissipation, the cyclotron frequency ! cyc = eB=m H c and !=(1 +), where ! = r v is the vorticity and is the degree of ionization, satisfy the same equations, and initial conditions ! cyc = ! = 0, so that, ! cyc (r; t) = !(r; t)=(1 +). The vorticity grows rapidly after caustics (extreme nonlinearities) develop in the cosmic uid. At this time it is shown that turbulence has developed into Kolmogoroo turbulence. Numerical simulations { 3 { do not yet have the resolution to demonstrate that, during the second phase, the magnetic elds are ampliied by the dynamo action of the turbulence. Instead, an analytic theory of the turbulent ampliication of magnetic elds is employed to explore this phase of the magnetic eld development. From this theory, it is shown that the dynamo action of the protogalactic turbulence is able to amplify the magnetic elds, during the collapse time of the protogalaxy, by such a large factor that …