The Protogalactic Origin for Cosmic Magnetic Fields

It is demonstrated that strong magnetic fields are produced from a zero initial magnetic field during the pregalactic era, when the galaxy is first forming. Their development proceeds in three phases. In the first phase, weak magnetic fields are created by the Biermann battery mechanism. During the second phase, results from a numerical simulation make it appear likely that homogenous isotropic Kolmogorov turbulence develops that is associated with gravitational structure formation of galaxies. Assuming that this turbulence is real, then these weak magnetic fields will be amplified to strong magnetic fields by this Kolmogorov turbulence. During this second phase, the magnetic fields reach saturation with the turbulent power, but they are coherent only on the scale of the smallest eddy. During the third phase, which follows this saturation, it is expected that the magnetic field strength will increase to equipartition with the turbulent energy and that the coherence length of the magnetic fields will increase to the scale of the largest turbulent eddy, comparable to the scale of the entire galaxy. The resulting magnetic field represents a galactic magnetic field of primordial origin. No further dynamo action after the galaxy forms is necessary to explain the origin of magnetic fields. However, the magnetic field will certainly be altered by dynamo action once the galaxy and the galactic disk have formed.

It is first shown by direct numerical simulations that thermoelectric currents associated with the Biermann battery build the field up from zero to 10^-21 G in the regions about to collapse into galaxies, by z ~ 3. For weak fields, in the absence of dissipation, the cyclotron frequency -ω_cyc = eB/m_H c and ω/(1 + χ), where ∇ × v is the vorticity and χ is the degree of ionization, satisfy the same equations, and initial conditions ω_cyc = ω = 0, so that, globally, -ω_cyc(r, t) = ω(r, t)/(1 + χ). The vorticity grows rapidly after caustics (extreme nonlinearities) develop in the cosmic fluid. At this time, it is made plausible that turbulence has developed into Kolmogorov turbulence. Numerical simulations do not yet have the resolution to demonstrate that, during the second phase, the magnetic fields are amplified by the dynamo action of the turbulence. Instead, an analytic theory of the turbulent amplification of magnetic fields is employed to explore this phase of the magnetic field development. From this theory, it is shown that, assuming the turbulence is really Kolmogorov turbulence, the dynamo action of this protogalactic turbulence is able to amplify the magnetic fields by such a large factor during the collapse of the protogalaxy that the power into the magnetic field must reach saturation with the turbulent power. For the third phase, there is as yet no analytic theory capable of describing this phase. However, preliminary turbulence calculations currently in progress seem to confirm that the magnetic fields may proceed to equipartition with the turbulent energy, and that the coherence length may increase to the largest scales. Simple physical arguments are presented that show that this may be the case. Such an equipartition field is actually too strong to allow immediate collapse to a disk. Possible ways around this difficulty are discussed.