Small Scale Dynamos and the Early Growth of Large Scale Magnetic Fields

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Reasonable estimates for the generation of primordial magnetic fields predict that galactic disks are born with large scale magnetic fields about 15 orders of magnitude below their current strength. Given plausible dynamo growth rates of roughly a tenth of the rotation rate, this implies that magnetic fields have just reached their current strength. Observations strongly suggest otherwise, with indications of coherent magnetic fields in disks of a few microgauss at redshifts of 3 or more. Here we consider the early generation of magnetic fields via disk turbulence, and the consequent generation of a long wavelength tail to the magnetic field power spectrum via the incoherent addition of contributions from many turbulent eddies. This process sets a lower limit for the large scale magnetic field strength required for the validity of mean field dynamo theory. We conclude that this effect dominates any small primordial field and produces annular magnetic domains with field strengths near $10^{-7}$ Gauss within a few hundred million years after disk turbulence develops. Large scale magnetic fields will reach equipartition in about $30\Omega^{-1}$, or 1-2 billion years. We comment briefly on the saturation level of these fields. We conclude that the observational prospects for finding unmagnetized galactic disks at high redshift are not promising and that this tells us virtually nothing about the generation of magnetic fields before the epoch galaxy formation.

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