[astro-ph/0410032] The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present

Authors:  Robi Banerjee, Karsten Jedamzik
Abstract:  (abridged) A detailed examination of the evolution of stochastic magnetic fields between high cosmic temperatures and the present epoch is presented. A simple analytical model matching the results of the 3D MHD simulations allows for the prediction of present day magnetic field correlation lengths and energy. Our conclusions are multi fold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields. (b) There exists a correlation between the strength of the magnetic field, B, at the peak of it's spectrum and the location of the peak, given at the present epoch by: B ~ 5x10^{-12} (L/kpc) Gauss, where L is the correlation length determined by the initial magnetic field. (c) Concerning studies of generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of B~10^{-9} Gauss on ~ 10 Mpc scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles l~10^6 where the signal is predicted to be the strongest. (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (pre-collapse) strength 10^{-12} - 10^{-11} Gauss with correlation lengths in the kpc range, and would also exist in voids of galaxies.
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Antony Lewis
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[astro-ph/0410032] The Evolution of Cosmic Magnetic Fields:

Post by Antony Lewis » October 06 2004

One of the interesting things this paper mentions is that primoridal magnetical fields with a blue spectrum might give an interesting CMB signature on very small scales [tex]l \sim 10^6[/tex]. The reasoning being that if the spectrum is sufficiently blue the spectrum will actual grow on small scales (up to the magnetic field decay cut-off) despite damping and finite last scattering width effects. Such primordial fields would not be immediately inconsistent with anything else.

However if there is a nG field on 10kpc scales having a blue spectrum, I would have thought the fields would violate the gravitational wave production argument of astro-ph/0106244 - namely that scales that were superhorizon in the early universe would have generated tensor modes sufficient to violate the bounds on the relativisitic energy density at nucleosynthesis?

Ruth Durrer
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[astro-ph/0410032] The Evolution of Cosmic Magnetic Fields:

Post by Ruth Durrer » November 17 2004

Hi Antony
Tina, Chiara and I have discussed a bit about this paper.
The limit in astro-ph/0106244 is relevant for magnetic fields on super horizon scales:
If the corresponding wavelength is super-horizon at generation, then the magnetic
field is severely damped due to gravity wave production until it passes through the
horizon. Once inside the horizon, gravity wave production becomes irrelevant.

Since they loose a significant amount (maybe 1/2 or more, we do not know since we have
not calculated back reaction) of their energy when passing through the horizon, this means
that the total energy energy on scales which are superhorizon at formation must be less
than the energy in typically 1/2 relativistic thermal degree of freedom (this is grossly the
nucleosynthesis bound). This has led to the serious limits presented in astro-ph/0106244.

So Banerjee and Jedamzik have to tell up whether their magnetic fields are
generated on super- or sub-horizon scales.
Another problem also is that causally produced fields can only have an n=2m spectrum,
where m is a positive integer, on scales on which it evolves linearly, so that B goes
like [tex]1/a^2.[/tex] It is not clear to me how this condition is taken into account in astro-ph/0410032.
Furthermore it would be interesting to know the critical wavelength [tex]\lambda_c(t) [/tex]at which
turbulence sets in and the spectrum is thus modified.

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