Evolution of Helical Cosmic Magnetic Fields as Predicted by Magnetohydrodynamic Closure Theory

Abstract: We extend our recent derivation of the time evolution equations for the energy content of magnetic fields and turbulent motions for incompressible, homogeneous, and isotropic turbulence to include the case of nonvanishing helicity. These equations are subsequently numerically integrated in order to predict the present day primordial magnetic field strength and correlation length, depending on its initial helicity and magnetic energy density. We find that all prior analytic predictions for helical magnetic fields, such as the epoch when they become maximally helical and their subsequent growth of correlation length L ~ a^{1/3} and decrease of magnetic field strength B ~ a^{-1/3} with scale factor a, are well confirmed by the simulations. An initially fully helical primordial magnetic field is a factor 4 10^4 stronger at the present epoch then its nonhelical counterpart when generated during the electroweak epoch.