The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present

TL;DR

The paper develops a unified framework for the evolution of stochastic cosmic magnetic fields from primordial magnetogenesis to the present, incorporating turbulent and viscous MHD, photon/neutrino diffusion, and ambipolar diffusion. It derives analytic scaling laws for the magnetic energy and coherence length across epochs, showing that even weakly helical fields naturally evolve toward maximal helicity and that the present-day relation $B_0 \approx 5\times 10^{-12}\,\text{G}\,(L_c/\text{kpc})$ emerges from the initial conditions. The work argues that strong fields on $10\,\text{Mpc}$ scales are unlikely for causal magnetogenesis and highlights the potential of small-scale CMB distortions (l ~ 10^6) as promising observables for primordial fields. It further suggests that cluster magnetic fields could be primordial in origin, with testable implications for intergalactic magnetic fields in voids and for upcoming high-resolution CMB and Faraday rotation measurements.

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.

Figures (22)

• Figure 1: Comparison of the time evolution of the magnetic (solid line) and the kinetic (dashed line) energy in the turbulent regime (${R_e} \gg 1$) for a magnetic field without initial helicity. For comparison, also the theoretical damping law, $E \propto t^{-1.3}$, is shown (dotted line). Here, the simulation was performed on a mesh with $128^3$ grid points and the magnetic field is excited up to $k_c \approx 16$ with a spectral index $n \approx 4$ (cf. Eqs. (\ref{['eq:energy_spectra']}) and (\ref{['eq:turb_damp_nh']} and Appendix \ref{['apx:numerics']}).
• Figure 2: Evolution of magnetic energy spectra in the turbulent regime for a magnetic field with no initial helicity. Here, the spectral index of the initial energy spectra is $n \approx 4$. Note that $E_k$ as opposed to $\tilde{E}_k$ is shown (cf. Eq. (\ref{['eq:Kolmogorov']})
• Figure 3: The evolution of the magnetic energy in the turbulent regime for different initial energy spectra $n$, where $E_k = k^3\,|b_k|^2 \propto k^n$ with a cut-off $k_c \approx 32$. Here, the initial magnetic field is non-helical. In this case, the damping law depends on the spectral index (cf. Eq. (\ref{['eq:turb_damp_nh']})). For comparison, the theoretical predicted damping laws for $n = 1$ ($E \propto t^{-0.67}$) and for $n = 5$ ($E \propto t^{-1.4}$) are also shown.
• Figure 4: Time evolution of $\Gamma = E_{\rm kin}/E_{\rm mag}$ for maximal helical magnetic fields with different spectral indices $n$ in the turbulent regime. The initial kinetic energy is set to $10^{-4}\,E_{\rm mag}$. The ratio $\Gamma$ is nearly constant in time, although, equipartition of kinetic and magnetic energy is not established for helical magnetic fields.
• Figure 5: The evolution of the ratio of the kinetic and magnetic energy spectrum $\Gamma_k = E^{\rm kin}_k/E^{\rm mag}_k$ for a maximal helical magnetic field in the turbulent regime. In this case equipartition ($\Gamma_k \approx 1$) is only established on very small scales. At the integral scale the kinetic energy is always much smaller than the magnetic energy.