Are Cluster Magnetic Fields Primordial?

We present results of a detailed and fully nonlinear numerical and analytical investigation of magnetic field evolution from the very earliest cosmic epochs to the present. We find that, under reasonable assumptions concerning the efficiency of a putative magnetogenesis era during cosmic phase transitions, surprisingly strong magnetic fields ${10}^{-13}–{10}^{-11}\mathrm{G}$ on comparatively small scales $100\mathrm{p}\mathrm{c}–10\mathrm{k}\mathrm{p}\mathrm{c}$ may survive to the present. Building on prior numerical work on the evolution of magnetic fields during the course of gravitational collapse of a cluster, which indicates that precollapse fields of $\sim 4\times {10}^{-12}\mathrm{G}$ extant on small scales may suffice to produce clusters with acceptable Faraday rotation measures, we argue that it seems possible for cluster magnetic fields to be entirely of primordial origin.

Figure 1

Decay of magnetic energy in different damping regimes and for different initial conditions as observed in our numerical simulations. The $t^{-1.2}$ line shows the theoretical damping law in the turbulent regime for $n=3$, $h_g=0$.

Figure 2

Evolution of comoving coherence length for different initial magnetic field configurations with $r_g=0.083$ and $n=3$ (solid lines from top to bottom: $h_g=1$, $h_g={10}^{-3}$, $h_g=0$). The mean free paths of neutrinos and photons are labeled by $l_{\nu }$ and $l_{\gamma }$, and $l_H$ is the Hubble length.

Figure 3

Final magnetic field strengths in the $r_g-h_g$ parameter space for $T_g=100\mathrm{M}\mathrm{e}\mathrm{V}$ (solid lines) and $T_g=100\mathrm{G}\mathrm{e}\mathrm{V}$ (dotted lines), where we assumed a spectral index of $n=3$.