Cluster magnetic fields from large scale structure shocks

The origin of the micro-Gauss magnetic fields in galaxy clusters is one of the outstanding problem of modern cosmology. We suggest that these fields could have been produced via the Weibel instability operating at shocks during the Large-Scale Structure formation and at accretion shocks in Galaxy Clusters. We have performed three-dimensional particle-in-cell simulations of the nonrelativistic Weibel instability in an electron-proton plasma (with the ion-to-electron mass ratio of 100), in conditions typical of cosmological shocks. These simulations indicate that cluster fields could have been produced by shocks propagating through the intergalactic medium during the formation of large-scale structure or by shocks within the cluster. The strengths of the shock-generated fields range from tens of nano-Gauss in the intercluster medium to a few micro-Gauss inside galaxy clusters. We discuss whether and how our results may change with the change the mass ratio to the realistic value of 1836. We stress that even if the Weibel-generated small-scale magnetic fields decay with time, they can serve as seed fields that can be further amplified and inverse-cascade to larger scales by turbulent motions of post-shock MHD turbulence.