{Supernova explosions in magnetized, primordial dark matter haloes}

The first supernova explosions are potentially relevant sources for the production of the first large-scale magnetic fields. For this reason, we present a set of high-resolution simulations studying the effect of supernova explosions on magnetized, primordial haloes. We focus on the evolution of an initially small-scale magnetic field formed during the collapse of the halo. We vary the degree of magnetization, the halo mass, and the amount of explosion energy in order to account for expected variations as well as to infer systematical dependences of the results on initial conditions. Our simulations suggest that core collapse supernovae with an explosion energy of 1051 erg and more violent pair instability supernovae with 1053 erg are able to disrupt haloes with masses up to about 106 and 107 M⊙, respectively. The peak of the magnetic field spectra shows a continuous shift towards smaller k-values, i.e. larger length scales, over time reaching values as low as k = 4. On small scales, the magnetic energy decreases at the cost of the energy on large scales resulting in a well-ordered magnetic field with a strength up to ∼10-8 G depending on the initial conditions. The coherence length of the magnetic field inferred from the spectra reaches values up to 250 pc in agreement with those obtained from autocorrelation functions. We find the coherence length to be as large as 50 per cent of the radius of the supernova bubble. Extrapolating this relation to later stages, we suggest that significantly strong magnetic fields with coherence lengths as large as 1.5 kpc could be created. We discuss possible implications of our results on processes like recollapse of the halo, first galaxy formation, and the magnetization of the intergalactic medium.