An analytical model predicting the growth rates, the absolute growth times and the saturation values of the magnetic field strength within galactic haloes is presented. The analytical results are compared to cosmological magnetohydrodynamics (MHD) simulations of Milky Way-like galactic halo formation performed with the N-body/spmhd code gadget. The halo has a mass of ≈3 × 1012 M⊙ and a virial radius of ≈270 kpc. The simulations in a Λ cold dark matter (ΛCDM) cosmology also include radiative cooling, star formation, supernova feedback and the description of non-ideal MHD.
A primordial magnetic seed field ranging from 10−10 to 10−34 G in strength agglomerates together with the gas within filaments and protohaloes. There, it is amplified within a couple of hundred million years up to equipartition with the corresponding turbulent energy. The magnetic field strength increases by turbulent small-scale dynamo action. The turbulence is generated by the gravitational collapse and by supernova feedback. Subsequently, a series of halo mergers leads to shock waves and amplification processes magnetizing the surrounding gas within a few billion years. At first, the magnetic energy grows on small scales and then self-organizes to larger scales. Magnetic field strengths of ≈10−6 G are reached in the centre of the halo and drop to ≈10−9 G in the intergalactic medium.
Analysing the saturation levels and growth rates, the model is able to describe the process of magnetic amplification notably well and confirms the results of the simulations.