Abstract

The Universe at present is highly magnetized, with fields of a few 10$^{-5}$ G and coherence lengths greater than 10 kpc in typical galaxies like the Milky Way. We propose that the magnetic field was already amplified to these values during the formation and the early evolution of galaxies. Turbulence in young galaxies is driven by accretion, as well as by supernova (SN) explosions of the first generation of stars. The small-scale dynamo can convert the turbulent kinetic energy into magnetic energy and amplify very weak primordial seed fields on short timescales. Amplification takes place in two phases: in the kinematic phase the magnetic field grows exponentially, with the largest growth rate on the smallest nonresistive scale. In the following nonlinear phase the magnetic energy is shifted toward larger scales until the dynamo saturates on the turbulent forcing scale. To describe the amplification of the magnetic field quantitatively, we modeled the microphysics in the interstellar medium (ISM) of young galaxies and determined the growth rate of the small-scale dynamo. We estimated the resulting saturation field strengths and dynamo timescales for two turbulent forcing mechanisms: accretion-driven turbulence and SN-driven turbulence. We compare them to the field strength that is reached when only stellar magnetic fields are distributed by SN explosions. We find that the small-scale dynamo is much more efficient in magnetizing the ISM of young galaxies. In the case of accretion-driven turbulence, a magnetic field strength on the order of 10$^{-6}$ G is reached after a time of 24-270 Myr, while in SN-driven turbulence the dynamo saturates at field strengths of typically 10$^{-5}$ G after only 4-15 Myr. This is considerably shorter than the Hubble time. Our work can help for understanding why present-day galaxies are highly magnetized.