The small-scale dynamo in the low-Mach number regime

Abstract

We present the first study on the amplification of magnetic fields by the small-scale turbulent dynamo (SSD) in the highly subsonic regime, with Mach numbers ranging from 10^{−3} to 0.4. We study the properties of the SSD as a function of the nature of turbulent driving, in particular the compressive (curl-free) and the solenoidal (divergence-free) driving. We find that for the lower Mach numbers, the saturation efficiency of the dynamo, (Emag/Ekin)sat, increases as the Mach number decreases. Even in the case when injection of energy is purely through longitudinal forcing modes (or no solenoidal component in the turbulent driving), (Emag/Ekin)sat ∼ 10^{−2} at a Mach number of 10^{−3}. We also find that increasing the solenoidal fraction in the driving field increases the saturation efficiency and the amplification rate of the SSD. We apply our results to magnetic field amplification in the early Universe and predict that a SSD can amplify magnetic fields to & 10^{−16} Gauss on scales of 0.1 pc and & 10^{−13} Gauss on scales of 100 pc. This result can explain the intergalactic magnetic fields inferred from blazer γ-ray observations on these scales. We also apply our findings on the low Mach number SSD to the solar corona and the hot interstellar medium in the galactic corona.