Efficient highly-subsonic turbulent dynamo and growth of primordial magnetic fields

We present the first study on the amplification of magnetic fields by the turbulent dynamo in the highly subsonic regime, with Mach numbers ranging from $10^{-3}$ to $0.4$. We find that for the lower Mach numbers the saturation efficiency of the dynamo, $(E_{\mathrm{mag}}/E_{\mathrm{kin}})_{\mathrm{sat}}$, increases as the Mach number decreases. Even in the case when injection of energy is purely through longitudinal forcing modes, $(E_{\mathrm{mag}}/E_{\mathrm{kin}})_{\mathrm{sat}}$ $\gtrsim 10^{-2}$ at a Mach number of $10^{-3}$. We apply our results to magnetic field amplification in the early Universe and predict that a turbulent dynamo can amplify primordial magnetic fields to $\gtrsim$ $10^{-16}$ Gauss on scales up to 0.1 pc and $\gtrsim$ $10^{-13}$ Gauss on scales up to 100 pc. This produces fields compatible with lower limits of the intergalactic magnetic field inferred from blazar $\gamma$-ray observations.