Small-scale Dynamo in Supernova-driven Interstellar Turbulence

Magnetic fields grow quickly even at early cosmological times, suggesting the action of a small-scale dynamo (SSD) in the interstellar medium (ISM) of galaxies. Many studies have focused on idealized turbulent driving of the SSD. We here simulate more realistic supernova-driven turbulence to determine whether it can drive an SSD. We vary the physical resistivity (and implicitly magnetic Reynolds number), as well as the numerical resolution and supernova rate to delineate the regime in which an SSD occurs. We find convergence for SSD growth rate with resolution approaching sub-parsec scale for a given supernova distribution {\sigma}. Despite higher Mach numbers and negative impact of compressibility expected on SSD, growth rates increase for {\sigma}={\sigma}_{\rm sn} versus 0.2{\sigma}_{\rm sn}, with {\sigma}_{\rm sn} the solar neighbourhood rate. Across the modelled range of 0.5 to 4 parsec resolution we find that for sufficiently low resistivity the SSD saturates consistently at about 5% of energy equipartion, independent of growth rate and low Prandtl numbers in our experiments. As the grid becomes coarser, the minimum resolved physical resistivity increases. The trend suggests that numerical resistivity suppresses SSD for grid spacing much exceeding 4 pc.