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Abstract

Magnetic fields grow quickly even at early cosmological times, suggesting the action of a small-scale dynamo (SSD) in the interstellar medium of galaxies. Many studies have focused on idealized turbulent driving of the SSD. Here we simulate more realistic supernova-driven turbulence to determine whether it can drive an SSD. Magnetic field growth occurring in our models appears inconsistent with simple tangling of magnetic fields, but consistent with SSD action, reproducing and confirming models by Balsara et al. that did not include physical resistivity eta. We vary eta, as well as the numerical resolution and supernova rate, (sigma) over dot, to delineate which an SSD occurs. For a given (sigma) over dot we find convergence for SSD growth rate with resolution of a parsec. For (sigma) over dot similar or equal to (sigma) over dot(sn), with (sigma) over dot(sn) the solar neighborhood rate, the critical resistivity below which an SSD occurs is 0.005 > eta(crit) > 0.001 kpc km s(-1), and this increases with the supernova rate. Across the modeled range of 0.5-4.pc resolution we find that for eta < eta(crit), the SSD saturates at about 5% of kinetic energy equipartition, independent of growth rate. In the range 0.2 (sigma) over dot(sn) <= (sigma) over dot <= 8 (sigma) over dot(sn) growth rate increases with (sigma) over dot. SSDs in the supernova-driven interstellar medium commonly exhibit erratic growth.