Asymptotic behaviour of galactic small-scale dynamos at modest magnetic Prandtl number

Magnetic fields are critical at many scales to galactic dynamics and structure, including multiphase pressure balance, dust processing, and star formation. Dynamo action determines their dynamical structure and strength. Simulations of combined large- and small-scale dynamos have successfully developed mean fields with strength and topology consistent with observations but with turbulent fields much weaker than observed, while simulations of small-scale dynamos with parameters relevant to the interstellar medium yield turbulent fields an order of magnitude below the values observed or expected theoretically. We use the Pencil Code accelerated on GPUs with Astaroth to perform high-resolution simulations of a supernova-driven galactic dynamo including heating and cooling in a periodic domain. Our models show that the strength of the turbulent field produced by the small-scale dynamo approaches an asymptote at only modest magnetic Prandtl numbers. This allows us to use these models to suggest the essential characteristics of this constituent of the magnetic field for inclusion in global galactic models. The asymptotic limit occurs already at magnetic Prandtl number of only a few hundred, many orders of magnitude below physical values in the the interstellar medium and consistent with previous findings for isothermal compressible flows.