Critical Magnetic Prandtl Number for Small-Scale Dynamo

We report a series of numerical simulations showing that the critical magnetic Reynolds number [Formula presented] for the nonhelical small-scale dynamo depends on the Reynolds number [Formula presented]. Namely, the dynamo is shut down if the magnetic Prandtl number [Formula presented] is less than some critical value [Formula presented] even for [Formula presented] for which dynamo exists at [Formula presented]. We argue that, in the limit of [Formula presented], a finite [Formula presented] may exist. The second possibility is that [Formula presented] as [Formula presented], while [Formula presented] tends to a very large constant value inaccessible at current resolutions. If there is a finite [Formula presented], the dynamo is sustainable only if magnetic fields can exist at scales smaller than the flow scale, i.e., it is always effectively a large-[Formula presented] dynamo. If there is a finite [Formula presented], our results provide a lower bound: [Formula presented] for [Formula presented]. This is larger than [Formula presented] in many planets and in all liquid-metal experiments.