We study numerically the dependence of the critical magnetic Reynolds number Rmc for the turbulent smallscale dynamo on the hydrodynamic Reynolds number Re. We are interested in the regime of low magnetic Prandtl number Pm = Rm/Re < 1, which is relevant for stellar convective zones, protostellar disks, and laboratory liquidmetal experiments. The two asymptotic possibilities are Rmc → const as Re → ∞ (small-scale dynamo exists at low Pm) or Rmc/Re = Pmc → const as Re → ∞ (no small-scale dynamo at low Pm). Results obtained in two independent sets of simulations of MHD turbulence using two different codes are brought together and found to be in quantitative agreement. We find that, at currently accessible resolutions, Rmc grows with Re with no sign of approaching a constant limit. We reach the maximum value of Rmc ∼ 500 for Re ∼ 3000. By comparing simulations with Laplacian viscosity, 4th- to 8th-order hyperviscosity, and Smagorinsky large-eddy viscosity, we find that Rmc is not sensitive to the particular form of the viscous cutoff. This work represents a significant extension of the studies previously published in Schekochihin et al. 2004, Phys. Rev. Lett., 92, 054502 and Haugen et al. 2004, Phys. Rev. E, 70, 016308 and the first detailed scan of the numerically accessible part of the stability curve Rmc(Re). Subject headings: magnetic fields — methods: numerical — MHD — turbulence The magnetic Prandtl number Pm, which is the ratio of the kinematic viscosity to magnetic diffusivity, is a key parameter of MHD turbulence. In fully ionised plasmas, Pm = 2.6 × 10 −5 T 4 /n, where T is the temperature in Kelvin and n the ion number density in cm −3. In hot thin plasmas, such as the warm and hot phases of the interstellar medium, as well as the intracluster medium, Pm ≫ 1. In contrast, in the Sun’s convective zone, Pm ∼ 10 −7...10 −4, in planets, Pm ∼ 10 −5, and in protostellar disks, while estimates vary, it is also believed tha
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