Journal
PHYSICAL REVIEW E
Volume 92, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.92.023010
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [SPP 1573, KL 1358/14-1, SCHL 1964/1-1, SCHL 1964/1-2, BO 4113/1-2]
- DFG [SFB 881, B1, B2]
- European Research Council under the European Community's Seventh Framework Programme(FP7) via the ERC Advanced Grant STARLIGHT [339177]
- Australian Research Council's Discovery Projects [DP130102078, DP150104329]
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The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. This process ends when the peak reaches a characteristic wave number k(star) which is determined by the critical magnetic Reynolds number. The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. With our model we find saturation levels between 43.8% and 1.3% for Pm >> 1 and between 2.43% and 0.135% for Pm << 1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.
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