Cosmic structure formation is characterized by the complex interplay between gravity, turbulence, and magnetic fields. The processes by which gravitational energy is converted into turbulent and magnetic energies, however, remain poorly understood. Here, we show with high-resolution, adaptivemesh simulations that MHD turbulence is efficiently driven by extracting energy from the gravitational potential during the collapse of a dense gas cloud. Compressible motions generated during the contraction are converted into solenoidal, turbulent motions, leading to a natural energy ratio of E sol /E tot ≈ 2/3. We find that the energy injection scale of gravity-driven turbulence is close to the local Jeans scale. If small seeds of the magnetic field are present, they are amplified exponentially fast via the small-scale dynamo process. The magnetic field grows most efficiently on the smallest scales, for which the stretching, twisting, and folding of field lines, and the turbulent vortices are sufficiently resolved. We find that this scale corresponds to about 30 grid cells in the simulations. We thus suggest a new minimum resolution criterion of 30 cells per Jeans length in (magneto)hydrodynamical simulations of self-gravitating gas, in order to resolve turbulence on the Jeans scale, and to capture minimum dynamo amplification of the magnetic field. Due to numerical diffusion, however, any existing simulation today can at best provide lower limits on the physical growth rates. We conclude that a small, initial magnetic field can grow to dynamically important strength on time scales significantly shorter than the free-fall time of the cloud.

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We explore the amplification of magnetic seeds during the formation of the first stars and galaxies. During gravitational collapse, turbulence is created from accretion shocks, which may act to amplify weak magnetic fields in the protostellar cloud. Numerical simulations showed that such turbulence is sub-sonic in the first star-forming minihalos, and highly supersonic in the first galaxies with virial temperatures larger than 10 4 K. We investigate the magnetic field amplification during the collapse both for Kolmogorov and Burgers-type turbulence with a semi-analytic model that incorporates the effects of gravitational compression and small-scale dynamo amplification. We find that the magnetic field may be substantially amplified before the formation of a disk. On scales of 1/10 of the Jeans length, saturation occurs after ∼10 8 yr. Although the saturation behaviour of the small-scale dynamo is still somewhat uncertain, we expect a saturation field strength of the order ∼10 −7 n 0.5 G in the first star-forming halos, with n the number density in cgs units. In the first galaxies with higher turbulent velocities, the magnetic field strength may be increased by an order of magnitude, and saturation may occur after 10 6 −10 7 yr. In the Kolmogorov case, the magnetic field strength on the integral scale (i.e. the scale with most magnetic power) is higher due to the characteristic power-law indices, but the difference is less than a factor of 2 in the saturated phase. Our results thus indicate that the precise scaling of the turbulent velocity with length scale is of minor importance. They further imply that magnetic fields will be significantly enhanced before the formation of a protostellar disk, where they may change the fragmentation properties of the gas and the accretion rate.

We present a simple semi-analytical model of nonlinear, mean-field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the `no-$z$' approximation to a nonlinear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where nonlinear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g., due to the galactic fountain or wind) and the other, arising from anisotropy of turbulence as suggested by Vishniac & Cho(2001). We argue that the latter is significant if the galactic differential rotation is strong enough: in our model, for $\Rw\la-10$ in terms of the corresponding turbulent magnetic Reynolds number. We confirm that the intensity of gas outflow from the galactic disc optimal for the dynamo action is close to that expected for normal spiral galaxies. The steady-state strength of the large-scale magnetic field supported by the helicity advection is still weaker than that corresponding to equipartition with the turbulent energy. However, the Vishniac-Cho helicity flux can boost magnetic field further to achieve energy equipartition with turbulence. For stronger outflows that may occur in starburst galaxies, the Vishniac-Cho flux can be essential for the dynamo action. However, this mechanism requires a large-scale magnetic field of at least $\simeq1\mkG$ to be launched, so that it has to be preceded by a conventional dynamo assisted by the advection of magnetic helicity by the fountain or wind.Comment: Accepted for publication in MNRA

Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an α‐effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first‐order smoothing approximation. For small values of Rm, α and turbulent diffusivity are proportional to Rm. Over finite time‐intervals, meaningful values of α and turbulent diffusivity can be obtained even when there is small‐scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small‐scale dynamo do not make a correlated contribution to the mean electromotive force.