Fausto Cattaneo

Simulations of magneto-convection in the solar photosphere: Equations, methods and results of the MURaM code

We have developed a 3D magnetohydrodynamics simulation code for applications in the solar convection zone and photosphere. The code includes a non-local and non-grey radiative transfer module and takes into account the effects of partial ionization. Its parallel design is based on domain decomposition, which makes it suited for use on parallel computers with distributed memory architecture. We give a description of the equations and numerical methods and present the results of the simulation of a solar plage region. Starting with a uniform vertical field of 200 G, the processes of flux expulsion and convective field amplification lead to a dichotomy of strong, mainly vertical fields embedded in the granular downflow network and weak, randomly oriented fields filling the hot granular upflows. The strong fields form a magnetic network with thin, sheet- like structures extending along downflow lanes and micropores with diameters of up to 1000 km which form occasionally at vertices where several downflow lanes merge. At the visible surface around optical depth unity, the strong field concentrations are in pressure balance with their weakly magnetized surroundings and reach field strengths of up to 2 kG, strongly exceeding the values corresponding to equipartition with the kinetic energy density of the convective motions. As a result of the channelling of radiation, small flux concentrations stand out as bright features, while the larger micropores appear dark in brightness maps owing to the suppression of the convective energy transport. The overall shape of the magnetic network changes slowly on a timescale much larger than the convective turnover time, while the magnetic flux is constantly redistributed within the network leading to continuous formation and dissolution of flux concentrations.

On the Origin of Magnetic Fields in the Quiet Photosphere

We consider the possibility that a substantial fraction of the magnetic field in the quiet photosphere is generated locally by dynamo action associated with the granular and supergranular flows. The argument is based on recent advances in the theory of fast dynamos and is supported by large-scale numerical simulations that show that thermally driven turbulent convection can indeed be an efficient source of small-scale, highly intermittent magnetic fields. Some aspects of the resulting magnetic field, such as its strength and degree of intermittency, are discussed.

Nonlinear restrictions on dynamo action

Astrophysical dynamos operate in the limit of small magnetic diffusivity. In order for magnetic reconnection to occur, very small magnetic structures must form so that diffusion becomes effective. The formation of small-scale fields is accompanied by the stretching of the field lines and therefore by an amplification of the magnetic field strength. The back reaction of the magnetic field on the motions leads to the eventual saturation of the dynamo process, thus posing a constraint on the amount of magnetic flux that can be generated by dynamo action, It is argued that in the limit of small diffusivity only a small amount of flux, many orders of magnitude less than the observed fluxes, can be created by dynamo processes.

ON THE INTERACTION BETWEEN CONVECTION AND MAGNETIC FIELDS

Turbulent convection in the solar photosphere can act as a small-scale dynamo, maintaining a disordered magnetic field that is locally intense. On the other hand, convection is inhibited in the presence of a strong, externally imposed magnetic field, as for instance, in a sunspot. Large-scale, three-dimensional, numerical experiments on highly nonlinear magnetoconvection in a Boussinesq fluid show that there is a continuous transition from a dynamo regime through a convective regime to an oscillatory regime as the strength of the imposed magnetic field is progressively increased. The patterns found in these different regimes are described and analyzed.

Turbulent compressible convection

Numerical simulations with high spatial resolution (up to 96-cubed gridpoints) are used to study three-dimensional, compressible convection. A sequence of four models with decreasing viscous dissipation is considered in studying the changes in the flow structure and transport properties as the convection becomes turbulent. 39 refs.

Suppression of turbulent transport by a weak magnetic field

Two-dimensional numerical simulations with high spatial resolution are used to study the effects of a large-scale magnetic field on its turbulent transport. It is commonly believed that the nonlinear back-reaction of the magnetic field on the turbulence becomes important when the field strength is close to equipartition. However, turbulent diffusion is effectively reduced even when the large-scale field is much weaker than equipartition. 15 refs.

Periodic and aperiodic dynamo waves

Abstract In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parkers dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity.

Magnetic field generation in Kolmogorov turbulence

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) approximately l(alpha), alpha<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.

Dynamo action in a rotating convective layer

We study dynamo processes in a convective layer of Boussinesq fluid rotating about the vertical. Irrespective of rotation, if the magnetic Reynolds number is large enough, the convection acts as an efficient small-scale dynamo with a growth time comparable with the turnover time and capable of generating a substantial amount of magnetic energy. When the rotation is important (large Taylor number) the characteristic horizontal scale of the convection decreases and the flow develops a well-defined distribution of kinetic helicity antisymmetric about the mid-plane. We find no convincing evidence of large-scale dynamo action associated with this helicity distribution. Even when the rotation is strong, the magnetic energy at large scales remains small, and comparable with that in the non-rotating case. By externally imposing a uniform field, we measure the average electromotive force. We find this quantity to be extremely strongly fluctuating, and are able to compute the associated

Dynamic alignment in driven magnetohydrodynamic turbulence

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