Large-scale dynamos in turbulent convection with shear

Kleeorin

et al. 2016

A&A

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Context. The formation of magnetic flux concentrations within the solar convection zone leading to sunspot formation is unexplained. Aims. We study the self-organization of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods. We perform simulations of magnetoconvection in Cartesian domains representing the uppermost 8.5−24 Mm of the solar convection zone with the horizontal size of the domain varying between 34 and 96 Mm. The density contrast in the 24 Mm deep models is more than 3 × 10 3 or eight density scale heights, corresponding to a little over 12 pressure scale heights. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow in set-ups where no small-scale dynamos are present. In the most highly stratified cases we employ the reduced sound speed method to relax the time step constraint arising from the high sound speed in the deep layers. We model radiation via the diffusion approximation and neglect detailed radiative transfer in order to concentrate on purely magnetohydrodynamic effects. Results. We find that super-equipartition magnetic flux concentrations are formed near the surface in cases with moderate and high density stratification, corresponding to domain depths of 12.5 and 24 Mm. The size of the concentrations increases as the box size increases and the largest structures (20 Mm horizontally near the surface) are obtained in the models that are 24 Mm deep. The field strength in the concentrations is in the range of 3-5 kG, almost independent of the magnitude of the imposed field. The amplitude of the concentrations grows approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in most of the domain, which is unfavourable for the operation of the negative effective magnetic pressure instability (NEMPI). Simulations in which a passive vector field is evolved do not show a noticeable difference from magnetohydrodynamic runs in terms of the growth of the structures. Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions. The linear growth of large-scale flux concentrations implies that their dominant formation process is a tangling of the large-scale field rather than an instability. One plausible mechanism that can explain both the linear growth and the concentration of the flux in the regions of converging flow pattern is flux expulsion. A possible reason for the absence of NEMPI is that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign. Furthermore, there may not be sufficient scale separation, which is required for NEMPI to work.

Section: Effective Magnetic Pressurecontrasting

confidence: 99%

Magnetic flux concentrations from turbulent stratified convection

Käpylä

Kleeorin

et al. 2016

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“…However, this interpretation is problematic because we cannot be certain that the magnetic field in the Sun is generated in the form of flux ropes. Indeed, simulations of successful large-scale dynamos suggest that concentrated tube-like structures are more typical of the early kinematic stage, but in the final nonlinear stage the field becomes more space-filling (Brandenburg 2005;Käpylä et al 2008). The idea that the dynamics of such tubes is governed by magnetic buoyancy is problematic too, because the solar convection zone is strongly stratified with concentrated downdrafts and broader upwellings.…”

Section: Introductionmentioning

confidence: 99%

Surface appearance of dynamo-generated large-scale fields

Warnecke

2010

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Aims. Twisted magnetic fields are frequently seen to emerge above the visible surface of the Sun. This emergence is usually associated with the rise of buoyant magnetic flux structures. Here we ask how magnetic fields from a turbulent large-scale dynamo appear above the surface if there is no magnetic buoyancy. Methods. The computational domain is split into two parts. In the lower part, which we refer to as the turbulence zone, the flow is driven by an assumed helical forcing function leading to dynamo action. Above this region, which we refer to as the exterior, a nearly force-free magnetic field is computed at each time step using the stress-and-relax method. Results. Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Strong current sheets tend to form above the neutral line, where the vertical field component vanishes. Time series of the magnetic field structure show recurrent plasmoid ejections. The degree to which the exterior field is force free is estimated as the ratio of the dot product of current density and magnetic field strength to their respective rms values. This ratio reaches values of up to 95% in the exterior. A weak outward flow is driven by the residual Lorentz force.

“…Nevertheless this constraint may be lifted if the system is able to rid itself of small-scale helicity through at least one of several ways such as open boundaries, advective, diffusive and shear-driven fluxes (Shukurov et al 2006;Zhang et al 2006;Sur et al 2007;Käpylä et al 2008;Brandenburg et al 2009;Guerrero et al 2010). Even though the helicity constraint in direct numerical simulations (DNS) of dynamos with strong shear have been clearly identified, the results can be matched with mean field models with a weaker algebraic quenching than α 2 dynamos .…”

Section: Introductionmentioning

confidence: 99%

Magnetic helicity fluxes in interface and flux transport dynamos

Chatterjee

Gómez

2010

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Context. Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. Aims. In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we aim to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. Methods. We consider a model with only radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic α owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic α effect that feeds back on the kinetic α effect. In some cases we compare these results with those obtained from a model with a simple algebraic α quenching formula.Results. In agreement with earlier findings, the magnetic α effect has the opposite sign compared with the kinetic α effect and leads to a catastrophic decrease of the saturation field strength proportional to the inverse magnetic Reynolds number. At high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward because of the opposite sign of α. These secondary dynamo waves are driven by small-scale magnetic helicity instead of the small-scale kinetic helicity. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching. Interestingly, supercritical diffusive helicity fluxes also give rise to secondary dynamo waves and grand minima-like episodes.