Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field

Brandenburg, Axel; Gressel, Oliver; Jabbari, Sarah; Kleeorin, N.; Rogachevskii, I.

doi:10.1051/0004-6361/201322681

Cited by 28 publications

(74 citation statements)

References 35 publications

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“…Recent DNS using isothermal layers have shown that strong circular flux concentrations can be produced in the case of a vertical magnetic field (Brandenburg et al , 2014. This is also observed in the present study of a polytropic layer; see Fig.…”

Section: Vertical Fieldssupporting

confidence: 89%

“…While NEMPI with horizontal magnetic field still leads to downflows in the nonlinear regime (the "potato-sack" effect), our present work now confirms that structures consisting of vertical A2, page 10 of 11 fields do not sink, but reach a strength comparable to or in excess of the equipartition value (Brandenburg et al , 2014. This makes NEMPI a viable mechanism for spontaneously producing magnetic spots in the surface layers.…”

Section: Discussionsupporting

confidence: 76%

“…In particular, the horizontal scale of structures was previously determined to be about 6-8 H ρ (Kemel et al 2013;Brandenburg et al 2014). Looking now at Fig.…”

Section: Discussionmentioning

confidence: 80%

“…The wavenumber of the energy-carrying turbulent eddies k f is in nondimensional form κ f ≡ k f H ρ , and the normalized horizontal wavenumber of the resulting magnetic structures is referred to as κ ⊥ = k ⊥ H ρ . For NEMPI, these values have been estimated to be κ ⊥ = 0.8-1.0, and can even be smaller for vertical magnetic fields (Brandenburg et al 2014). Using an approximate aspect ratio of unity for magnetic structures, we have κ = √ 2κ ⊥ ≈ 1.1-1.4.…”

Section: Governing Parameters and Estimatesmentioning

confidence: 87%

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Magnetic flux concentrations in a polytropic atmosphere

Losada

Brandenburg

Kleeorin

2014

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Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout. Aims. We now want to know whether earlier conclusions regarding the size of magnetic structures and their growth rates carry over to the case of polytropic layers, in which the scale height decreases sharply as one approaches the surface. Methods. To allow for a continuous transition from isothermal to polytropic layers, we employ a generalization of the exponential function known as the q-exponential. This implies that the top of the polytropic layer shifts with changing polytropic index such that the scale height is always the same at some reference height. We used both mean-field simulations (MFS) and direct numerical simulations (DNS) of forced stratified turbulence to determine the resulting flux concentrations in polytropic layers. Cases of both horizontal and vertical applied magnetic fields were considered. Results. Magnetic structures begin to form at a depth where the magnetic field strength is a small fraction of the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic case the growth rate of NEMPI decreases for structures deeper down. Moreover, the structures that form higher up have a smaller horizontal scale of about four times their local depth. For vertical fields, magnetic structures of super-equipartition strengths are formed, because such fields survive downward advection that causes NEMPI with horizontal magnetic fields to reach premature nonlinear saturation by what is called the "potato-sack" effect. The horizontal cross-section of such structures found in DNS is approximately circular, which is reproduced with MFS of NEMPI using a vertical magnetic field. Conclusions. Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon.

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Section: Vertical Fieldssupporting

confidence: 89%

Section: Discussionsupporting

confidence: 76%

“…In particular, the horizontal scale of structures was previously determined to be about 6-8 H ρ (Kemel et al 2013;Brandenburg et al 2014). Looking now at Fig.…”

Section: Discussionmentioning

confidence: 80%

Section: Governing Parameters and Estimatesmentioning

confidence: 87%

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Magnetic flux concentrations in a polytropic atmosphere

Losada

Brandenburg

Kleeorin

2014

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“…In the above-mentioned studies the field concentrations often form a spot-like structure because the ratio between the domain size and forcing scale is sufficiently large (e.g. Brandenburg et al 2013Brandenburg et al , 2014Losada et al 2014). …”

Section: Imposed Vertical Fieldmentioning

confidence: 99%

Magnetic flux concentrations from turbulent stratified convection

Käpylä

Brandenburg

Kleeorin

et al. 2016

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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.

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