Properties of the negative effective magnetic pressure instability

Kemel, Koen; Brandenburg, Axel; Kleeorin, N.; Rogachevskii, I.

doi:10.1002/asna.201111638

Cited by 29 publications

(52 citation statements)

References 25 publications

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“…This was qualitatively confirmed by Kemel et al (2012b). Using numerical solutions of the full mean-field equations, they found furthermore that the growth rate of the instability is actually independent of v A .…”

supporting

confidence: 53%

Solar Dynamics and Magnetism from the Interior to the Atmosphere

Mansour¹,

Kosovichev²,

Komm³

et al. 2014

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The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.

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supporting

confidence: 53%

Solar Dynamics and Magnetism from the Interior to the Atmosphere

Mansour¹,

Kosovichev²,

Komm³

et al. 2014

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“…In addition to β p and β , we also list the values of q p0 = β 2 /β 2 p , as well as the minimum position of the P eff (β) curve, namely (cf. Kemel et al 2012b)…”

Section: Parameter Sensitivitymentioning

confidence: 99%

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

Brandenburg

Gressel

Jabbari

et al. 2014

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Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots. Aims. We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. Methods. We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. Results. Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about eight density scale heights. Despite being ≤1% equipartition strength, it is important that their lower part is included within the computational domain to achieve the full strength of the instability. Conclusions. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated. Application to sunspots remains a viable possibility.

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“…This equation can be understood as a quenching formula for the effective magnetic pressure; see Jabbari et al (2013). The coefficients β p and β are related to P min at β min via (Kemel et al 2012a) In Fig. 8 we show these fitting parameters for the function q p (β) for polytropic layer with different γ for horizontal and vertical mean magnetic fields.…”

Section: Effective Magnetic Pressurementioning

confidence: 99%

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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Properties of the negative effective magnetic pressure instability

Cited by 29 publications

References 25 publications

Solar Dynamics and Magnetism from the Interior to the Atmosphere

Solar Dynamics and Magnetism from the Interior to the Atmosphere

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

Magnetic flux concentrations in a polytropic atmosphere

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