Magnetic flux concentrations in a polytropic atmosphere

Abstract: 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 for which the density scale height is constant throughout. We now study the validity of earlier conclusions about the size and growth rate of magnetic structures in the case of polytropic layers, which scale height decreases sharply towards the surface. To allow for a continuous transition from isothermal to polytropic layers, we employ a generalization of the exponential function known as the q-exponential. Now, the top of the polytropic layer shifts with the polytropic index such that the scale height at some reference height is always the same. We use both mean-field and direct numerical simulations of forced stratified turbulence to determine the resulting flux concentrations. Magnetic structures begin to form at a depth where magnetic field strength is about 3-4% 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 one the growth rates decreases for structures deeper down. For vertical fields, magnetic structures of super-equipartition strengths are formed because such fields survive downward advection, unlike NEMPI under horizontal magnetic fields. The horizontal cross-section of such structures is approximately circular. 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.

• The paper demonstrates that magnetic flux concentrations form at shallow depths where fields are below equipartition, activating NEMPI in polytropic layers.
• The paper finds that vertical magnetic fields yield robust 'potato-sack' structures exceeding equipartition strength, unlike horizontal fields that saturate early.
• The paper implies that near-surface magnetic flux concentrations may drive sunspot formation, challenging the deep-seated magnetic field paradigm in solar physics.

Analysis of Magnetic Flux Concentrations in Polytropic Atmospheres

The paper by Losada et al. investigates the self-organization of magnetic fields in strongly stratified hydromagnetic turbulence characterized by the Negative Effective Magnetic Pressure Instability (NEMPI). The examination extends previous findings from isothermal atmospheres to more complex polytropic layers. The main objective is to verify if earlier deductions regarding magnetic structures' dimensions and growth rates apply to polytropic scenarios.

Key Findings and Methodology

The paper employs a dual-approach technique consisting of mean-field simulations (MFS) and direct numerical simulations (DNS) to study magnetic flux concentrations in polytropic atmospheres. The primary parameter of interest is the density scale height, which decreases significantly towards the surface layer in a polytropic atmosphere. This adaptation allows observation of the behavior of magnetic fields under more astrophysical conditions compared to isothermal models where the density scale height is constant.

1. Formation of Magnetic Structures: Losada et al. discovered that magnetic structures originate at depths where local magnetic fields are significantly weaker than the equipartition field strength. Notably, the growth of NEMPI decreases at greater depths, unlike in isothermal ladders where deeper structures can form due to less turbulent suppression.
2. Role of Vertical and Horizontal Magnetic Fields: The study reveals that for vertical magnetic fields, super-equipartition strength structures emerge. These structures, termed "potato-sack" formations, are resistant to being advected downward, unlike their horizontal magnetic field counterparts, which saturate prematurely.
3. Application to Solar Physics: The insights suggest that while findings from isothermal models can be locally transposed onto polytropic layers, the vertical magnetic fields in particular signal that powerful, shallow magnetic flux concentrations, akin to sunspots, might arise predominantly near the solar surface rather than at greater depths.

Numerical Results and Implications

Quantitatively, the analysis demonstrates a significant difference in growth rates between MFS and DNS when comparing polytropic and isothermal layers. Notably, maximum growth rates for the polytropic configurations appeared lower compared to their isothermal counterparts. The horizontal extent of emerging structures aligns with previous estimates of 6–8 local scale heights, underscoring the dimensional robustness of the NEMPI model across different atmospheric conditions.

The implications of these results are profound for both theoretical and practical aspects of solar and stellar magnetic field studies. The research explicitly supports the hypothesis of shallow sunspot formation, providing a potential resolution to debates surrounding the depths at which these phenomena originate. This effect is critical in light of the inability of classical models to explain all features of solar activity through deep-seated magnetic fields alone.

Future Directions

The study presents several promising avenues for subsequent research. Future investigations could benefit from incorporating the effects of convection, ionization layers, and realistic solar radiation conditions to further refine the applicability of NEMPI. Extending the research to include non-turbulent induced convection zones and varying polytropic indices will provide further clarity on the universality of these findings.

Overall, Losada et al. have significantly expanded the comprehension of magnetic flux concentrations in stratified atmospheres. This work invites a reexamination of commonly held assumptions in solar and stellar magnetic field generation and aligns with a growing body of evidence toward surface-oriented magnetic phenomena.