Magnetorotational instability in a solar near-surface mean-field dynamo

TL;DR

This paper addresses whether the magnetorotational instability (MRI) can operate in the Sun's near-surface shear layer (NSSL) and how it interacts with mean-field dynamos. Using two-dimensional hydromagnetic mean-field simulations in a shearing box with $\alpha$-effects and turbulent diffusivities, it characterizes MRI onset and energy redistribution between magnetic and kinetic energies. The key finding is that MRI occurs only for negative shear ($C_\Omega<0$) when the negative shear exceeds a critical threshold that scales as $C_\Omega^{crit} \approx 30\,\mathcal{B}_{eq}^{-1}$; MRI activity increases kinetic energy and dissipation and can supplant or suppress certain magnetic-energy modes. Applying solar parameters suggests turbulent diffusivity likely prevents MRI excitation in the NSSL, implying that the standard $\Omega$-effect remains the dominant dynamo mechanism there; this constrains MRI's role in solar magnetism and informs modeling of solar near-surface dynamos.

Abstract

We address the question whether the magnetorotational instability (MRI) can operate in the near-surface shear layer (NSSL) of the Sun and how it affects the interaction with the dynamo process. Using hydromagnetic mean-field simulations of $αΩ$-type dynamos in rotating shearing-periodic boxes, we show that for negative shear, the MRI can operate above a certain critical shear parameter. This parameter scales inversely with the equipartition magnetic field strength above which $α$ quenching set in. Like the usual $Ω$ effect, the MRI produces toroidal magnetic field when the field is sufficiently strong. The work done by the Lorentz force is positive, so the magnetic field drives kinetic energy and not the other way around, as in a turbulent dynamo. This results in strong kinetic energy production and dissipation, which occurs at the expense of the magnetic energy. In view of the application to the solar NSSL, we conclude that the turbulent magnetic diffusivity may be too large for the MRI to be excited and that therefore only the standard $Ω$ effect is expected to operate.

Figures (10)

• Figure 1: Flow of energy in a hydromagnetic mean-field dynamo.
• Figure 2: Sketch illustrating the generation of $\overline{B}_y$ from $\overline{B}_x$ through the $\Omega$ effect and from $\overline{B}_z$ through the MRI, and the generation of both $\overline{B}_x$ and $\overline{B}_z$ from $\overline{B}_y$ through the $\alpha$ effect.
• Figure 3: Rädler diagram for the $\alpha^2\Omega$ dynamo with $z$ extent (solid line) and the $\alpha^2$ dynamo with $x$ extent in a domain with $L_z/L_x=1/2$ (horizontal dash-dotted line). The onset location in the pure $\alpha\Omega$ approximation ($C_\alpha C_\Omega=2$) is shown as dashed lines. The case with the vertical field boundary condition is shown as the dotted line and is marked BC.
• Figure 4: Time dependence of ${\cal E}_{\rm M}$ (dotted black line), ${\cal E}_{\rm M}^Z$ (solid blue line), and ${\cal E}_{\rm M}^X$ (dashed red line), all normalized by ${\cal E}_{\rm M}^\mathrm{eq}$, and $\overline{B}_y$ versus $t$ and $z$ for a fratricidal dynamo (Run F) with $C_\alpha=1$, $C_\Omega=150$, $q=-3/2$ (positive shear), and $B_{\rm eq}\to\infty$ (no $\alpha$ quenching). Here, $\overline{B}_y$ has been normalized by its instantaneous rms values so as to see the dynamo wave also during the early exponential growth phase and during the late decay phase.
• Figure 5: Similar to Figure \ref{['pfratri_bm']}, but for a suicidal dynamo with $C_\alpha=0.49$ and $C_\Omega=7.5$ (Run B).