Impacts of small-scale dynamo on rotating columnar convection in stellar convection zones

TL;DR

This study demonstrates that small-scale dynamo (SSD) action markedly alters rotating equatorial convection by strengthening entropy fluctuations, sustaining a weakly subadiabatic layer near the base, and shifting the force balance from Coriolis-Inertia-Archimedean (CIA) to magneto-Archimedean-Coriolis (MAC) at small scales. SSD suppresses convective velocities more than in HD cases, increases the effective rotational constraint on columnar modes, and enhances Maxwell stresses that counter Reynolds stresses, quenching mean shear flows. The dominant scale of columnar convection moves to smaller longitudinal extents under SSD due to elevated $Co_ extell$, while the Maxwell stress arises primarily from shear in the columnar patterns rather than small-scale field alignment. Overall, SSD effects are crucial for realistic solar/stellar convection modeling and motivate subgrid-scale approaches to capture their impact on heat and angular-momentum transport, even though the local equatorial box setup omits meridional circulation and global dynamo processes.

Abstract

Understanding the complex interactions between convection, magnetic fields, and rotation is key to modeling the internal dynamics of the Sun and stars. Under rotational influence, compressible convection forms prograde-propagating convective columns near the equator. The interaction between such rotating columnar convection and the small-scale dynamo (SSD) remains largely unexplored. We investigate the influence of the SSD on the properties of rotating convection in the equatorial regions of solar and stellar convection zones. A series of rotating compressible magnetoconvection simulations is performed using a local f-plane box model at the equator. The flux-based Coriolis number Co is varied systematically. To isolate the effects of the SSD, we compare results from hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations. The SSD affects both convective heat and angular momentum transport. In MHD cases, convective velocity decreases more rapidly with increasing Co than in HD cases. This reduction is compensated by enhanced entropy fluctuations, maintaining overall heat transport efficiency. Furthermore, a weakly subadiabatic layer is maintained near the base of the convection zone even under strong rotational influence when the SSD is present. These behaviors reflect a change in the dominant force balance: the SSD introduces a magnetostrophic balance at small scales, while geostrophic balance persists at larger scales. The inclusion of the SSD also reduces the dominant horizontal scale of columnar convective modes by enhancing the effective rotational influence. Regarding angular momentum transport, the SSD generates Maxwell stresses that counteract the Reynolds stresses, thereby quenching the generation of mean shear flows. These SSD effects should be accounted for in models of solar and stellar convection.

Figures (23)

• Figure 1: Sketch of the local Cartesian model of the stellar convection zone. The local $f$-plane box is located at the equator, where the $x$, $y$, and $z$ axes point to the longitudinal, latitudinal, and radial directions, respectively.
• Figure 2: Temporal evolution of the volume-integrated kinetic and magnetic energies $E_{\mathrm{kin}}$ (dashed curves) and $E_{\mathrm{mag}}$ (solid curves) from the MHD runs. Different colors represent the results with different Co$_{*}$.
• Figure 3: Temporal snapshots of (a) the vertical velocity $v_{z}$ from case HD-Co1, (b) $v_{z}$ from case MHD-Co1, and (c) the vertical magnetic field $B_{z}$ from MHD-Co1 in the statistically-stationary states at $t \approx 80~\tau_{*}$. Top and middle panels show the horizontal cuts near the top surface, $z=2.2~H_{r}$, and in the middle convection zone $z=1.2~H_{r}$. Bottom panels show the vertical cuts at $y=0$. An animation of this figure is available https://drive.google.com/file/d/1H_O0N2IodQlydZlGmBx8n7wW6egkAh91/view?usp=sharing.
• Figure 4: Same as Fig. \ref{['fig:snap_vz_Co1']} but from the simulation cases HD-Co2 and MHD-Co2. An animation of this figure is available https://drive.google.com/file/d/10gmD3rqc8ZywXuIj2fhU0LfChBDvg4pd/view?usp=sharing.
• Figure 5: Same as Fig. \ref{['fig:snap_vz_Co1']} but from the simulation cases HD-Co5 and MHD-Co5. An animation of this figure is available https://drive.google.com/file/d/1qMr4RnmgonlIrPpvW16R7COS9HJYSfZ9/view?usp=sharing.