A Dynamo Confinement Scenario for the Solar Tachocline and its Implications for Spin-down in the Radiative Spreading Regime

TL;DR

This work extends the dynamo confinement scenario for tachocline confinement into a radiative-spreading regime by conducting global 3D anelastic HD/MHD simulations in a solar-like CZ–RZ system. It shows that nonaxisymmetric dynamo modes generate Maxwell stresses that penetrate the tachocline via a magnetic skin effect, enabling confinement and rigidification of the deeper radiative zone as stratification (Bu) increases and dynamo cycles lengthen. The study carefully characterizes spin-down via angular-momentum torques, finding that radiative spreading dominates in the deepRZ for most cases and that Maxwell stresses can transmit spin-down well below the tachocline, offering a mechanism for outward angular-momentum transport. These results imply a potentially fruitful link between solar/dstellar dynamos and tachocline confinement, suggesting that dynamos may help communicate surface spin-down into the deep interior, provided sufficiently enhanced turbulent diffusivities to extend skin depths in real stars.

Abstract

At the base of the Sun's convective zone, a narrow shear layer called the tachocline separates strong latitudinal differential rotation above from nearly rigid rotation in the radiative zone below. The observed thinness of the tachocline is a long-standing dynamical puzzle because the tachocline should have spread significantly due to inward-burrowing meridional circulation, also called "radiative spreading." We recently presented the first pair of global simulations to reveal a statistically stationary tachocline confined against radiative spreading by the Maxwell stresses from the nonaxisymmetric modes of a dynamo, which penetrated into and below the tachocline through a novel magnetic skin effect. In the work presented here, we systematically examine how this "dynamo confinement scenario" works against radiative spreading in a suite of simulations as the governing parameters trend in the direction of the true solar regime. We find that as the stable stratification of the radiative zone is made progressively stronger, the dynamo cycles get longer, the magnetic field consequently penetrates deeper due to the skin effect, and the tachocline becomes more confined. Furthermore, these results have interesting consequences for solar spin-down. In all of our radiatively spreading simulations, the tachocline region spins down due to the burrowing circulation. Below the tachocline, the Maxwell stresses transmit this spin-down further to rigidify the deeper radiative zone. We thus speculate that, in addition to confining the tachocline, the dynamo may provide a pathway to communicate spin-down from the near-surface layers to the deep interior.

Figures (14)

• Figure 1: (a) Schematic of our three-dimensional spherical-shell simulation domain. The yellow region depicts the CZ with bulk overturning fluid motions represented by circular arrows. The CZ lies atop a thin stably stratified region (green) with significant nonlinear effects from overshoot and a deep RZ (purple) where the motion is essentially linear, represented by curvy "radiation" arrows. (b) Schematic of the reference state which enforces the geometry of panel (a). Convection is forced in roughly the bottom third of the CZ by a prescribed internal heating $\tilde{Q}_{\rm rad}^*$, which causes an accompanying "nonradiative" energy flux $4\pi r^{*2}\tilde{F}_{\rm{nr}}^*$ that convection and conduction must carry in a steady state to maintain thermal equilibrium (see Featherstone2016a). The stable stratification is enforced through the background positive squared buoyancy frequency $\widetilde{N}^{*2}$ in the RZ. These are the shapes of the profiles used for cases 0, 3, 4, and 6 and have been normalized to all lie on the same scale. The dashed circle (panel a) and line (panel b) mark the location of the true solar surface.
• Figure 2: Location in parameter space (${\rm{Bu}}$ and $\sigma$) of the different simulations and the Sun. Cases 1 and 2 have the same ${\rm{Bu}}$ and $\sigma$, but different ${\rm{Ra}}_{\rm{f}}$ (see Table \ref{['tab:inputnondim']}). The viscous and radiative spreading regimes are separated at $\sigma=\sigma_c\approx10$ (see Appendix \ref{['ap:sigmac']}).
• Figure 3: Spherical and meridional surfaces cut out of the simulation domain showing snapshots of the simulated flows in Case M6 for (a) the fluctuating axial vorticity $\omega_z^\prime$ and (b) the colatitudinal component of the poloidal magnetic field, $B_\theta$. Red/yellow/blue tones indicate positive/zero/negative values. Each snapshot is taken toward the end of the simulation ($t={t_{\rm{run}}}$). The inner and outer spherical surfaces bounding the shell are taken just above and below the inner and outer domain boundaries ${r_{\rm in}}$ and ${r_{\rm out}}$, respectively. The meridional surfaces are located $90^\circ$ apart, at $\phi=-30^\circ$ and $\phi=60^\circ$ (with $\phi=0^\circ$ being the central viewing longitude). Each radial level is normalized separately by the rms of the field at that level, leading to enhanced signal from the deeper regions, whose flows and fields are in fact much weaker-amplitude than they are higher up. The interface $r=r_{\rm c}$ is marked by dashed black curves. Animated versions of the separate panels are available in the online journal.
• Figure 4: Steady-state differential rotation $\left\langle2\Omega-1\right\rangle_{t}$ for the full simulation suite, plotted in the meridional plane. Red/yellow/blue tones indicate positive/zero/negative values. The outer ticks in each color bar mark the the saturation values (which are labeled) and the inner tick marks zero. Contours are equally spaced (for positive and negative values separately) and the zero contour is dashed. The dashed interior semicircle marks $r=r_{\rm bcz}$. A dotted vertical line separates the viscous spreading regime (Case 0) from the radiative spreading regime (Cases 1--6). In the radiative spreading regime, the stratification (${\rm{Bu}}$) mostly increases to the right, as shown schematically by the arrow.
• Figure 5: (a) Differential rotation contrast in the RZ defined in Equation \ref{['eq:drrz']}, plotted with respect to case number. (b) Differential rotation contrast in the CZ defined in Equation \ref{['eq:drcz']}. (c) The confinement ratio $f$ defined in Equation \ref{['eq:f']}. Note that because of the chosen ordering, $f$ monotonically decreases for the MHD cases within the radiative spreading regime. (d) The RZ's shear-layer thickness defined in Equation \ref{['eq:dtach']}.