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Abstract We recently presented the first 3D numerical simulation of the solar interior for which tachocline confinement was achieved by a dynamo-generated magnetic field. In this follow-up study, we analyze the degree of confinement as the magnetic field strength changes (controlled by varying the magnetic Prandtl number) in a coupled radiative zone (RZ) and convection zone (CZ) system. We broadly find three solution regimes, corresponding to weak, medium, and strong dynamo magnetic field strengths. In the weak-field regime, the large-scale magnetic field is mostly axisymmetric with regular, periodic polarity reversals (reminiscent of the observed solar cycle) but fails to create a confined tachocline. In the strong-field regime, the large-scale field is mostly nonaxisymmetric with irregular, quasi-periodic polarity reversals and creates a confined tachocline. In the medium-field regime, the large-scale field resembles a strong-field dynamo for extended intervals but intermittently weakens to allow temporary epochs of strong differential rotation. In all regimes, the amplitude of poloidal field strength in the RZ is very well explained by skin-depth arguments, wherein the oscillating field that gives rise to the skin depth (in the medium- and strong-field cases) is a nonaxisymmetric field structure at the base of the CZ that rotates with respect to the RZ. These simulations suggest a new picture of solar tachocline confinement by the dynamo, in which nonaxisymmetric, very long-lived (effectively permanent) field structures rotating with respect to the RZ play the primary role, instead of the regularly reversing axisymmetric field associated with the 22 yr cycle. 

Abstract Inspired by observations of sunspots embedded in active regions, it is often assumed that large-scale, strong magnetic flux emerges from the Sun’s deep interior in the form of arched, cylindrical structures, colloquially known as flux tubes. Here, we continue to examine the different dynamics encountered when these structures are considered as concentrations in a volume-filling magnetic field rather than as isolated entities in a field-free background. Via 2.5D numerical simulations, we consider the buoyant rise of magnetic flux concentrations from a radiative zone through an overshooting convection zone that self-consistently (via magnetic pumping) arranges a volume-filling large-scale background field. This work extends earlier papers that considered the evolution of such structures in a purely adiabatic stratification with an assumed form of the background field. This earlier work established the existence of a bias that created an increased likelihood of the successful rise for magnetic structures with one (relative) orientation of twist and a decreased likelihood for the other. When applied to the solar context, this bias is commensurate with the solar hemispherical helicity rules (SHHRs). This paper establishes the robustness of this selection mechanism in a model incorporating a more realistic background state, consisting of overshooting convection and a turbulently pumped mean magnetic field. Ultimately, convection only weakly influences the selection mechanism, since it is enacted at the initiation of the rise, at the edge of the overshoot zone. Convection does however add another layer of statistical fluctuations to the bias, which we investigate in order to explain variations in the SHHRs. 

Abstract Solar active regions and sunspots are believed to be formed by the emergence of strong toroidal magnetic flux from the solar interior. Modeling of such events has focused on the dynamics of compact magnetic entities, colloquially known as “flux tubes,” often considered to be isolated magnetic structures embedded in an otherwise field-free environment. In this paper, we show that relaxing such idealized assumptions can lead to surprisingly different dynamics. We consider the rise of tube-likeflux concentrationsembedded in a large-scale volume-filling horizontal field in an initially quiescent adiabatically stratified compressible fluid. In a previous letter, we revealed the unexpected major result that concentrations whose twist is aligned with the background field at the bottom of the tube are more likely to rise than the opposite orientation (for certain values of parameters). This bias leads to a selection rule which, when applied to solar dynamics, is in agreement with the observations known as the solar hemispheric helicity rule(s) (SHHR). Here, we examine this selection mechanism in more detail than was possible in the earlier letter. We explore the dependence on parameters via simulations, delineating the Selective Rise Regime, where the bias operates. We provide a theoretical model to predict and explain the simulation dynamics. Furthermore, we create synthetic helicity maps from Monte Carlo simulations to mimic the SHHR observations, and to demonstrate that our mechanism explains the observed scatter in the rule, as well as its variation over the solar cycle.