The Rise of Buoyant Magnetic Structures through Convection with a Background Magnetic Field

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.

On the Origin of Solar Hemispherical Helicity Rules: Simulations of the Rise of Magnetic Flux Concentrations in a Background Field

“…Tobias et al 2001) of the field out of the convection zone into the overshoot layer below, down the gradient of the turbulent intensity (referred to as the γ-effect in mean-field theory). The more self-consistent convective simulations of Manek et al (2022), that included penetrative convection and the turbulent pumping process (in 2.5D), confirmed that this approximation to the missing dynamics in the earlier works was reasonable and did not affect the major results significantly. Our initial conditions are then analytical prescriptions for the end state of the following complex system of processes: first, turbulent magnetic pumping drives some fraction of the large-scale poloidal dynamo field from the convection zone into the overshoot zone; then, an Ω-effect mechanism related to inductive stretching of that poloidal field by the differential rotation that is present creates strong toroidal field in the overshoot zone; finally, some instability mechanism (likely magnetic buoyancy) (see e.g.…”

“…The model setup used in this work is the three dimensional extension of Manek et al (2018); Manek & Brummell (2021). Note that here, for an initial foray into three dimensions, we do not include a convection zone atop a convectively-stable region, as in Manek et al (2022), but rather consider a single, adiabatic, initially-quiescent layer. Within this non-convecting layer of fluid, we add magnetic field, in the form of a prescribed cylindrical twisted flux tube embedded deep in a large-scale horizontal background field that varies exponentially in the vertical.…”

“…An alternate theory was introduced and expanded upon in a series of papers by Manek et al (Manek et al 2018;Manek & Brummell 2021;Manek et al 2022). This theory is based on a completely different effect and has been validated and demonstrated using simulations of finite-sized magnetic structures under a range of circumstances.…”

“…This mechanism has been shown to be robust, not only in parameter space when the magnetic structure is rising through a quiescent hydrodynamic background containing a prescribed large-scale horizontal magnetic field (Manek & Brummell 2021), but also when rising through a convective background containing a self-consistent large-scale horizontal background field (Manek et al 2022). These papers also offer reasonable explanations for other observed nuances of the SHHR, such as the violations leading to the weakness of the rule, and potential solar cycle modulations of the effect.…”

“…Here, we report results that explore the buoyant rise dynamics of magnetic concentrations in a volume-filling field in the full three dimensions. Earlier 2.5D work in this series (Manek et al 2018;Manek & Brummell 2021;Manek et al 2022) established the remarkable fact that the twist orientation of a flux concentration relative to the background field affected it's likelihood to rise and emerge, regardless of whether the buoyant rise took place in the absence or presence of convection. The contrasting dynamics between structures with differing orientations leads to a selection mechanism that reproduces characteristics of the "solar hemispheric helicity rule(s)" (SHHR) observations strikingly well.…”