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

Abstract

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-like flux concentrations embedded 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.