Potential origins of the solar hemispherical helicity rule: Simulations of rising flux tubes in a background field

Abstract:

Based on the observations of solar active regions (ARs) and sunspots, it is theorized that large-scale magnetic flux emerges from the solar interior in the form of toroidal “magnetic flux tubes (MFTs)”. Numerical simulations of MFTs have typically focused on the rise of preconceived, highly idealized structures with no account taken of their formation. However, simulations that have studied the formation of MFTs have shown that structures akin to toroidal MFTs are formed, but that these differ substantially in many aspects. In particular, these naturally-formed structures are concentrations of twisted magnetic flux embedded in a large-scale background field, and are not isolated magnetic entities.

Motivated by these studies, we have carried out 2.5D numerical simulations of the rise of a finite-size, twisted magnetic flux concentration (MFC) embedded in a large-scale background field. In concept, our simulations lie between the previous mentioned two examples, since we do not examine the origin of the magnetic structure, but yet it is a concentration in a volume-filling field, rather than isolated. We find dramatically different dynamics, discovering that: (a) a relatively weak background field can inhibit the rise of the MFC; and, (b) the relative orientation of the background field and MFC twist can dictate different dynamics for the two cases at certain parameters. Result (b) reveals a selection mechanism that in the solar context agrees in detail with the Solar Hemispheric Helicity Rule(s) (SHHR). The SHHR primarily states that 60-80% of ARs observed have preferably negative (positive) current helicity in the solar northern (southern) hemisphere.

The dynamics elucidated from our model provide a plausible explanation for many aspects of the SHHR, not only the net bias, but also the scatter and the observed violations at the transition between cycles. We demonstrate this with Monte Carlo simulations of the rise of multiple MFCs with random properties, from which we generate synthetic helicity maps akin to the SHHR observations. We further provide a predictive analytical model of the mechanism and its dependence on the parameters that could help us use the solar observations to infer the underlying conditions in the solar interior at the point of the MFC generation.