The Minimal Helicity of Solar Coronal Magnetic Fields

TL;DR

This study investigates the local topological structures of the Sun's coronal magnetic fields by analyzing field line helicities, revealing that local helicity patches are linked to active regions and their magnetic interactions.

Contribution

It introduces a method to compute and analyze field line helicities from potential field extrapolations, uncovering the local helicity structures not captured by global helicity measures.

Findings

Local helicity patches arise from linking between active regions and overlying fields.

Unsigned helicity correlates with the product of photospheric and open fluxes.

Cycle 24 had a peak in unsigned helicity due to a large active region.

Abstract

Potential field extrapolations are widely used as minimum-energy models for the Sun's coronal magnetic field. As the reference to which other magnetic fields are compared, they have -- by any reasonable definition -- no global (signed) magnetic helicity. Here we investigate the internal topological structure that is not captured by the global helicity integral, by splitting it into individual field line helicities. These are computed using potential field extrapolations from magnetogram observations over Solar Cycle 24, as well as for a simple illustrative model of a single bipolar region in a dipolar background. We find that localised patches of field line helicity arise primarily from linking between strong active regions and their overlying field, so that the total unsigned helicity correlates with the product of photospheric and open fluxes. Within each active region, positive and negative helicity may be unbalanced, but the signed helicity is only around a tenth of the unsigned helicity. Interestingly, in Cycle 24, there is a notable peak in unsigned helicity caused by a single large active region. On average, the total unsigned helicity at the resolution considered is approximately twice the typical signed helicity of a single real active region, according to non-potential models in the literature.