Time variations of the non-potential and volume-threading magnetic helicities

TL;DR

This paper analytically examines the time variations of non-potential and volume-threading magnetic helicities in solar coronal dynamics, revealing they are not conserved and are dominated by transformation terms, impacting their observational estimation.

Contribution

It provides the first analytical formulas for the time evolution of these helicities and confirms their non-conservation through 3D MHD simulations, highlighting their dynamic behavior.

Findings

Non-potential and volume-threading helicities are not conserved in ideal MHD.

Transformation terms often dominate their dynamics.

Surface flux measurements are insufficient for their evolution analysis.

Abstract

Relative magnetic helicity is a gauge invariant quantity suitable for the study of the magnetic helicity content of heliospheric plasmas. Relative magnetic helicity can be decomposed uniquely into two gauge invariant quantities, the magnetic helicity of the non-potential component of the field, and a complementary volume-threading helicity. Recent analysis of numerical experiments simulating the generation of solar eruptions have shown that the ratio of the non-potential helicity to the total relative helicity is a clear marker of the eruptivity of the magnetic system, and that the high value of that quantity could be a sufficient condition for the onset of the instability generating the eruptions. The present study introduces the first analytical examination of the time variations of these non-potential and volume-threading helicities. The validity of the analytical formulas derived are confirmed with analysis of three-dimensional (3D) magnetohydrodynamics (MHD) simulations of solar coronal dynamics. Both the analytical investigation, and the numerical application show that, unlike magnetic helicity, the non-potential and the volume-threading helicities are not conserved quantities, even in the ideal MHD regime. A term corresponding to the transformation between the non-potential and volume-threading helicities frequently dominates their dynamics. This finding has an important consequence for their estimation in the solar corona: unlike with relative helicity, their volume coronal evolution cannot be ascertained by the flux of these quantities through the volume's boundaries. Only techniques extrapolating the 3D coronal field will enable both the proper study of the non-potential and volume-threading helicities, and the observational analysis of helicity-based solar-eruptivity proxies.