Time Variations of the Nonpotential and Volume-threading Magnetic Helicities

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 volumethreading 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 helicitybased solar-eruptivity proxies.

Energy and helicity fluxes in line-tied eruptive simulations

“…Moreover, as with the flux emergence simulations presented in Linan et al (2018), the eruption is accompanied by a sharp decrease of the transfer term. However, unlike in Linan et al (2018), the sign of dH j /dt| Transf does not change here during the onset phase of the eruption. During the eruption phase, the dissipation terms, dH j /dt| Diss and dH pj /dt| Diss , dominate the variation of the helicities.…”

“…9.3. Linan et al (2018) validated the time-variations equations established for the volume-threading helicity, H pj , and the currentcarrying helicity, H j . The accuracy of the computation is related to difference factors such as the discretization and the remapping of the data, spatial and temporal, as well as to nonexplicit numerical diffusive terms that are not accounted for in our analytical resistive MHD model.…”

“…From this decomposition, Linan et al (2018) obtained an equation for the time-variation that is composed only of gaugeinvariant terms:…”

“…We performed a similar time variation for E v as Linan et al (2018) did for helicities as we summarized in Sect. 2.…”

“…As mentioned in the introduction (see Sect. 1), Linan et al (2018) showed for two different eruptive simulations that the exchange between H pj and H j is controlled by the gauge-invariant transfer term dH j /dt| Transf (see Eq. 10), which therefore plays a key role in evolving these helicities.…”