Abstract
Context.Conservation properties of magnetic helicity and energy in the quasi-ideal and low-βsolar corona make these two quantities relevant for the study of solar active regions and eruptions.Aims.Based on a decomposition of the magnetic field into potential and nonpotential components, magnetic energy and relative helicity can both also be decomposed into two quantities: potential and free energies, and volume-threading and current-carrying helicities. In this study, we perform a coupled analysis of their behaviors in a set of parametric 3D magnetohydrodynamic (MHD) simulations of solar-like eruptions.Methods.We present the general formulations for the time-varying components of energy and helicity in resistive MHD. We calculated them numerically with a specific gauge, and compared their behaviors in the numerical simulations, which differ from one another by their imposed boundary-driving motions. Thus, we investigated the impact of different active regions surface flows on the development of the energy and helicity-related quantities.Results.Despite general similarities in their overall behaviors, helicities and energies display different evolutions that cannot be explained in a unique framework. While the energy fluxes are similar in all simulations, the physical mechanisms that govern the evolution of the helicities are markedly distinct from one simulation to another: the evolution of volume-threading helicity can be governed by boundary fluxes or helicity transfer, depending on the simulation.Conclusions.The eruption takes place for the same value of the ratio of the current-carrying helicity to the total helicity in all simulations. However, our study highlights that this threshold can be reached in different ways, with different helicity-related processes dominating for different photospheric flows. This means that the details of the pre-eruptive dynamics do not influence the eruption-onset helicity-related threshold. Nevertheless, the helicity-flux dynamics may be more or less efficient in changing the time required to reach the onset of the eruption.
Highlights
Magnetic helicity is a volume-integrated ideal magnetohydrodynamic (MHD) invariant describing the level of twist and entanglement of the magnetic field lines
We introduce the different components of the magnetic energy and their time-variation written for the specific case of resistive MHD
In order to comparatively analyze the evolution of helicities and energies and to study the time-variation of the energy, we used magnetic field data produced by parametric 3D MHD simulations of eruptive events of the solar corona that were initially presented in Zuccarello et al (2015)
Summary
Magnetic helicity is a volume-integrated ideal magnetohydrodynamic (MHD) invariant describing the level of twist and entanglement of the magnetic field lines. The transfer term is expressed as a volume integral: these two helicities are not classically conserved quantities in the sense that they cannot be independently expressed as a flux through the boundaries, even in ideal MHD, unlike the relative magnetic helicity. This finding strengthens the knowledge of the properties of nonpotential and volume-threading helicity that was first studied by Moraitis et al (2014). Hj and Hp j are not conserved quantities in resistive or ideal MHD
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