Investigation of Force-Freeness of Solar Emerging Magnetic Field via Application of the Virial Theorem to MHD Simulations

TL;DR

This study uses MHD simulations and the virial theorem to analyze how the force-free range of emerging solar magnetic fields develops and depends on the initial twist of the magnetic flux.

Contribution

It provides new insights into the evolution of the force-free range in emerging flux regions and assesses the virial theorem's applicability to dynamic solar magnetic structures.

Findings

The upper limit of the force-free range increases during emergence.

The lower limit approaches a constant near the photospheric pressure scale height.

Reduced twist leads to an increased and saturated lower limit.

Abstract

Force-freeness of a solar magnetic field is a key to reconstructing invisible coronal magnetic structure of an emerging flux region on the Sun where active phenomena such as flares and coronal mass ejections frequently occur. We have performed magnetohydrodynamic (MHD) simulations which are adjusted to investigate force-freeness of an emerging magnetic field by using the virial theorem. Our focus is on how the force-free range of an emerging flux region develops and how it depends on the twist of a pre-emerged magnetic field. As an emerging flux region evolves, the upper limit of the force-free range continuously increases while the lower limit is asymptotically reduced to the order of a photospheric pressure scale height above the solar surface. As the twist becomes small the lower limit increases and then seems to be saturated. We also discuss the applicability of the virial theorem to an evolving magnetic structure on the Sun.