Investigation of force-freeness of a solar emerging magnetic field via application of the virial theorem to magnetohydrodynamic simulations

Force-freeness of a solar magnetic field is a key to reconstructing the 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 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.