RELATION BETWEEN VIRIAL ENERGY AND MAGNETIC ENERGY PROVIDED BY AN EMERGING FLUX TUBE ON THE SUN

The MHD virial theorem applied for observed photospheric field may be the one of way to estimate magnetic energy of generally invisible coronal magnetic structure. However, the photospheric field is not in a force-free state, so the application of virial theory needs some care. Here we use a series of MHD simulations of emerging field to investigate how we can apply the virial theorem to the emerging field. In early emerging phase, virial energy has a minus value although positive area at the photosphere is continuously generated toward a late emerging phase. We discuss why this tendency occurs. Then we derive the critical height where the actual emerging magnetic energy is almost comparable to the virial energy. If the difference between virial energy and magnetic energy becomes 10 percentage of the magnetic energy, we define this is the critical height, and assume the emerging field is close to force-free. We also discuss how the critical height changes with the initial twist of an emerging flux tube.