Prediction of free magnetic energy stored in a solar active region via a power-law relation between free magnetic energy and emerged magnetic flux

To estimate free magnetic energy stored in an active region is a key to the quantitative prediction of activity observed on the Sun. This energy is defined as an excess over the potential energy that is the lowest energy taken by a magnetic structure formed in the solar atmosphere including the solar corona. It is, however still difficult to derive the configuration of a coronal magnetic field only by observations, so we have to use some observable quantity to estimate free magnetic energy. Recently, by performing a coordinated series of three-dimensional magnetohydrodynamic simulations of an emerging flux tube that transfers intense magnetic flux to the solar atmosphere we have found an universal power-law relation between free magnetic energy and emerged magnetic flux, the latter of which is a possibly observed quantity. We further investigate what causes this relation through a comparison with a model of linear force-free field.