  This Letter reports scaling laws of free magnetic energy stored in a solar
emerging flux region which is a key to understanding the energetics of solar
active phenomena such as solar flares and coronal mass ejections. By performing
3-dimensional magnetohydrodynamic simulations that reproduce several emerging
flux regions of different magnetic configurations, we derive power law
relationships among emerged magnetic flux, free magnetic energy and relative
magnetic helicity in these emerging flux regions. Since magnetic flux is an
observable quantity, the scaling law between magnetic flux and free magnetic
energy may give a way to estimate invisible free magnetic energy responsible
for solar active phenomena.
