We investigated scaling laws for magnetic quantities in an emerging flux
region, which could contribute to studying energetics of an active phenomenon observed in that region, such
as a solar flare and coronal mass ejection. By performing a series of three-dimensional magnetohydrodynamic
simulations with different degrees of field-line twist applied to an emerging flux tube, we obtained a set of emerging flux regions with different
magnetic field configurations, and derived power-law relations between magnetic
flux, free magnetic energy, and relative magnetic helicity in each of these emerging flux regions.
Since the magnetic flux could be estimated via a surface integral of the magnetic field observed at a solar surface (photosphere), the scaling laws for the magnetic flux
and the free magnetic energy/relative magnetic helicity could give a way to estimate the latter, which usually requires a volume integral of the magnetic field distributed in and above the photosphere.
This work was later developed into more general one.
Reference
Magara, T. 2014, PASJ, 66, L5
