Scaling laws of free magnetic energy stored in a solar emerging flux region

TL;DR

This paper derives scaling laws relating magnetic flux, free magnetic energy, and magnetic helicity in solar emerging flux regions using 3D MHD simulations, aiding in estimating energy responsible for solar eruptions.

Contribution

It presents new power law relationships among magnetic flux, free magnetic energy, and helicity in emerging flux regions based on simulations.

Findings

Power law relationship between magnetic flux and free magnetic energy.

Scaling laws linking magnetic helicity with flux and energy.

Potential to estimate invisible magnetic energy from observable flux.

Abstract

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.