Distribution of magnetic helicity and energy with height in solar atmosphere

Abstract

Magnetic helicity and magnetic energy are key to understanding the solar dynamo and eruptions, and their three-dimensional distributions are of great significance. However, how these quantities vary with height remains poorly understood. Moreover, because the three-dimensional distribution depends on magnetic field extrapolation, determining the optimal extrapolation height from physical rather than empirical criteria remains an open problem. To address this issue, this work investigates the vertical distributions of magnetic helicity and magnetic energy in the solar corona within active regions. We analyze 150 active regions observed by the Solar Magnetic Field Telescope (SMFT) from 1988 to 2019, grouped by absolute magnetic flux, perform nonlinear force-free field (NLFFF) extrapolations, and compute the relative magnetic helicity with a finite volume method. It is found that an extrapolation height of at least 81 Mm retains 97% of the total magnetic helicity and energy while reducing computational costs by approximately 38% under the adopted configuration. This work provides important parameter constraints for the long-term statistical study of magnetic helicity in solar active regions.