# A Research on the Force-Freeness of Photosphere Magnetic Field

## TL;DR

This study statistically analyzes the force-freeness of photospheric magnetic fields in active regions using Hinode observations, revealing how force indicators vary with thresholds and resolution changes.

## Contribution

It introduces a new method using three parameters to evaluate force-freeness and examines the effects of resolution and threshold adjustments on these parameters.

## Key findings

- $F_{x}/ F_{p}$ and $F_{y}/ F_{p}$ increase with thresholds and resolution changes.
- $F_{z}/ F_{p}$ shows complex trends depending on thresholds and resolution.
- Force indicators behave differently at various thresholds and resolutions.

## Abstract

In this paper, the statistical studies on the force-freeness of photosphere magnetic fields are given. The studies are based on the vector magnetic fields observed by Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) on board Hinode. Three parameters ($F_{x}/ F_{p}$, $F_{y}/ F_{p}$, and $F_{z}/ F_{p}$) are introduced to investigate the force-freeness of active regions photosphere magnetic field. Various thresholds and reductions of original resolutions are selected to calculated parameters. As for the resolutions, the reductions of original resolution data by a factor of 2, 4 and 8 are applied. While for thresholds, they are calculated from individual active region with the average of 75/77/57 G for $B_{x}$/$B_{y}$/$B_{z}$ for all original data. When the resolution are reduced by 2, 4 and 8, the corresponding averages are 72/75/55, 66/68/49 and 57/59/41 G for $B_{x}$/$B_{y}$/$B_{z}$, respectively. It is found that the forces indicated by $F_{x}/ F_{p}$ and $F_{y}/ F_{p}$ increase as thresholds/resolutions increase/decrease. While for $F_{z}/ F_{p}$ the trends become more complex. For low threshold, when the resolution decrease the trends of $F_{z}/ F_{p}$ are similar as those of $F_{x}/ F_{p}$ and $F_{y}/ F_{p}$, while for high threshold the trends of $F_{z}/ F_{p}$ are different from those of $F_{x}/ F_{p}$ and $F_{y}/ F_{p}$. For original resolution, the forces indicated by $F_{y}/ F_{p}$ increase as thresholds increase, while for others resolution they decrease as the thresholds increase contrarily.