# Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part III: Twist Number Method

## TL;DR

This paper evaluates the twist number method for estimating magnetic helicity in solar flux ropes across various models, demonstrating its effectiveness and agreement with other helicity measures in different magnetic field configurations.

## Contribution

It introduces and validates the twist number method for magnetic helicity estimation in diverse solar magnetic field models, including force-free and non-force-free configurations.

## Key findings

- The twist method's helicity estimates agree with finite volume calculations within uncertainties.
- The current-carrying magnetic field significantly contributes to the flux rope's helicity.
- The Berger--Prior formula effectively computes twist for arbitrary geometries.

## Abstract

We study the writhe, twist and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov--D\'emoulin equilibrium solution, non force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger--Prior formula that is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.