The writhe of helical structures in the solar corona

TL;DR

This paper investigates the relationship between the shape, writhe, and helicity of magnetic flux ropes in the solar corona, providing insights into their role in eruptions and CMEs through quantitative analysis and simulations.

Contribution

It introduces a method to decompose and measure writhe and twist in flux ropes, linking shape to helicity distribution and eruption dynamics.

Findings

Writhe correlates with the S shape of coronal structures.

Writhe measurement helps interpret filament eruptions.

Model constraints are improved by understanding helicity exchange.

Abstract

Helicity is a fundamental property of magnetic fields, conserved in ideal MHD. In flux rope topology, it consists of twist and writhe helicity. Despite the common occurrence of helical structures in the solar atmosphere, little is known about how their shape relates to the writhe, which fraction of helicity is contained in writhe, and how much helicity is exchanged between twist and writhe when they erupt. Here we perform a quantitative investigation of these questions relevant for coronal flux ropes. The decomposition of the writhe of a curve into local and nonlocal components greatly facilitates its computation. We use it to study the relation between writhe and projected S shape of helical curves and to measure writhe and twist in numerical simulations of flux rope instabilities. The results are discussed with regard to filament eruptions and coronal mass ejections (CMEs). We conclude that the writhe is useful in interpreting S shaped coronal structures and in constraining models of eruptions.