Magnetohydrostatic equilibrium. I: Three-dimensional open magnetic flux tube in the stratified solar atmosphere

TL;DR

This paper models a stable, three-dimensional open magnetic flux tube in the stratified solar atmosphere, providing an analytical magnetohydrostatic equilibrium solution that aligns with observations and can serve as a background for studying energy transport.

Contribution

It presents an analytical, self-similar 3D model of a solar magnetic flux tube in equilibrium, incorporating realistic stratification and free parameters for broader applicability.

Findings

Analytical solution for magnetic flux tube in equilibrium

Magnetic field divergence-free and consistent with observations

Model adaptable to various physical problems

Abstract

A single open magnetic flux tube spanning the solar photosphere (solar radius R) and the lower corona (R + 10 Mm) is modelled in magnetohydrostatic equilibrium within a realistic stratified atmosphere subject to solar gravity. Such flux tubes are observed to remain relatively stable for up to a day or more, and it is our aim to apply the model as the background condition for numerical studies of energy transport mechanisms from the surface to the corona. We solve analytically an axially symmetric 3D structure for the model, with magnetic field strength, plasma density, pressure and temperature all consistent with observational and theoretical estimates. The self similar construction ensures the magnetic field is divergence free. The equation of pressure balance for this particular set of flux tubes can be integrated analytically to find the pressure and density corrections required to preserve the magnetohydrostatic equilibrium. The model includes a number of free parameters, which makes the solution applicable to a variety of other physical problems and it may therefore be of more general interest.