Equilibrium models of coronal loops that involve curvature and buoyancy

TL;DR

This paper develops magnetostatic models of coronal loops that incorporate curvature and buoyancy, linking loop shape to thermodynamics without detailed heating or cooling processes.

Contribution

It introduces a method to model coronal loops as thin magnetic fibrils with thermodynamics consistent with their geometry, considering curvature and buoyancy effects.

Findings

Density and temperature profiles are highly sensitive to curvature variations.

Models show different profiles for loops with constant magnetic Bond number versus constant radius of curvature.

The approach connects loop shape directly to thermodynamic properties without detailed heating/cooling models.

Abstract

We construct magnetostatic models of coronal loops in which the thermodynamics of the loop is fully consistent with the shape and geometry of the loop. This is achieved by treating the loop as a thin, compact, magnetic fibril that is a small departure from a force-free state. The density along the loop is related to the loop's curvature by requiring that the Lorentz force arising from this deviation is balanced by buoyancy. This equilibrium, coupled with hydrostatic balance and the ideal gas law, then connects the temperature of the loop with the curvature of the loop without resorting to a detailed treatment of heating and cooling. We present two example solutions: one with a spatially invariant magnetic Bond number (the dimensionless ratio of buoyancy to Lorentz forces) and the other with a constant radius of curvature of the loop's axis. We find that the density and temperature profiles are quite sensitive to curvature variations along the loop, even for loops with similar aspect ratios.