Vol. 584
In section 9. The Sun

Limitations of force-free magnetic field extrapolations: Revisiting basic assumptions

Force-free magnetic field extrapolation is a technique that is widely used to extrapolate measurements of the photospheric magnetic field of the Sun and stars to their respective outer atmospheres, where the field controls heating and dynamics. These extrapolations rest on the assumption that the ratio of the internal energy of the plasma to its magnetic energy is negligible, while both observations and theory indicate that this ratio can be on the order of 10% in the solar corona and is therefore not vanishingly small there. The authors examine the consequences of this non-vanishing thermal pressure on the dynamics of the solar corona and find that while force-free extrapolation might capture the magnetic structure, the derived currents and energetics are not reliable. Together with recent demonstrations that existing extrapolation algorithms do not always identify the optimal force-free solution, this is cause for caution when using this technique to evaluate heating and energy storage in the outer atmosphere of the Sun.