Magnetohydrostatic atmospheres

We show that the atmospheric and magnetic height variations are coupled in all magnetohydrostatic (MHS) equilibria with gravity if any isolated weak evacuated flux tubes or hydrostatically connected non-force-free fields are present. In gas-dominated regimes, as in stellar photospheres, flux tubes expand with height to maintain pressure balance with the ambient giving a ‘magnetic canopy’ in the relatively small-scale-height cool atmosphere. But in magnetically dominated regimes, as in stellar coronae, the lines of the large-scale background magnetic field determine the spreading of embedded flux tubes. There rigidly held flux tubes require a specific minimum surrounding atmosphere with a unique temperature profile for equilibrium. The solar static equilibrium atmosphere exhibits the correct transition-region properties and base coronal temperature for the sun’s main magnetic spherical harmonic. Steady flows along field lines may contribute to the overall pressure, so equilibria with accelerated wind outflows are possible as well. Flux tubes do not play a dynamical role, but rather indicate a mathematical degeneracy in the form of non-force-free magnetic fields. Equilibria are naturally self restoring and dynamics tend to maintain the MHS atmosphere. Outflows are produced in perturbed equilibria that fill a depleted or cool atmosphere to the equilibrium gas profile, which heats the gas compressively.