Application of double beltrami states to solar eruptions

We show that the general class of Double Beltrami (DB) states, which are the lowest energy equilibria of Hall magnetohydrodynamics, can have characteristics similar to those of active regions in the solar corona and is capable of undergoing a catastrophe that can cause a solar eruption, such as a flare or coronal mass ejection (CME). We then show that the qualitative evolution of the DB state is consistent with that of a solar eruption. Finally, we make two quantitative comparisons of DB states to CMEs, which are the simplest result of the catastrophe. First, we show that the DB expansion by a factor of 1-2 before the catastrophe is consistent with the increase in the height of the leading edges of Large-Angle Spectrometric Coronagraph (LASCO C1) CMEs in the quasi-equilibrium stage. Secondly, we use the assumption that DB states are randomly chosen from the allowed phase space of coronal structures to predict that the probability of a coronal structure erupting is 0.046. Identifying active regions with DB states and using observational constraints to estimate that the state is replaced every 60 min by emerging loops results in a CME rate of 11 d^-1, which is in reasonable agreement with the actual rate of about 6 d^-1 at solar maximum.