A first-principles approach to forecasting solar eruptive events

Solar eruptive events – coronal mass ejections and their associated flares – are a principal source of the transient disturbances that drive space weather. Their high-energy particles reach Earth from the Sun just several minutes later, posing prompt hazards to spacecraft and astronauts. The bulk ejecta follow within a very few days. Upon impact with Earth, they can cause geomagnetic storms attended by disruptions of spacecraft environments, electromagnetic propagation properties of the atmosphere, and terrestrial power grids.

It is generally accepted that the energy powering the eruptions is stored in the magnetic fields of the outer solar atmosphere, the corona, and that the release is triggered suddenly when some critical threshold is attained. Methods currently used to forecast such events are based on empirical measures of the magnetic stresses in coronal structures known to be prone to eruption. The methods are qualitative or semiquantitative at best, due to limited understanding of the underlying physical mechanism(s).

We have initiated development of a quantitative, first-principles approach to forecasting solar eruptions. The method is based upon our observationally supported “breakout” model for coronal mass ejections, combined with a widely accepted maximum-energy principle for closed magnetostatic equilibria in the corona. The energy principle states that for every coronal structure there is a well-defined energy at which its magnetic field must expand outward until it opens, i.e., until the field lines stretch arbitrarily far from the Sun into interplanetary space. This expansion will be gradual rather than explosive, however, if all of the overlying field is forced to open along with the stressed field low in the atmosphere. In a sufficiently magnetically complex corona, on the other hand, a null point with an associated directional discontinuity can occur in the overlying field. Magnetic field lines eventually break and reconnect across the null in this configuration, thereby removing part of the overlying field and reducing the amount of energy required for the remainder to open. The pent-up excess energy is liberated in a violent expulsion of the stressed field, which “breaks out” through the formerly restraining field overhead.

Applying these concepts to forecasting requires a method to calculate the energies needed to open the coronal field (1) in the absence of any reconnection, which maximizes the open energy, and (2) in the presence of optimal reconnection, which minimizes the open energy. These two energies, together with that of the relaxed post-eruption field configuration, determine the threshold energy for eruption onset and the energy available to power both the coronal mass ejection and its associated flare. We demonstrate how to compute the event energies for the idealized case of an axisymmetric Sun, and we compare the results with detailed, time-dependent simulations of solar eruptions. We also discuss additional numerical experiments needed to verify the physical model, the mathematical advances required to extend the technique to general three-dimensional configurations, and the observational data needed to initiate and validate solar forecasts.