Given a known radial magnetic field distribution on the Sun’s photospheric surface, there exist well-established methods for computing a potential magnetic field in the corona above. Such potential fields are routinely used as input to solar wind models, and to initialize magneto-frictional or full magnetohydrodynamic simulations of the coronal and heliospheric magnetic fields. We describe an improved magnetic field model that calculates a magneto-frictional equilibrium with an imposed solar wind profile (which can be Parker’s solar wind solution, or any reasonable equivalent). These “outflow fields” appear to approximate the real coronal magnetic field more closely than a potential field, take a similar time to compute, and avoid the need to impose an artificial source surface. Thus they provide a practical alternative to the potential field model for initializing time-evolving simulations or modeling the heliospheric magnetic field. We give an open-source Python implementation in spherical coordinates and apply the model to data from solar cycle 24. The outflow tends to increase the open magnetic flux compared to the potential field model, reducing the well-known discrepancy with in situ observations.

We apply the magneto-frictional approach to investigate which quantity or quantities can best predict the loss of equilibrium of a translationally-invariant magnetic flux rope. The flux rope is produced self-consistently by flux cancellation combined with gradual footpoint shearing of a coronal arcade which is open at the outer boundary. This models the magnetic field in decaying active regions on the Sun. Such a model permits two types of eruption: episodic small events caused by shearing and relaxation of the overlying arcade, and major eruptions of the main low-lying coronal flux rope. Through a parameter study, we find that the major eruptions are best predicted not by individual quantities but by thresholds in the ratios of squared rope current to either magnetic energy or relative magnetic helicity. We show how to appropriately define the latter quantity for translationally-invariant magnetic fields, along with a related eruptivity index that has recently been introduced for three-dimensional magnetic fields. In contrast to previous configurations studied, we find that the eruptivity index has only a weak predictive skill, and in fact is lower prior to eruption, rather than higher. This is because the overlying background magnetic field has the same direction as the arcade itself. Thus we propose that there are a whole class of solar eruptions that cannot be predicted by a high eruptivity index.

Coronal mass ejections (CMEs) – among the most energetic events originating from the Sun – can cause significant and sudden disruption to the magnetic and particulate environment of the heliosphere. Thus, in the current era of space-based technologies, early warning that a CME has left the Sun is crucial. Some CMEs exhibit signatures at the solar surface and in the lower corona as the eruption occurs, thus enabling their prediction before arriving at near-Earth satellites. However, a significant fraction of CMEs exhibit no such detectable signatures and are known as “stealth CMEs”. Theoretical and observational studies aiming to understand the physical mechanism behind stealth CMEs have identified coronal streamers as potential sources. In this paper, we show that such streamer-blowout eruptions – which do not involve the lift-off of a low-coronal magnetic flux rope – are naturally produced even in the quasi-static magnetofrictional model for the coronal magnetic field. Firstly, we show that magnetofriction can reproduce in this way a particular stealth CME event observed during 1 – 2 June 2008. Secondly, we show that the magnetofrictional model predicts the occurrence of repeated eruptions without clear low-coronal signatures from such arcades, provided that the high, overlying magnetic field lines are sufficiently sheared by differential rotation. A two-dimensional parameter study shows that such eruptions are robust under variation of the parameters, and that the eruption frequency is primarily determined by the footpoint shearing. This suggests that magnetofrictional models could, in principle, provide early indication – even pre-onset – of stealth eruptions, whether or not they originate from the eruption of a low-coronal flux rope.

Oliver Rice discusses work in modelling the magnetic field in the solar corona, and one way in which this may be used to predict the eruptions of magnetic flux ropes

We apply the magneto-frictional approach to investigate which quantity or quantities can best predict the loss of equilibrium of a translationally-invariant magnetic flux rope. The flux rope is produced self-consistently by flux cancellation combined with gradual footpoint shearing of a coronal arcade which is open at the outer boundary. This models the magnetic field in decaying active regions on the Sun. Such a model permits two types of eruption: episodic small events caused by shearing and relaxation of the overlying arcade, and major eruptions of the main low-lying coronal flux rope. Through a parameter study, we find that the major eruptions are best predicted not by individual quantities but by thresholds in the ratios of squared rope current to either magnetic energy or relative magnetic helicity. We show how to appropriately define the latter quantity for translationally-invariant magnetic fields, along with a related eruptivity index that has recently been introduced for three-dimensional magnetic fields. In contrast to previous configurations studied, we find that the eruptivity index has only a weak predictive skill, and in fact is lower prior to eruption, rather than higher. This is because the overlying background magnetic field has the same direction as the arcade itself. Thus we propose that there are a whole class of solar eruptions that cannot be predicted by a high eruptivity index.