Influence of the geometrical shape of a prominence and the structure of the coronal magnetic field on the probability of eruption, flare and coronal mass ejection development

Abstract

The equilibrium conditions of the magnetic flux rope containing the prominence depend on the properties of the surrounding magnetic field in the corona and the geometry of the flux rope itself. The eruption of a prominence is usually associated with a loss of stability in the external magnetic field upon reaching a height above which the decay index of the field exceeds the critical value for the development of eruptive instability. For flux ropes with an axis in the form of a straight line or a circle, the critical value of the decay index of the field lies in the range of 1.0—1.5. Based on extrapolation of the magnetic field into the corona from field measurements in the photosphere, it would be possible to predict the probability of eruption of a particular prominence. However, taking into account the fact that the ends of the magnetic flux rope are rooted in the photosphere and remain fixed due to being frozen into the photospheric plasma significantly affects the critical value of the index and complicates the forecast problem. If the magnetic flux rope retains the shape a segment of a torus in the process of evolution, then the critical value of the decay index for its apex depends on what part of the torus it constitutes, being minimal for approximately half of the torus and having a value significantly less than unity. How the eruption of the flux rope will develop after the loss of equilibrium also depends on what part of the complete torus it constitutes at the moment of the onset of the eruption. Shorter flux ropes accelerate very vigorously, but only for a short time, generating stronger electric induction fields that initiate flare processes. However, the final speed that a short flux rope can achieve during acceleration is less than that of longer flux ropes that accelerate less intensely but for a longer time. The induction effects of the latter are less pronounced, so that they are capable of producing only weak flare-like manifestations. Thus, the eruption of a short prominence, which has gained a relatively low speed, can be stopped at a certain height in the corona without generating a coronal mass ejection. But such a “failed eruption” contributes to the development of flare phenomena. On the contrary, eruptions of longer prominences more often lead to the formation of coronal mass ejections and weak flare manifestations.