Influence of the Geometrical Shape of a Prominence and Structure of the Coronal Magnetic Field on the Probability of Eruption, Flare Development, and Coronal Mass Ejection

The equilibrium conditions of a magnetic flux rope containing a prominence depend on the properties of the surrounding magnetic field of the corona and geometry of the flux rope itself. The eruption of a prominence is usually associated with a loss of stability in the external field upon reaching a height above which the field decay index exceeds the critical value for eruptive instability development. For flux ropes with an axis in the form of a straight line or a circle, the critical value of the field decay index is 1-1.5. By extrapolating the magnetic field in 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 because they are frozen in the photospheric plasma, significantly affects the critical value of the index and complicates the forecasting problem. If the magnetic flux rope retains the shape of a torus segment in its evolution, then the critical value of the field decay index for its vertex depends on what part of the torus it constitutes, being minimal for approximately half the torus and having a value significantly less than unity. How the eruption of a flux rope will develop after loss of equilibrium also depends on what part of the complete torus it constitutes at the time of onset of eruption. Shorter flux ropes are accelerated very energetically, but briefly, generating stronger electric induction fields that trigger flare processes. However, the terminal velocity that a short flux rope can achieve during acceleration is less than that of longer 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 flarelike manifestations. Thus, the eruption of a short prominence, which has gained a relatively low velocity, 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. Conversely, eruptions of long prominences more often lead to coronal mass ejections and weak flare manifestations.