Solar eruptions, which are usually referred to as coronal mass ejections (CMEs) and solar flares, are the cause of disastrous space weather, which have potential impacts on high-tech activities such as aerospace, communication and navigation. There are two types of solar eruptions: one is successful eruption that causes both solar flare and coronal mass ejection. The other is failed eruption, where there is only solar flare but no coronal mass ejection. They have different effects on space environment. Therefore, in order to predict the space weather, we need to explore two key questions: what mechanisms trigger the solar eruptions and what factors determine if they are successful or failed. While there are a large number of studies devoted to the first question, the second question is less studied and largely unknown.
A widely used theoretical model for predicting if a solar eruption is successful or failed is the torus instability model. This model considers a thin magnetic flux rope beneath an overlying magnetic field. The overlying poloidal field (perpendicular to the axis of the flux rope) produces a downward strapping force which counteracts the upward hoop force of the flux rope. In the case that the overlying field decays with height fast enough, the strapping force can no longer balance the hoop force and the flux rope can escape from the solar surface, thus yielding a successful eruption. Otherwise, the eruption is failed. A quantitative parameter to discriminate between the success and failure of an eruption is the critical decay index of the overlying field, which lies in a range of 0.8-1.5, depending on different studies. Such a critical decay index has been largely used in observational studies that try to explain the eruption behavior. However, in quite some cases, such a criterion does not work, in which the decay index exceeds the critical value but the eruption is still failed.
A recent study (Myers et al. 2015, Nature, 528, 526) revealed that another force component, the tension force generated by the toroidal field along the flux rope, can also play an important role in constraining the eruption. Such a scenario has been nicely tested through laboratory experiments. However, it is still unknown if this mechanism works in a real solar eruption and if there are other factors missed in previous models which can change the eruption behavior.
Motivated by the above thoughts, the Solar Physics Group at Nanjing University, including Mingde Ding, Yang Guo and Ze Zhong (Ph. D. student), initiated a project investigating the causes of failed solar eruptions. They have developed a data-driven MHD simulation code to model various solar eruptions (Guo et al. 2019, ApJL, 870, L21), and in particular, modeled a failed eruption that really occurred on 30 January 2015 (Fig. 1).
Fig. 1 The failed solar eruption on 30 January 2015. The left part shows the solar image at 171 Å observed by SDO/AIA and the position of the eruption; the right part shows the magnetic flux rope, photospheric magnetogram observed by SDO/HMI and flare ribbons at 1600 Å observed by SDO/AIA.
In the simulation, the bottom boundary is updated with time-varying observed quantities (vector magnetic fields and velocity fields), and therefore the evolution of the flux rope can be reproduced with high fidelity. The simulation successfully reproduces what have been observed in the failed eruption, a solar flare without a CME. This enables them to analyze in detail what factors make the eruption finally failed.
They find that a force component, resulting from the radial magnetic field of the flux rope, can also prevent the flux rope from successful eruption (Fig. 2). This force component has never been included in previous models. Note that the radial field distorts the cross section and leads to a non-axisymmetry of the flux rope. Since real flux ropes are more or less non-axisymmetric, such a force should not be neglected in predicting the eruption behavior.
Fig. 2 Sketch map of different Lorentz force components that can influence the eruption behavior of the magnetic flux rope. From left to right, the three panels show the strapping force, tension force and non-axisymmetry induced force, respectively.
They also find that in this event, the strapping force can change direction from downward in the initial phase to upward in the later phase, resulting from a change of the overlying poloidal field. Thus, in the later phase, it is the non-axisymmetry induced force, but not the strapping force, that plays the major role in constraining the eruption. This also implies that, in order to accurately predict an eruption, one needs to consider the geometrical structure of the flux rope and also the time variation of the overlying field. It is insufficient to judge the eruption behavior solely based on the decay index of the background field at one specific time.
For more information, please refer to: https://www.nature.com/articles/s41467-021-23037-8