Magnetohydrodynamic simulations of the ejection of a magnetic flux rope

Astronomy & Astrophysics A&A 554, A77 (2013) DOI: 10.1051/0004-6361/201220947 c ESO 2013  Magnetohydrodynamic simulations of the ejection of a magnetic flux rope P. Pagano1 , D. H. Mackay1 , and S. Poedts2 1 School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, Scotland KY16 9SS, UK e-mail: 2 Centre for Plasma-Astrophysics, K. U. Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium Received 18 December 2012 / Accepted 20 March 2013 ABSTRACT Context. Coronal mass ejections (CME’s) are one of the most violent phenomena found on the Sun. One model to explain their occurrence is the flux rope ejection model. In this model, magnetic flux ropes form slowly over time periods of days to weeks. They then lose equilibrium and are ejected from the solar corona over a few hours. The contrasting time scales of formation and ejection pose a serious problem for numerical simulations. Aims. We simulate the whole life span of a flux rope from slow formation to rapid ejection and investigate whether magnetic flux ropes formed from a continuous magnetic field distribution, during a quasi-static evolution, can erupt to produce a CME. Methods. To model the full life span of magnetic flux ropes we couple two models. The global non-linear force-free field (GNLFFF) evolution model is used to follow the quasi-static formation of a flux rope. The MHD code ARMVAC is used to simulate the production of a CME through the loss of equilibrium and ejection of this flux rope. Results. We show that the two distinct models may be successfully coupled and that the flux rope is ejected out of our simulation box, where the outer boundary is placed at 2.5 R . The plasma expelled during the flux rope ejection travels outward at a speed of 100 km s−1 , which is consistent with the observed speed of CMEs in the low corona. Conclusions. Our work shows that flux ropes formed in the GNLFFF can lead to the ejection of a mass loaded magnetic flux rope in full MHD simulations. Coupling the two distinct models opens up a new avenue of research to investigate phenomena where different phases of their evolution occur on drastically different time scales. Key words. Sun: coronal mass ejections – Sun: corona – magnetic fields – magnetohydrodynamics (MHD) 1. Introduction Coronal mass ejections (CMEs) are one of the few solar phenomena that directly affect the Earth, therefore they are one of the main drivers of space weather (Schwenn 2006). Understanding their origin and propagation is therefore key, not only for the Earth but also for understanding how the Sun loses both magnetic flux and magnetic helicity (Low 1996; Lynch et al. 2005). Over the years, a wide variety of models have been put forward to explain the origin of CMEs, and a discussion of these can be seen in the reviews of Forbes et al. (2006) and Chen (2011). While a variety of models exist, one of the leading models for explaining CMEs is the flux rope ejection model (Forbes & Isenberg 1991; Amari et al. 2000; Fan & Gibson 2007). The flux rope ejection model may itself be split into two categories. Flux ropes formed quasi-statically from perturbations of already existing coronal arcades (Aulanier et al. 2005; Mackay & van Ballegooijen 2006a) or those formed dynamically during the emergence of magnetic flux (Manchester et al. 2004; Archontis & Hood 2008). Within the present paper we focus on those formed quasi-statically from existing coronal arcades. For this category of flux rope, the life span normally undergoes three separate stages of evolution: the formation, equilibrium and eruption phases. To begin with, the flux rope forms over time periods of days to weeks as a coronal arcade is  Movies are available in electronic form at http://www.aanda.org perturbed by photospheric motions and flux cancellation at a PIL (van Ballegooijen & Martens 1989; Forbes 1991). An example can be seen in Cheng et al. (2010) where the flux rope formation was observed over three days, along with the signature of flux cancellation at the photosphere. Similar dynamics have been observed by Liu et al. (2010), where a sigmoidal flux rope was formed by the joining of two J-shaped loops which then quickly erupt. The formation phase is then followed by a period during which the flux rope lies in near equilibrium with its surroundings. Evidence for this exists in the form of sigmoids (McKenzie & Canfield 2008), solar filaments (Mackay et al. 2010), and coronal cavities (Hudson et al. 1999). During both the formation and equilibrium phases the magnetic structure does not change significantly over time scales much longer than the characteristic Alfvén time. Finally, there is the ejection phase where the flux rope loses equilibrium and is ejected out of the solar corona due to magnetic forces. This occurs over time periods of a few hours, where flux rope ejections are believed to be one of the main progenitors of CMEs. It is possible to track the evolution of a flux rope in observed CMEs from the ejection phase (Cheng et al. 2011) to their propagation into interplanetary space (Wood et al. 1999). While many flux ropes follow the evolution described above, there are also situations where flux ropes are simultaneously formed and ejected (Cheng et al. 2011; Archontis et al. 2009). It can be seen that the formation and ejection of magnetic flux ropes involve a wide variety of time scales. The formation phase happens very slowly (days to weeks or months). Under Article published by EDP Sciences A77, page 1 of 11 A&A 554, A77 (2013) these circumstances the formation can be approximated using a quasi-static zero-β model where the magnetic field evolves through a series of equilibrium states (Forbes 1991; Mackay & van Ballegooijen 2006a,b; Yeates & Mackay 2009; Yeates et al. 2010). In contrast the ejection phase is rapid, where a flux rope can travel at the speed of several hundreds of km s−1 and within a few hours the coronal magnetic field reconfigures to a state significantly different from the pre-eruption state. One important aspect of the ejection is that the coronal plasma is compressed and heated. As a result, the plasma may no longer be in the low β-regime and full MHD modelling must now be applied. The wide variety of time scales involved, in the formation of the flux rope and then its eruption, poses a considerable challenge to theoretical models. Within the present paper our aim is to combine two models, which we believe accurately reproduce individual aspects of flux rope formation and ejection over their individual time scales. We will first use the global non-linear force-free field (GNLFFF) model of Mackay & van Ballegooijen (2006a) which neglects the role of the plasma to consider the formation of the flux rope in the zero-β, quasi-static approximation. Once the flux rope forms and is about to erupt, we apply a full MHD approach, through using the stressed magnetic field configuration from the GNLFFF model as an initial conditio (...truncated)