The Astrophysical Journal, 663:592Y597, 2007 July 1 # 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A.
A CATASTROPHIC FLUX ROPE IN A QUADRUPOLE MAGNETIC FIELD FOR CORONAL MASS EJECTIONS Y.-Z. Zhang and J.-X. Wang National Astronomical Observatories, Chinese Academy of Sciences, 100012 Beijing, China;
[email protected] Received 2007 January 13; accepted 2007 March 18
ABSTRACT We propose a flux-rope model for the initiation of flare-associated CMEs. The model triggers the eruption with a catastrophic loss of MHD equilibrium and then requires magnetic reconnection to sustain the eruption’s acceleration. We carry out 2.5-dimensional time-dependent resistive MHD simulations, choosing the initial state such that a flux rope embedded in a quadrupole field is attached to the solar surface; we then increase the magnetic flux of the rope by two different amounts, thus obtaining two cases. One exhibits a gradual acceleration of the flux rope, whereas the other produces an immediate acceleration. In both cases, the maximum speed of the flux rope is representative of a fast CME. Thus, we conclude that the flux-rope dynamics depends on the intensity of the emergent magnetic flux. Our model does reproduce the three-component structure of CMEs. Subject headingg s: Sun: corona — Sun: coronal mass ejections (CMEs) — Sun: flares — Sun: magnetic fields 1. INTRODUCTION
MHD model in which the newly emerging flux triggers CMEs (Chen & Shibata 2000; Lin et al. 2001; Shiota et al. 2005) and reconnection occurs between the emerging flux and the preexisting large-scale magnetic field (see the evidence presented by Wang & Shi 1993). This research builds upon our earlier work. In a previous paper (Zhang et al. 2005), we found that a double catastrophe exists for an isolated flux rope embedded in a quadrupole background field and that, after the catastrophe, two current sheets coexist with the flux rope, a transverse one above the rope and a vertical one below. Subsequently (Zhang et al. 2006), we showed that the flux rope erupts from the initial state when reconnection occurs in the two current sheets and that the dynamics of the flux rope depends on the sequence of reconnection in the two sheets. The initial state used in the latter work was taken to be just after the first catastrophic point, and the flux-rope system included the two current sheets. The twoYcurrent-sheet reconnection model exhibited concurrence of the flare and CME when reconnection set in within the two sheets. Based on these results, here we investigate a new initial state in which the flux rope is attached to the photospheric surface, which is different from that used in Zhang et al. (2006). The rope erupts when the catastrophe occurs during the evolution of the flux-rope system. We describe the numerical solution in x 2, discuss the evolution of the flux-rope system in x 3, and conclude in x 4.
In recent years, coronal mass ejections (CMEs) have been one of the major topics of solar physics research. Both space-borne and ground-based observations provide a great deal of important data for the study of CME source regions, their initiation, and their early acceleration and propagation (Schwenn et al. 2006; Gopalswamy et al. 2006). Furthermore, many researchers have used numerical and analytical approaches to investigate the initiation and evolution of CMEs. However, many fundamental questions regarding the nature of CMEs are still unanswered (Forbes 2000; Low 2001; Lin et al. 2003; Forbes et al. 2006; Mikic´ & Lee 2006; Pick et al. 2006). In particular, the mechanism of CME initiation remains poorly understood. There is a type of hybrid model that initiates CME eruption by a purely ideal-MHD catastrophic process and then requires the nonYideal-MHD process of magnetic reconnection to sustain the acceleration of the eruption. Both analytical studies and numerical simulations have been used to explain the mechanisms that initiate solar eruptive phenomena (van Tend & Kuperus 1978; Martens & Kuin 1989; van Ballegooijen & Martens 1989; Priest & Forbes 1990; Forbes & Isenberg 1991; Isenberg et al. 1993; Mikic´ & Linker 1994; Forbes & Priest 1995; Titov & De´moulin 1999; Lin & Forbes 2000; Lin & van Ballegooijen 2002; Ding et al. 2006). Most of these studies are associated with a bipolar magnetic configuration. Antiochos et al. (1999) developed a breakout model that involves a quadrupole configuration and requires external magnetic reconnection to occur at the top of the sheared arcade. In addition, recent simulations of breakout by MacNeice et al. (2004) agree with the major observed properties of CMEs. Besides two- and 2.5-dimensional simulations, a series of fully three-dimensional simulations, based on the twisted flux rope model, have been carried out by some authors (Amari et al. 2000; Roussev et al. 2003; Manchester et al. 2004; Fan 2005; To¨ro¨k & Kliem 2005). Moreover, a few other types of models have painted some interesting pictures of the initiating mechanism. One is an idealMHD model in which a catastrophic loss of equilibrium occurs when the magnetic energy of the flux-rope system exceeds a particular threshold value. However, during this process, no reconnection occurs in the vertically stretched current sheet ( Hu & Liu 2000; Hu 2001; Hu & Jiang 2001; Hu et al. 2003; Sun & Hu 2005; Ding & Hu 2006; Chen et al. 2006a). Another is a resistive
2. NUMERICAL SOLUTION Our model is based on time-dependent, resistive, 2.5-dimensional MHD simulations of the evolution of a flux-rope system in spherical coordinates (r, , ’). One may introduce a magnetic flux function (t, r, ) that is related to the magnetic field by B¼:
