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Jan 17, 2006 - S. E. GIBSON AND Y. FAN. High Altitude Observatory, National Center for Atmospheric Research,1 Boulder, CO 80307-3000. Received 2005 ...


The Astrophysical Journal, 637:L65–L68, 2006 January 20 䉷 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE PARTIAL EXPULSION OF A MAGNETIC FLUX ROPE S. E. Gibson and Y. Fan High Altitude Observatory, National Center for Atmospheric Research,1 Boulder, CO 80307-3000 Received 2005 October 23; accepted 2005 December 14; published 2006 January 17

ABSTRACT We demonstrate the partial expulsion of a three-dimensional magnetic flux rope, in which an upper, escaping rope is separated from a lower, surviving rope by cusped, reconnecting loop field lines. We use the threedimensional magnetohydrodynamic model recently presented by Fan, extended to examine the erupting rope’s end state. As in that work, the modeled flux rope in spherical coordinates erupts when enough twist has emerged to induce a loss of equilibrium. After multiple reconnections at current sheets that form during the eruption, the rope breaks in two, so that only a part of it escapes. We consider the details of how this separation occurs and discuss the observational significance of such a partially expelled flux rope for partially erupting filaments and re-forming X-ray sigmoids. Subject headings: MHD — Sun: corona — Sun: magnetic fields Online material: mpeg animations gence of a twisted magnetic flux rope, as described in Fan (2005). The simulation presented in this Letter is modified from run A of Fan (2005) as follows: (1) The simulation domain is extended to a radius of r p 10 R,, allowing us to follow the erupting flux rope to a greater height and a later stage in its evolution, after significant reconnection has taken place. (2) The field strength of the emerging flux rope is increased relative to the preexisting arcade field strength, with Bt p 8B0 (instead of Bt p 6B0 as in Fan 2005). The resulting evolution of the coronal magnetic field is very similar to run A of Fan (2005), except that the onset of the eruption takes place earlier. We stop the emergence at t p 86 (Fig. 1a), when the field-line twist in the emerged tube reaches about 1.7 winds. As in run A, we find that the flux rope is unable to find an equilibrium after the emergence stops. The rope apex eventually exits the outer boundary at r p 10 R, with a speed of about 1000 km s⫺1. Our purpose in running this modified, extended simulation is to determine the ultimate fate of the erupting flux rope. Figures 1b–1d demonstrate that in the end the rope splits in two, with some of its helicity propagating out as a flux rope rooted in the original arcade field’s lower boundary and some of it remaining behind in a rope rooted in the original rope’s magnetic bipole. The two ropes are separated by field lines that smoothly transition from sheared field lines lying along the lower rope and rooted in the rope bipole to more potential field lines straddling the lower rope, some (e.g., Figs. 1b–1d, black line) with footpoints in the arcade boundary. When viewed along the current sheet that lies between the two ropes, these more potential loops possess a clear cusped shape (Fig. 1c). How did the rope break in two? In a standard schematic view of an erupting flux rope (Fig. 2, left), the rope completely escapes with reconnection at the X-point below the rope. Indeed, in a related simulation, To¨ro¨k & Kliem (2005) found that reconnections occurred in a vertical current sheet that formed in the vicinity of the X-line below the rope, yielding a classic eruptive flare scenario of cusped field lines closing down behind the expelled rope. An important difference between the To¨ro¨k & Kliem simulation and ours is that theirs contains an X-line, that is, a line along which the poloidal field comes to an X-point (the axial component of the field is not necessarily zero). In our simulation, the flux rope extends all the way down to the photosphere, with dipped field lines that graze the photo-

1. INTRODUCTION

Magnetic flux rope models are often used to describe coronal mass ejections (CMEs) in eruption (Forbes 2000). Magnetic flux ropes may form in the corona as a natural consequence of the conservation of magnetic helicity (Low 1994). However, the question whether the flux rope is formed during the eruption (Amari et al. 2003a; Lynch et al. 2004) or whether it exists prior to the eruption (Amari et al. 2000; Linker et al. 2003; Amari et al. 2003b, 2004, 2005; Fan 2005) remains controversial. Many observations of the preeruption corona are consistent with a pre-CME flux rope, including those of magnetic flux emergence (Tanaka 1991; Lites et al. 1995; Leka et al. 1996), apparent shear or rotational motions at the photosphere (Lo´pez Fuentes 2000; Green et al. 2002; Gibson et al. 2004), filaments (Priest et al. 1989; Rust 1994; Aulanier & De´moulin 1998; Amari et al. 1999; van Ballegooijen 2004), and longlived X-ray sigmoids (Amari et al. 2000; Fan & Gibson 2006). The bodily eruption of a filament with its cavity into a socalled three-part CME is also consistent with a pre-CME flux rope (Wolfson et al. 1987; Low & Hundhausen 1995; Linker et al. 2003; Gibson et al. 2006), as are transient sigmoid brightenings (Rust & Kumar 1996; Fan & Gibson 2003, 2004; Kliem et al. 2004) and their transition to cusped postflare loops (Amari et al. 2003b; To¨ro¨k & Kliem 2005). However, some post-CME observations appear inconsistent with the total expulsion of a preexisting flux rope: for example, partially or non-erupting filaments and the immediate re-formation of long-lived X-ray sigmoids after eruptions (Tang 1986; Gilbert et al. 2000; Pevtsov 2002; Gibson et al. 2002) A three-dimensional flux rope has the potential to break in two during eruption, with one rope leaving the corona and the other staying behind. Such a partial expulsion of a preexisting flux rope could explain the full range of observations, before, during, and after a CME. 2. MODEL END STATE: PARTIALLY EXPELLED FLUX ROPE

We employ a three-dimensional MHD model in spherical geometry to simulate the evolution of an initially potential coronal arcade field driven at the lower boundary by the emer1 The National Center for Atmospheric Research is sponsored by the National Science Foundation

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Fig. 2.—Two-dimensional illustrations of erupting flux ropes. Left two images: The case in which reconnection occurs at an X-point below the rope, resulting in the total expulsion of the flux rope. Right two images: The case in which the rope grazes the photosphere and reconnection occurs internally, resulting in a partial expulsion of the flux rope (and possibly of the filament entrained in the rope’s dips, represented here with gray shading). Adapted from Gilbert et al. (2001).

Fig. 1.—(a) The original flux rope when emergence is stopped at t p 86. This figure is also available as an mpeg animation in the electronic edition of the Astrophysical Journal. (b–d) Three views of the eruption end state at t p 106: two flux ropes separated by cusped loops. The lower boundary shows radial magnetic field strength (red, positive; blue, negative). We refer to the lower boundary of the original flux rope as the rope bipole (red and blue circular poles), and that of the originally potential arcade as the arcade boundary (horizontal red and blue bands). The pink field lines rooted in the rope bipole represent the lower, surviving rope and show the bald-patch separatrix surface (BPSS). The red field lines rooted in the rope bipole are dipped field lines within the lower, surviving rope that intersect the X p 0, Z p 0 vertical axis. The orange and yellow lines are nondipped but non-escaping field lines that intersect the vertical axis just above the red dipped lines. The black line is a non-escaping field line rooted in the arcade boundary, and the purple field line in (b) represents the upper, escaping flux rope rooted in the arcade boundary. The red, orange, yellow, black, and purple lines intersect the vertical axis at evenly spaced intervals.

spheric neutral line along a so-called bald patch (BP; see Gibson et al. [2005a] for further discussion and comparison between the two types of simulations). Photosphere-grazing dipped field lines are not free to escape upward, and we might expect the upward-straining rope to reconnect internally, resulting in a partially expelled flux rope (Fig. 2, right). However, twodimensional models of the eruption of BP-grazing ropes show that such internal reconnections are unlikely to occur. Rather, a current sheet forms below the erupting rope, which extends down to the photosphere (Lin et al. 1998; Fan & Gibson 2006). Reconnections along this current sheet then would yield an arcade lying below a totally escaping flux rope. Our model is three-dimensional, and it is the combination of its three-dimensionality with the presence of a flux rope BP that allows for its partial expulsion. We refer to the set of dipped, flux rope field lines that graze the BP as the bald-patch separatrix surface (BPSS). These field lines are not free to escape upward but rather evolve by means of a process of reconnections with surrounding field lines, both within the rope and in the surrounding arcade. As is true in any numerical simulation, reconnections result from numerical diffusion in regions of large gradients and do not model realistic reconnection rates. However, the locations of our numerically driven reconnections have clear physical origins. For example, topology-mixing rope-arcade reconnections occur along the current sheets that form at the BPSS, as discussed in Gibson et al. (2004) and predicted by Titov & De´moulin (1999) and Low & Berger

(2003). The reconnections that break the rope in two occur at a central vertical current sheet that forms as the rope writhes and expands upward. Figure 3 illustrates this: each field line in the BPSS, except the symmetric line at its center, has a high, arched end, and a low, dipped end. The dipped end is anchored to the photosphere, but the high arched end expands upward and is squeezed toward the rope’s vertical axis as the rope writhes and rotates. This squeezing forms a central, vertical current sheet where field lines meet and reconnect (Fig. 3d). The two high, arched halves of the reconnecting field lines form a new, dipped field line that escapes. The two low, dipped

Fig. 3.—Evolution of the set of dipped field lines that just graze the photosphere, i.e., the bald-patch separatrix surface. (a) BPSS at t p 86, when rope emergence is stopped; (b) BPSS at t p 91, after the rope has broken in two; (c) BPSS at t p 106, showing the lowest (i.e., photosphere-grazing) dipped field lines of the surviving rope; (d) central reconnection that breaks the flux rope in two. The two blue field lines exist at t p 89 and reconnect to form the two orange field lines at t p 90. The high, arched half of the pale blue BPSS field line reconnects with the high part of the dark blue field line, forming the light orange escaping flux rope line. The low, dipped half of the pale blue BPSS field line reconnects with the low part of the dark blue field line, forming the dark orange flux rope line that ultimately sinks down to be part of the BPSS of the rope that is left behind. This figure is also available as an mpeg animation in the electronic edition of the Astrophysical Journal.

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Fig. 4.—Sample reconnections leading to escape of the arcade-boundary–rooted upper flux rope. In both panels, the blue field lines exist at the earlier time and reconnect to form the orange field lines one time step later. (a) The central axial flux rope field line (dark blue) symmetrically reconnects with two arcade loops (light blue), forming an escaping flux rope line (dark orange) completely rooted in the arcade boundary and, also, two mixed-topology (one foot in rope bipole, one in arcade boundary) loops (light orange). (b) Two initially dipped field lines (dark and light blue), having already undergone a rope-arcade reconnection so that each has a footpoint in one of the arcade boundary poles, meet at the central current sheet and reconnect. They form an arcade-boundary–rooted, escaping flux rope line (dark orange) bearing most of the combined helicity of the light and dark blue field lines, and a cusped but relatively unsheared loop (light orange) rooted in the rope bipole that lies above the surviving flux rope.

halves reconnect and settle back down as part of the lower, less twisted flux rope that survives the eruption. Fan (2005) described how the writhing rotation of the flux rope relative to the overlying arcade facilitates its loss of confinement, allowing it to erupt upward while most of the arcade field remains closed. This rotation relative to the overlying arcade also results in the rooting of the escaping rope in the arcade field’s lower boundary. This is demonstrated in Figure 3: as the high ends of the BPSS lines expand upward and rotate, their footpoints move from the rope bipole to the arcade boundary by means of a process of interchange reconnection with neighboring field lines, both rope and arcade. By the time the central, rope-breaking reconnection occurs for the field lines shown in Figure 3d, the upper, arched portions of the lines are rooted in the arcade boundary, so that the escaping flux rope field line at t p 90 is likewise rooted in the arcade boundary. For the central axial field line (Fig. 4a), simultaneous reconnections occur between the erupting rope-bipole–rooted axial line and two arcade-boundary–rooted loops, forming an arcadeboundary–rooted escaping flux rope line and two mixedtopology (arcade-rope) loops. More commonly, the escape of the upper flux rope is a two-step process: first a rope-arcade reconnection occurs, which moves one rope field-line footpoint (generally the one on the higher, arched end, which is closest to the external field) to the arcade boundary, and second a central reconnection occurs between two complementary ropearcade and arcade-rope rooted field lines. In the case of flux rope lines near the BPSS (e.g., Fig. 3d), this yields two flux rope field lines: one completely rooted in the arcade boundary and one rooted in the rope bipole. In the case of flux rope field lines whose dips lie higher up in the rope (e.g., Fig. 4b), the result is an escaping, arcade-boundary–rooted flux rope line and a cusped loop rooted in the rope bipole. Thus the three types of field lines shown in Figure 1—the arcade-boundary– rooted escaping rope, the rope-bipole–rooted surviving rope, and the cusped loops separating them—are formed.

3. OBSERVATIONAL IMPLICATIONS OF PARTIALLY EXPELLED FLUX ROPES

It is well known that filaments often re-form after eruptions as active regions evolve: one possible explanation is flux rope re-formation due to turbulent boundary flux diffusion as active regions gradually disperse (Amari et al. 2003b; van Ballegooijen 2004). Such models may explain how filaments form and/or reform over the course of several days or weeks, but they do not explain cases in which filaments immediately re-form after a CME or, indeed, appear partly or totally unaffected by a CME occurring right above them (Tang 1986; Gilbert et al. 2000; Pevtsov 2002; Gibson et al. 2002). In the flux rope model, the filament is supported by the dips within the winding rope, so that the total expulsion of the rope necessarily implies the total expulsion of the filament. In a partially expelled flux rope, however, the degree to which the dipped field is filled with filament mass, and the location of this mass relative to where the rope breaks in two, determines whether all, some, or none of the filament will escape (see, e.g., Fig. 2, right). In our simulation, some of the dipped field of the original flux rope escapes, and some survives the eruption. The pink and red field lines seen in Figures 1b–1d are examples of dipped field lines that survive the eruption. As discussed above and demonstrated in Figure 3, these field lines reconnect when the rope breaks in two, but their reconnections occur above the dipped portion of the field lines. Thus, although we might expect some temporary reconnectiondriven heating, the filament mass in these dips would not be expelled. The blue lines shown in Figure 4b are examples of initially dipped field lines that reconnect to form the arcadeboundary–rooted dark orange escaping flux rope line. In this case, the reconnections happen well behind the initially dipped field-line apexes, so filament mass could be carried outward in the escaping dark orange flux rope line. Eruptive X-ray sigmoids appear as sharply defined S or backward-S shapes, often transitioning into postflare cusped shapes (Pevtsov 2002). Even after eruptions and sigmoid-to-cusp tran-

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sitions, however, active regions can exhibit sigmoid structures again within a matter of hours (Gibson et al. 2002). One proposed explanation for X-ray sigmoids is heating due to reconnections along the BPSS. Magnetic connectivity is discontinuous across the BPSS, because the field lines are line-tied to the (assumed) rigid photosphere, so perturbations of the field in this region are likely to form current sheets (Parker 1994; Titov & De´moulin 1999; Low & Berger 2003). Gibson et al. (2004) demonstrated that current sheets do indeed form along the BPSS as expected during flux rope eruption, and this holds true for the simulation discussed here. Thus, in our simulation a bright, transient eruptive X-ray sigmoid that transitions to a postflare cusp is consistent with reconnecting sigmoid loops at the current sheets that form along the BPSS followed by reconnections at the central vertical sheet, where cusped posteruption loops form below the expelled portion of the flux rope. However, as Figure 3c demonstrates, a BPSS survives the eruption and lies below the cusped posteruption loops. Such a topological surface would likely soon be perturbed by the everdynamic photosphere (Gibson et al. 2005a), so we would expect the persistent (i.e., non-eruptive) X-ray sigmoid to quickly reform below the fading cusp—as is indeed observed. 4. CONCLUSIONS AND DISCUSSION

We find that the loss of equilibrium of a twisted coronal flux rope results in the splitting of the rope in two, with one rope

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successfully being expelled and the other remaining behind. Such a partial expulsion of a preexisting rope is consistent with a range of observations, before, during, and after CME eruptions, as discussed above. In particular, a partially expelled rope explains observations that are at odds with the total expulsion of a preexisting flux rope, such as filaments that are expelled partly or not at all during a CME, and sigmoids that quickly re-form after eruption. The critical factors that lead to the partially expelled rope are its three-dimensionality and its possession of dipped field lines grazing the photosphere (i.e., a bald patch). The BP keeps part of the rope behind, and its three-dimensionality leads to the multiple reconnections, both internal and external, enabling a part of it to go. It is possible that the “degree of emergence” of a preeruption flux rope, that is, whether it possesses a BP or whether it is high enough in the corona to possess an X-line, determines whether the rope is expelled totally or partially. If this is indeed so, we can make a specific, testable observational prediction, that is, that partially erupting filaments should be more likely to possess a BP (or BPs) than totally erupting filaments. We thank B. C. Low, Tom Holzer, and Tibor To¨ro¨k for helpful discussions, and Holly Gilbert for permitting us to adapt her partially erupting filament diagrams. This work was supported in part by the Air Force Office of Science Research, grant F49620-02-0191.

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