MHD simulations on eruption triggered by flux emergence

*/25MHD simulations on eruptiontriggered by flux emergenceT. YokoyamaUniversity of Tokyo

CollaboratorsK. Nagashima (Stanford U.), S. Notoya, T. Kaneko (U. Tokyo)

Based on the papersNotoya, 2006, master degree thesis, U. TokyoNagashima et al., 2007, ApJ, 668, 533Kaneko & Yokoyama, 2011, in preparationFEW20112011.8.22-25 Berkeley, USA

*/25IntroductionFlare/CME trigger is one of the important issues that are still open.It is suggested that there is a close relation between the plasma eruption and the flare/CME onset (e.g. Priest & Forbes 2002) because, at the onset of a large flare, an eruption of a plasma is frequently observed (e. g. Martin 1980; Ohyama & Shibata 1997). So understanding the trigger of a plasma eruption is probably a key for understanding that of a flare/CME. Martin et al. (1985) and Livi et al. (1989) suggested an importance of flux cancellations near a filament for the eruption. Feynman & Martin (1995) found a strong correlation of flux emergence and filament eruptions.

*/25Chen & Shibata (2000)Based on the flux rope model, an emerging flux trigger mechanism is proposed for the onset of CMEs (and flares) using 2D MHD simulations.The basic idea comes from the catastrophe model (Hood & Priest 1980; Priest & Forbes 1990; Forbes & Priest 1995)

Initially a flux rope is supported by the tension force of the overlying arcade. When magnetic flux emerges in the vicinity, it reconnects with the overlying field. Then the balance of the force is lost and leads to the eruption of the flux rope.

*/25Introduction (continued)Todays my talkWhat happens to a filament long before its eruption ?Observations of a filament eruption and its slow motion and mini-flares before the eruption(Nagashima et al. 2007)How does an eruption is triggered by an emerging flux ?MHD 3D & 2D simulations of an eruption induced by an emerging flux into the coronal arcade(Notoya 2006, Kaneko & TY 2011)Note that I am not saying all of the filament eruptions are due to the emerging flux. (Kink instability [Rust & Kumar 1996]; Torus instability [Kliem & Trk (2006)] etc.)

*/25Chen & Shibata (2000)In the initial condition of the simulation by Chen & Shibata, the flux rope was already in the equilibrium state close to the critical point. So once a magnetic flux emerges in the vicinity, then the flux rope immediately erupted.What happens to a filament long before its eruption ? How the flux ropes equilibrium approaches to the critical point ?

*/25Filament eruption on 2005 Sep. 13X1.5flareaccompanied by filament eruption and a halo CMENagashima et al. (2007)Chifor et al. (2007); H. Wang et al. (2007); see also H. Li et al. (2007)

*/25Small flares and motion of the magnetic elementsThere were frequent occurrence of mini-flares around the filament. and magnetic patches moving in the vicinity of the neutral line. These are the signature of magnetic reconnection events around the filament magnetic field.

*/25Slow and long-lasting motion of the filamentThe distance between the filament and the magnetic neutral line increases in time with speed of about 0.1 km/sec. This motion continues more than 40 hours. This motion indicates a change of the magnetic structure around the filament in this long time scale.Eruptionmagnetic neutral linefilamentNagashima et al. (2007)

*/25filamentEvolution and triggering mechanism of the filament eruption

Many small flares that occurredin the vicinity of the filament played a role in changing the topology of the magnetic field lines overlying the filament through small scale reconnection. Over two days, they changed its equilibrium state gradually and allowed the filament to ascend slowly. In the end, when the filaments were probably very close to the critical point for loss of equilibrium (Forbes 1990), a flare occurred and lead to the catastrophic filament eruption directly.Nagashima et al. (2007)Key observations are: (1) many mini flares (2) motions of magnetic elements and (3) relative motion of the filament away from the neutral line.

*/25Chen & Shibata (2000)How does an eruption is triggered by an emerging flux ? We performed MHD Simulations in 2D & 3D.The purpose of this study is to simulate the processes not only of the eruption but also of the approach to the stability/non-equilibrium critical point.

*/25convection zone, photosphere,chromospherecorona60,000 km sheared arcade field in the corona (24G @ btm; scale height 30000km)twisted flux tube in the convection zoneInitial conditionNotoya (2006)r=1200km, 2p/q=4000km, B=15kG, 7e20Mx @ -4300km

TemperatureResults of 2D simulation 1/2plasmoid formation and eruptionA plasmoid is formed and erupted by the reconnection in the RHS arcade which is deformed by the flux emergence.Eruption speed ~ 0.4 CA

Results of 2D simulation 2/2Structure of reconnection regionJxSince the anomalous resistivity is assumed, the fast reconnection by the Petschek type is preferred.The "X"-letter structure of slow-mode MHD shocks is obtained.

*/25Chen & Shibata (2000)What happens in a 3D situation ?

*/25convection zone, photosphere,chromospherecorona60,000 km sheared arcade field in the corona (24G @ btm; scale height 30000km)twisted flux tube in the convection zoneInitial conditionNotoya (2006)r=1200km, 2p/q=4000km, B=15kG, 7e20Mx @ -4300km

*/2510^5 kmInitial condition etc. (continued)Notoya et al. (2007)resistive MHD equations with gravity no heat conduction, no radiative coolinganomalous resistivity (h is a function of j/r )Modified Lax-Wendroff scheme300^3 grid points with non-uniform spacingconstant-gradient condition for other boundaries plus wave damping zones

*/25Emerging flux

*/253D Simulation resultsNotoya et al. (2007)

*/253D Simulation resultscurrent sheet within the arcadeA deformation of the arcade fields takes place by the pushing motion of the emerging flux. A current sheet is produced inside the arcade.unreconnected linesreconnected linesemerging flux

*/253D Simulation results (continued) The magnetic reconnection takes place in the current sheet. A flux rope is formed by the reconnection and is erupted by the magnetic force of the reconnected field lines.

*/25 The flux rope is accelerated to 30% of the typical coronal Alfven velocity at the altitude of 1e5 km.Height and Velocity of the flux ropeIsosurface of T=0.4 MK

*/25ConclusionWhat happens to a filament long before its eruption ?A long-term slow (maybe ascending) motion induced by many small flares were observed. It suggests a intermittent change of the field topology due to multiple reconnection events.How does an eruption is triggered by an emerging flux ?By 2D & 3D MHD simulations, we have shown processes of formation and eruption of a flux rope. It is formed by the reconnection in the pre-existing coronal field and is erupted through, again, by the reconnection.

*/25

*/2512kGBtube=9kG The emerging flux with weaker field strength make the smaller deformation of the arcade field.Dependence on tube field strength

*/25Temporal behavior

*/25Filament eruption on 2005 Sep. 139/13 19:27 X1.5flareaccompanied by filament eruptions and a halo CME

About 40 minutes before the flare peak (~18:50), small brightenings in EUV were observed at the foot point of the dark filament to erupt. (C2.9 flare

TRACE 195 movie18:00-21:00)500 400,000km squarewhite-light image (SOHO MDI)bright filamentdark filament1 hour before the eruption2 dark filaments eruption

*/25~19:30 (main phase) filament eruption~20:00 halo CME (LASCO/C2)~20:002nd eruption (faint)~18:50 (preflare)C2.9 flare

GOES SXR lightcurve (9-hour)0.5-4 1-8 CME SOHO/LASCOCMESep. 13th 0:00 - 14th 0:00It was not so geoeffective (Wang et al. 2006)

*/25Long-time evolution of the filaments in AR NOAA 10808To investigate the triggering mechanism of the eruption, we concentrate on the evolution of the filaments before the eruption.another filament eruption9/119/139/129/149/109/9We focus on the data taken on 9/11 23:36- 9/11 16:00 and 9/11 23:30 9/13 21:00.9/13 19:27/11 13:12TRACE 195dataM3.0X1.5

*/25slow and long-lasting ascending motion of the filamentspeed0.1km/sThe filament displaced ~25arcsec(18,000 km) from the neutral line during the period of 40hours. Eruption:150-250km/sSuch a slow and long-lasting ascending motion is probably different from so-called slow-rise phase of the erupting filaments.magnetic neutral linefilamentBright filament : 1.5102km/s Dark filament : 2.5102km/s more than 5 minutes (fast-rise?)Bright filament :1.3102km/s Dark filament : 5.810 km/s more than 10 minutesslow-rise?)Eruption:150-250km/s

*/25Preflare brightenings on Sep. 12th and 13th During the slow rise of the filament, several M- and C-class flares and small brightenings in EUV occurred.

Location of the flares on Sep. 12th and 13th (:C-classM-class)Most of them occurred in the vicinity of the footpoints of the filament.At these sites, magnetic elements emerged and moved distinctively.Red dashed line : magnetic neutral line

*/25Long-time evolution of filamentsWe set a slit and made height-time profile along this slit.

We investigate the evolution of the filament over 2 days before the eruption.bright filamentdark filament

*/252. Deformation of the arcadeGold:current sheet within the arcadeDeformation of the arcade takes place since the emerging flux expands in the corona and current sheet is produced inside the arcade since the footpoints of it approach each other.

*/253.Formation and Eruption of flux rope

Current sheets are dissipated through the reconnection and produced structure is ejected into higher corona.The formation of the flux rope occurs since the reconnection takes place in the produced current sheet.

*/25What is happening ?Notoya et al. (2007)

*/25Simulation resultsNotoya et al. (2007)

*/25Catastrophe model(Priest & Forbes 1990; Forbes & Priest 1995;Hood & Priest 1980)

*/25MHD 3D simulations of an eruption induced by an emerging flux

Notoya et al. (2007)The interaction between the coronal field and emerging flux has been studied numerically by many authors: (Forbes & Priest 1984; Shibata et al. 1992; Yokoyama & Shibata 1996; Isobe et al. 2006; Archontis et al. 2005; Galsgaard et al. 2005 etc.)

*I would like to talk about an eruption of a magnetic flux triggered by an emerging flux. This talk is based on the collaboration with these people. The contents of this talk is described in these papers in detail.

*Flare/CME trigger is one of the important issues that are still open. It is suggested that there is a close relation between the plasma eruption and the flare/CME onset. At the onset of a large flare, an eruption of a filament is frequently observed (e. g. Martin 1980). Rapid increase in the plasma erupting speed was seen at the onset of the HXR impulsive emission (Ohyama & Shibata 1997).What causes the eruptions ? What is the trigger ? Martin et al. (1985) and Livi et al. (1989) suggested an importance of flux cancellations near a filament for the eruption. Feynman & Martin (1995) found a strong correlation of flux emergence and filament eruptions.

*This is a figure taken from the paper by Chen & Shibata. Based on the flux rope model, an emerging flux trigger mechanism is proposed by them for the onset of CMEs and flares. The basic idea of the simulation comes from the catastrophe model proposed by these people. It is already shown by Shibata-san yesterday in his nice review. So I skip the detailed explanation. The topics in my talk is in some sense extensions of this study in some directions.*I would like to touch 3 topics. I would like to address 3 questions in terms of the plasma eruptions. The first one is what magnetic structure does the filament has in the equilibrium? Is it a flux rope on not ? For this question, I would like to show you the Hinode observation of the photospheric magnetic structure beneath a filament. The second is what happens to a filament before its eruption from this study. For this question I would like to show you the observations of a filament eruption and its preceding slow motion and mini-flares. The third one is how does an eruption is triggered by an emerging flux. I would like to show you the MHD 3D simulation results of an eruption induced by an emerging flux into the coronal arcade. * In the initial condition of the simulation by C&S, the flux rope was already in the equilibrium state very close to the critical point. So once a magnetic flux emerges in the vicinity, then the flux rope immediately erupted. How the flux ropes equilibrium approaches to the critical point ?

*In terms of this question, I would like to introduce you an interesting observation by Nagashima-san. This is her master thesis work. This is an X1.5 flare accompanied by a filament eruption and a halo CME, that occurred on 2005 Sep. 13.

*We studied the long-term evolution in magnetogram and in TRACE 195 A EUV images. This figure shows the location of the mini-flares observed in EUV that occurred before this X-class flare in two days. This black line is the location of the filament which erupted during the X-class flare. It is found that there were frequent occurrence around the filament. Also you may notice in this magnetogram movie magnetic patches moving in the vicinity of the neutral line. She interpreted that these mini-flares are the signature of magnetic reconnection events around the filament magnetic field.*Another interesting observational fact was the slow and long-lasting motion of the filament. This figure is a stack plot along this slit in the EUV image. The duration of the plot is about three days. The distance between the filament and the magnetic neutral line increases in time with speed of about 0.1 km/sec. This motion continues more than several tens hours. This motion indicates a change of the magnetic structure around the filament in this long time scale.

*This is her interpretation. Although it is not clear that the moving magnetic patches were emerging poles. But I think it is possible.

*Now we have observations of a flux rope and its eruption. So what about the numerical experiments? Chen & Shibatas work is done in two-dimension. So we try to extend this into 3D. *This is an initial set up of the simulation. In the corona, there exists magnetic arcades in the linear force-free equilibrium state. In the convection zone, we put a twisted flux tube. By adding a perturbation, the flux tube starts to emerge and interacts with the coronal field.

*Now we have observations of a flux rope and its eruption. So what about the numerical experiments? Chen & Shibatas work is done in two-dimension. So we try to extend this into 3D. *This is an initial set up of the simulation. In the corona, there exists magnetic arcades in the linear force-free equilibrium state. In the convection zone, we put a twisted flux tube. By adding a perturbation, the flux tube starts to emerge and interacts with the coronal field.

*And what you see here is the top-view of the previous figure. As you see, the arcade field is highly sheared to its neutral line.To initiate emerging process, we perturbed the center of the flux tube.*First, we talk about the emerging and expansion processes.As a first stage, there are emerging and expansion processes.This figure shows the field lines of only the emerging flux. The perturbed part of the flux tube rises up and down stream along the field lines is produced, making the perturbed part more buoyant. And the perturbed flux tube rises up into the photosphere due to the Parker Instability and expand in the corona, making the omega-configuration.*This is a result. As the flux emerges from the surface, it pushes and deforms the coronal arcade field. Then the arcade is elongated in the vertical direction. A current sheet is formed inside. Then, reconnection occurs in the sheet. As a result a flux rope is produced. The flux rope is ejected due to the magnetic pressure force of the reconnected field lines.This is a shot from the side. The light blue lines are the field lines of the emerging fields, the orange lines are the reconnected fields or the lines of the flux rope. the green lines are of the overlying field. *Deformation of the arcade takes place since the emerging flux expands in the corona. And current sheet is produced inside the arcade since the footpoints of it approach each other.*The formation of the flux-rope occurs because the reconnection takes place in the current sheet. These current sheets are dissipated through the reconnection process and produced structure is ejected into higher corona.From now we will look at the driving force of this eruption process.*And this figure show the height and velocity of the ejected flux rope. Left axis and solid line show the height of the flux rope, and right axis and dashed line show the velocity of it. This figure says that the flux rope is accelerated to 30% of the coronal alfven velocity at this height and this is consistent results with the observations.*Today's my talk is about a filament eruption triggered by emerging fluxes. I would like to touch 3 topics. The first one is on the Hinode observation of the photospheric magnetic structure beneath a filament. This study is for answering the question what magnetic structure does the filament has in the equilibrium. The second is on the observations of a filament eruption and its preceding slow motion and mini-flares. We learned what happens to a filament before its eruption from this study. The last topic is the MHD 3D simulations of an eruption induced by an emerging flux into the coronal arcade. From the simulations, we try to clarify how does an eruption is triggered by an emerging flux. So I start from the first one.

***Deformation of the arcade takes place since the emerging flux expands in the corona. And current sheet is produced inside the arcade since the footpoints of it approach each other.*The formation of the flux-rope occurs because the reconnection takes place in the current sheet. These current sheets are dissipated through the reconnection process and produced structure is ejected into higher corona.From now we will look at the driving force of this eruption process.*From these simulations, we succeeded to produce a flux rope structure by an interaction between the emerging flux and the coronal field. But as you notice that this flux rope does not stay in the equilibrium state but it erupts away sooner after its formation. So I do not say this is modeling the long lasting filament and its eruption directly. Bu I would like to emphasize that we have had another possible model to trigger the eruption.

*This is a result. As the flux emerges from the surface, it pushesand deforms the coronal arcade field. Then the arcade is elongated in the vertical direction. A current sheet is formed inside. Then, reconnection occurs in the sheet. As a result a flux rope is produced. The flux rope is ejected due to the magnetic pressure force of the reconnected field lines.This is a shot from the side. The light blue lines are the field lines of the emerging fields, the orange lines are the reconnected fields or the lines of the flux rope. the green lines are of the overlying field. *The basic idea of the simulation comes from the catastrophe model proposed by these people. In the initial condition of the simulation by C&S, the flux rope was already in the equilibrium state very close to the critical point. So once a magnetic flux emerges in the vicinity, then the flux rope immediately erupted. How the flux ropes equilibrium approaches to the critical point ?

*So we are doing 3D simulations of an emerging flux interacting with the coronal field. Hour goal is to produce the flux rope and make it erupts by this interaction. This work is done by Notoya-san in Univ. Tokyo. In the following a few slides, I would like to introduce the results of the simulation.