Onset mechanism of solar eruptions

Accepted Manuscript Onset mechanism of solar eruptions Satoshi Inoue, Yumi Bamba, Kanya Kusano PII:

S1364-6826(17)30480-7

DOI:

10.1016/j.jastp.2017.08.035

Reference:

ATP 4683

To appear in:

Journal of Atmospheric and Solar-Terrestrial Physics

Received Date: 30 November 2016 Revised Date:

17 August 2017

Accepted Date: 24 August 2017

Please cite this article as: Inoue, S., Bamba, Y., Kusano, K., Onset mechanism of solar eruptions, Journal of Atmospheric and Solar-Terrestrial Physics (2017), doi: 10.1016/j.jastp.2017.08.035. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Onset Mechanism of Solar EruptionsI

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Satoshi Inoue1,2 , Yumi Bamba3 and Kanya Kusano2 1 Max-Planck-Institut F¨ ur Sonnensystemforschung, Justus-von-Liebig 3, 337077 G¨ ottingen Germany

2 Institute of Space-Earth Environmental Research, Nagoya University, Furo-Cho Chikusa-ku Nagoya 464-8601, Japan

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3 Institute of Space and Astronautical Science (ISAS) / Japan Aerospace Exploration Agency (JAXA), 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan

Abstract

Solar eruptions are the most energetic phenomena observed in the solar system observed as flares, coronal mass ejections (CMEs) and filament/prominence eruption. The helically twisted flux tube is widely thought to be the source and driver of solar eruptions and to carry the plasma into the interplanetary space. Those may eventually reach the magnetosphere and cause strong disturbances

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of the geomagnetic field. Therefore, the understanding of the onset of solar eruptions is important not only in the framework of solar physics but also for the space weather forecast. In this paper, we report on new insight into the onset mechanism of solar eruptions recently obtained from our new studies. We

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perform the studies in terms of the observational approach with state-of-the-art solar physics satellites and the numerical one with the latest super computer system. We specified two types of small magnetic perturbations of the pho-

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tospheric magnetic field. These can enhance the magnetic reconnection in the pre-existing non-potential magnetic field, which produces a large flux tube

and then drives the eruption. We further confirmed that this reconnection is a key process for the eruption in our latest data-constrained simulation. We report our latest results and our interpretation of the onset mechanism of solar eruptions. I Fully

documented templates are available in the elsarticle package on CTAN.

Preprint submitted to Journal of LATEX Templates

August 30, 2017

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Keywords: elsarticle.cls, sun:magnetic fields, sun:solar flares, sun:coronal

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mass ejections (CMEs), Magnetohydrodynamics, Space Weather 2010 MSC: 00-01, 99-00

1. Introduction

Solar eruptions are one of the dramatical phenomena observed in the solar

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corona, which suddenly launch the coronal plasma away from the solar surface. They are observed as solar flares, filament/prominence eruptions, and 5

coronal mass ejections(CMEs). In particular, CMEs are well known as a source

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of disturbances of the electromagnetic field in the geospace. Therefore, the understanding of solar eruptions is important not only to uncover the nonlinear dynamics of the solar coronal plasma but also to establish the space weather forecast. 10

The magnetic flux rope, which is a bundle of helical twisted field lines, is widely thought to be the source and driver of solar eruptions because it can

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accumulate the required free magnetic energy and support dense plasma against gravity. Furthermore, the magnetic reconnection can be allowed in the solar corona: then the observed phenomena during the eruption are well explained by 15

the standard flare (CSHKP) model(Carmichael 1964, Sturrock 1966, Hirayama 1974, Kopp & Pneuman1976).

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On the other hand, several basic problems still remain, in particular, when and how is the flux tube formed and why does it show a sudden launching?

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To those questions, big efforts have been dedicated. Based on the observations 20

and also the CSHKP model, for instance, Forbes & Isenberg 1991 and Forbes & Priest 1995 proposed the loss of equilibrium model. They first assumed a flux tube in equilibrium embedded in the ambient coronal magnetic field and could show the eruption due to the change of the photospheric boundary condition. In contrast to that, Mikic et al. 1998 and Kusano et al. 1995 first assumed

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the simple coronal arcade initially without the flux tube. They showed that the shearing motion given on the bottom boundary can induce the magnetic

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reconnection between the sheared field lines stretched by the boundary motion;

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eventually the flux tube is formed and then shows its eruption. Recent supercomputing allows us to perform the three-dimensional (3D) 30

magnetohydrodynamic (MHD) simulations of the solar phenomena including

the solar eruption. Amari et al. 2000 and their subsequent series of papers showed the solar eruption in their simulation in which the potential field is set

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as the initial state and the helicity injection through the twisting and converging

motion on the bottom polarities can create a twisted flux tube which eventually 35

can escape from the lower corona. Several studies support the kink unstable

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flux tube converting into failed or ejective eruptions (T¨or¨ok & Kliem 2005, Fan 2005, Inoue & Kusano 2006). Recently, the torus instability (Kliem & T¨or¨ok 2006) is also widely accepted as one of the possible instabilities occurring in the solar corona (Liu 2008, Aulanier et al. 2010, Jiang et al. 2014, Schmieder et al. 40

2015). Because this instability can be observed at the same point where the loss of equilibrium discussed above occurs, these are the same phenomena from different view points (D´emoulin & Aulanier 2010, Kliem et al. 2014).

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Although many MHD models have been proposed to explain solar eruptions, most of them were constructed in the theoretical model, i.e., the convenient 45

models were applied to the MHD simulations as the initial states, which easily cause the solar eruption. As pointed out in D´emoulin & Aulanier 2010, for

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instance, several simulations started with the unstable flux tube. A major questions is how do the stable magnetic fields convert into the unstable state? In order to address this question, recently our group carried out several comprehensive studies: one is the careful data analysis of the photospheric magnetic

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field, another is the analysis of the 3D coronal magnetic field extrapolated form the photospheric magnetic field, and a third one is MHD simulation based on the observed information in order to understand the 3D dynamics. In this paper, we will report our latest results and interpretations of the onset mechanism

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of the solar eruptions.

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2. Data Analysis of the Photospheric Magnetic Field

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In order to reveal the magnetic structure causing the solar eruption, it is

essential to analyze the observed magnetic field, in particular, before the flare

onset. Fortunately, the Solar Optical Telescope (SOT: Tsuneta et al. 2008) and 60

Helioseismic and Magnetic Imager (HMI: Scherrer et al. 2012 ) onboard the

recent solar physics satellites Hinode (Kosugi et al. 2008) and Solar Dynamics

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Observatory (SDO: Pesnell et al. 2012), respectively, have provided the pho-

tospheric magnetic fields with unprecedented spatial and temporal resolutions. On 2006 December 13, for instance, Hinode could observe the X 3.4 class flare produced in the solar active region (AR) 10930. The Stokes-V/I image corre-

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sponding to the line-of-sight (LOS) magnetic field and two flare ribbons observed in the Ca II H line are shown in Figs. 1a and 1b. The AR 10930 was composed of the bipolar field in which the smaller positive polarity located in the south of the large negative polarity showed a strong counterclockwise motion 70

and a motion toward the east, while the negative polarity was relativity fixed.

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The rotation angle and helicity injection were measured for the positive sunspot motion in e.g., Zhang et al. 2007, Magara & Tsuneta 2008, Min & Chae 2009. On the other hand, Hinode also captured the fine and very complex magnetic structure in the region surrounding the polarity inversion lines (PILs). Kubo 75

et al. 2007, Wang et al. 2008 and Lim et al. 2010 discussed the fine magnetic

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structure, in particular, the origin and structure of the magnetic channel. Park et al. 2010, Ravindra et al. 2011 and Inoue et al. 2012 also pointed out that, due to the emergence of the twisted flux tube, a complex magnetic structure

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developed in the local area surrounding the PILs where positive and negative

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current density and magnetic helicity co-existed. Regarding the flare trigger process, recently Bamba et al. (2013) carefully

analyzed Stokes-V/I images, photospheric magnetic field and chromospheric emission covering the flare occurrence time. They studied AR 10930 and several other ARs, which also caused huge solar flares, and could find a common

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interpretation for the onset. They assumed the cartoon model for the magnetic

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field in the AR prior to the flare as shown in Fig. 2a, in which a small mag-

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netic disturbance (e.g., magnetic flux emergence) appears in the global sheared magnetic field constituting the AR. The small magnetic disturbances in the photosphere, in particular, close to the PILs are one of the promising candidates for 90

the triggering processes of solar flares (Shibata & Magara 2011), and recently Kusano et al. 2012 successfully showed the eruption in their numerical model

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using the magnetic field shown in Fig. 2a. Bamba et al. 2013 first analyzed the spatio-temporal correlation between the Stokes-V/I image and the chromo-

spheric emission Ca II H line, focusing on the flaring region for several hours prior to the onset of the flares. From this relationship, taking into account the

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magnetic field structure seen in Fig. 2a, they inferred the flare-triggering region. Next they measured the global magnetic shear angle (θ) which represents how much the horizontal component of the global magnetic field deviates from the direction (N ) perpendicular to the averaged PILs. The relationship of these 100

angles are described in Fig. 2b. The average was performed by a low-pass filtering of the LOS magnetic field through a Fourier transformation (see details in

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Bamba et al. 2013). Furthermore, the azimuth of the horizontal field (φ) in the flare triggering region was measured, where φ is defined between the direction (n) perpendicular to the local PILs in the flare triggering region and N . Note 105

that the local PILs are not averaged. Fig. 3 shows the important result which is

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the flare phase diagram for four large solar flares, characterized in the parameter space in θ-φ. The distribution tends to concentrate in two locations. That was well explained by the numerical study of Kusano et al. (2012), which is detailed

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later. Interestingly, they also found that the flare-triggering flux derived from 110

their analysis increases when the flare occurrence is approached.

3. Nonlinear Force-Free Field Extrapolation As seen above, high spatially and temporally resolved photospheric data

help us to suggest the flare triggering region. On the other hand, the 3D AR magnetic field is not yet specified with only the photospheric magnetic field.

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The free energy required for the solar eruption is accumulated in the corona,

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so it is important to understand the 3D magnetic structure. The accurate photospheric vector magnetic field, however, can allow us to extrapolate the 3D coronal magnetic field. Before moving onto the extrapolation, in order to address the plasma state in the solar corona, we introduce the plasma β which is 120

defined as a ratio of the gas and magnetic pressure P/(B 2 /2µ0 ) where B, P ,

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and µ0 correspond to the magnetic field, gas pressure and magnetic permeability, respectively. Following Gary 2001, because the solar corona is in a low-β

condition (10−4 − 10−1 ), the force-free condition, J × B = 0 or ∇ × B = αB,

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can be adopted by neglecting the gas pressure and gravity, where J is the current density and α corresponds to a coefficient which in general is a function of space. The potential field is obtained by assuming that the current density vanishes everywhere. That field is easily reconstructed from the normal component of the photospheric magnetic field (Sakurai 1989). However, the potential field is not a proper model of erupting ARs because it has no free magnetic 130

energy. Therefore, we have to seek the solution by directly solving the force-free

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equation, given the three components of the photospheric magnetic field. We call this solution nonlinear force-free field (NLFFF). There are several methods for seeking the NLFFF solution, the details of which are beyond the scope of this paper. Those can be found in the other comprehensive reviews, e.g., Wiegelmann & Sakurai (2012) or Inoue (2016).

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For the AR 10930, Schrijver et al. 2008 extrapolated the NLFFF based on the photospheric magnetic field before and after the X3.4 class flare. They

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successfully reproduced the highly twisted field lines accumulating the strong current density, which disappears after the flare. He et al. (2014) demonstrated

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the temporal evolution of the NLFFF, also covering the states before and after a flare. They showed the evolving 3D magnetic field and current density resulting from the sunspot rotation. Inoue et al. 2011 & Inoue et al. 2012 also performed the NLFFF extrapolation and found that the magnetic twist reached a full

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turn, using the expression in Berger & Prior 2006. That formula is written as R (1/4π) (J · B/|B|2 )dl where dl is a line element. Three-dimensional magnetic 6

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fields are drawn in Fig. 4a where the field lines are extrapolated before the flare

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and have strong current density in the central area of the AR. This confirms that significant magnetic twist can indeed be built up prior to the flare, which relaxes after the flare. As shown in Fig. 4b, the highest twist was 1.5 turn, 150

however, after the flare twisted lines with more than a half-turn disappeared as seen in Fig. 4c. This result suggests that at least a twist of more than a

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half turn would be required for causing the eruption. Inoue et al. 2011 further

investigated the twist values of the field lines which are anchored in the flare ribbons at both ends and plotted in Fig. 4d. Note that the field lines were extrapolated before the flare at 20:30 UT on December 12 but those footpoints

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are well in agreement with the location of the flare ribbons observed at each time during the flare as shown in Fig. 4e. nterestingly, when the flare ribbons begin to brighten, the field lines rooted in the ribbons have only a very small twist (Fig. 4d). This result suggests that this solar flare may not be 160

triggered by strongly twisted lines.

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4. Numerical MHD models of the Solar Eruption In the previous section we inferred the flare-triggering region and the 3D coronal magnetic field. Here we address the question how the highly twisted flux tube causing the eruption is created and then disappears in the lower corona. In order to find the answer, 3D MHD simulations are a strong tool. As mentioned

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in the introduction, several MHD models for eruptions were proposed. Among these models we focused on the MHD simulations of solar eruptions performed

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by Kusano et al. 2012, where the observed information was taken into account. They first set the initial magnetic field as shown in Fig. 2a, i.e., the large-scale

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magnetic field is assumed to be a stable arcade of sheared field lines, which is belonging to the class of linear force-free fields. Emerging flux is prescribed locally at the PIL and plays the role of a perturbation to the global sheared field. In this configuration, a highly twisted flux tube does not exist in the initial state, which is a situation similar to that obtained from the NLFFF extrapolation in

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Inoue et al. (2011, 2012). Based on the simulation results, Kusano et al. 2012

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made a flare phase diagram in the parameter space θ-φ, as shown in Fig. 5. The background color range shows the value of the kinetic energy converted from the free magnetic energy contained in the highly sheared arcades.The colored diamonds show eruption, and no eruption is marked by open squares. Two types 180

of the eruption process were found as identified by the color of the diamonds.

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Pink diamonds indicate the eruption-induced reconnection in which the flare-

reconnection is observed after the flux tube eruption, whereas the blue diamonds correspond to the reconnection-induced eruption: here the flare reconnection

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starts before the onset of the flux tube eruption. The 3D views in the cases of the eruption-induced reconnection and reconnection-induced eruption are shown in Figs. 6a and 6b, respectively . In each case we obviously see that a flux tube is created in the uniformly sheared field, and is ascending. Therefore, according to this result, the flares 1, 2 and flares 3, 4 as seen in Fig. 3 can be classified into the eruption-induced reconnection and the reconnection-induced eruption 190

cases, respectively. Those flares are large solar flares, which fit well in the flare

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phase diagram obtained in the numerical study. The eruption process is different between them, but, as a common point, the flux tube formation is basically in agreement with the tether-cutting reconnection scenario (Moore et al. 2001). Even though a highly twisted flux tube approaching the kink or tours unstable condition does not exist in the initial

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state, these two types of disturbances having different angle φ can produce the flux tube in the uniformly sheared field lines, and it can show the eruption.

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Recently, Inoue et al. (2014, 2015), and also see a Inoue (2016), performed MHD simulation of solar eruptions in a more realistic magnetic environment.

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The target active region was AR 11158 producing the X2.2 class solar flare observed on 2011 February 15. A detailed NLFFF analysis was performed by Inoue et al. 2013 and showed results similar to those obtained in Inoue. et al. (2011, 2012). First, the NLFFF based on the photospheric magnetic field measured by SDO/HMI approximately 90 minutes before the flare was put in

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the MHD simulation as the initial sate. It was found that the NLFFF is quite 8

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stable, and no eruptions were obtained in their simulation without any external

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forcing (Inoue et al. 2014). However, when they allowed the tether-cutting reconnection in the strong current region, in particular, between two sheared

field lines as shown in Fig. 7a, the long twisted lines are formed as seen in Fig. 7b, 210

and then the newly formed twisted lines can show the eruption. Interestingly,

the launched twisted lines further reconnect with the ambient twisted lines,

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consequently, a larger flux tube can be formed as shown in Fig. 7c.

5. Conclusion

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We analyzed the onset process of solar eruptions using two approaches: observation and MHD simulation. Bamba et al. (2013, 2014) analyzed the spatiotemporal correlation between the magnetic structures and the chromospheric emissions to detect the flare-triggering region. They carefully measured the global shear angle and the azimuth angle of newly emerging flux in the inferred flare-triggering region. These results are consistent with the numerical study done by Kusano et al. 2012. Kusano et al. 2012 found that two types

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of flare-triggering flux can cause the formation of a large flux tube through tether-cutting reconnection in the global sheared magnetic fields, which eventually leads to the eruption. Inoue et al. (2014, 2015) performed simulations in a more realistic environment and their results showed that the long twisted field lines formed through tether-cutting reconnection can break the equilibrium

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state of the magnetic field. Their basic scenario is similar to the one in Kusano et al. 2012.

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As future work, more extended statistical studies would be required, because

Bamba (2013, 2014) and more recently Bamba(2017a, 2017b) analyzed totally

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six huge solar flares which occurred in three active regions, these are not yet enough to draw fully gneral conclusions. Moreover, the MHD simulations performed by Inoue (2014, 2015) cannot exactly take into account the triggering process inferred by the observations, i.e., the tether-cutting reconnection was here strongly depending on the numerical process by using an anomalous re-

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sistivity (Yokoyama & Shibata 1994). Therefore, we have to take into account

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the more realistic observed information, e.g., as studied in Kusano et al. 2012. Furthermore, although we pointed out the tether-cutting reconnection causing the solar eruption, the detailed understanding of the physical process is not

yet fully clarified, e.g., we need to determine how much twist should be accu240

mulated in the newly formed highly twisted field lines to break an equilibrium.

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Also, its was not yet determined how much triggering flux is required to cause an eruption. Even after the onset of an eruption, the nonlinear dynamics e.g., the process growing into the CME, is not yet clear too.

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In addition, several studies have tried to reveal the interplanetary CME (ICME), in particular, its flux tube structure, from in-situ observations, (.e.g., Hu et al. 2014). Although the latest photospheric magnetic field measurements and the resulting NLFFF can allow us to estimate the magnetic twist as shown above, the values estimated from both approaches in the solar corona and in the interplanetary space still have a large gap. Yamamoto et al. 2010 made 250

efforts to reduce this gap by using the magnetic flux and helicity conservations,

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however, full agreement is not yet reached. The large scale-MHD simulations tracing the flux tube for a long period might help to resolve this problem and provide full insight into the ICME development. Although several problems are still open, we expect that comprehensive studies combining observation and simulation will resolve these problems step by step.

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Acknowledgement

We are grateful to the organizers of VarSTI for inviting us to the first VarSTI

General Symposium held in Albena, Bulgaria. We also grateful to the reviewers

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for careful reading and constructive comments. This work was supported by the Alexander von Humboldt foundation and JSPS KAKENHI Grant Numbe JP15H05814. Y. B. is supported by JSPS KAKENHI Grant Numbers 16H07478 and 15J10092. The visualization was done using VAPOR(Clyne & Rast 2005,

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Clyne et al. 2007).

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Figure 1: (a) The Stokes-V/I image corresponding to the LOS magnetic field observed by Hinode/SOT at 02:40 UT on 2006 December 13. Back and white correspond to the negative and positive polarities, respectively. (b) Two flare ribbons during the X3.4 class solar flare at 02:40 UT, which was also observed by Hinode/SOT.

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Figure 2: (a) Cartoon of the magnetic field lines in the solar active region made by Kusano

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et al. 2012. White and black correspond to the positive and negative polarities of the LOS magnetic fields, respectively. In the square region the large-scale sheared field dominates in which the free energy is accumulated while the disturbance region (e.g., emerging flux region) is described in the circle area. (b) Top view of LOS magnetic field. Vector N is perpendicular

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to the averaged PIL while the vector n is perpendicular to the non-averaged local PIL in the perturbation region, i.e., flare-triggering region. The averaging means that a low-path filtering was imposed on the LOS magnetic field through the Fourier transformation (See in Bamba et al. 2013). The averaged PILs were derived from them. θ is the counterclockwise twisted angle measured between the directions of the horizontal component of the global sheared field lines in red and N , while the φ is the counterclockwise angle between N and n. Both panels are

from Bamba et al. 2013.

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Figure 3:

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The flare phase diagram in the parameter space θ-φ for four large solar flares,

obtained from the observation study Bamba et al. 2013, where the flares 1, 2, 3, and 4

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correspond to the X3.4 flare in AR 10930 on 2006 December 13, X1.5 flare in AR 10930 on 2006 December 14, M6.6 flare in AR 11158 on 2011 February 13, and X2.2 flare in AR 11158 on 2011 February 15, respectively. The upper and right small panels show the blue and red vector arrows regarding to the direction of the magnetic field line in the flare triggering region

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and in the solar active region, respectively. White and black colors correspond to the positive and negative polarities of the LOS magnetic field. From Bamba et al. 2013.

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magnetic field was taken at 20:30 UT on 2006 December 12. The field lines and strong current density are plotted as green lines and a purple surface, respectively. (b) The distribution of the magnetic twist plotted in the space Bz -Tw before the X3.4 class flare. Each dotted point corresponds to the intensity of the footpoint of a magnetic field line. (c) The same plot but

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after the X3.4 class flare. (d) The magnetic twist measured on the field lines of the NLFFF based on the photospheric magnetic field at 20:30 UT on 2006 December 12. The field lines are traced from a one side of the flare-ribbons observed at each time. (e) The field lines in green extrapolated before the flare are superimposed on the flare-ribbons taken at 02:20 UT on 2006 December 13 where the blue and red contours correspond to the negative and positive polarities, respectively. All figures are from Inoue et al. (2011, 2012)

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Figure 5: The flare phase diagram in the parameter space θ-φ obtained from the numeri-

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cal study by Kusano et al. 2012. The format is almost same as that in Fig. 3, except the color contours which indicate the intensity of the released kinetic energy. The pink and blue diamonds show the eruption based on the eruption-induced reconnection and reconnectioninduced eruption, respectively, whereas the no eruptive cases are marked by open squares.

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From Kusano et al. 2012.

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Figure 6: The temporal evolution of the magnetic field in the eruption-induced reconnection in a and in the reconnection-induced eruption in b, respectively. The green lines indicate the magnetic field lines and white and black correspond to the positive and negative polarities. The

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strong current region formed in association with the dynamics is plotted as an red isosurface. From Kusano et al. 2012.

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Figure 7: (a) Yellow lines show the magnetic field lines in a top view superimposed on the Bz distribution of the photospheric magnetic field. These magnetic field lines correspond to the NLFFF extrapolated form the photospheric magnetic field. The photospheric magnetic

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field was taken by SDO/HMI observed around 00:00 UT on 2011 February 15, approximately 90 minutes before the X2.2 flare in AR11158. The strong current density region is plotted as a sky blue isosurface. (b) The magnetic field lines after the tether-cutting reconnection from

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which the long twisted lines are obviously formed. (c) The field lines during the eruption.

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The numerical study made the flare phase diagram classifying into the two types of eruptions which well explained it obtained from the observed study.

disturbances appearing on the polarity inversion line.

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The two types of eruptions are induced by two types of magnetic

The two types of magnetic disturbances can destroy the stable sheared magnetic field constituting the solar active region through the tether-cutting

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reconnection.

Following the NLFFF extrapolation, the twists of the stable sheared field

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lines are at least required in the range from 0.5 to 1.0 prior to the large flare. The tether-cutting reconnection is key issue also confirmed in the latest

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data-constrained simulation.