Two Step Filament Eruption During 14-15 March 2015

TL;DR

This study analyzes a unique two-step filament eruption in March 2015, combining multi-instrument observations to understand the eruption process and its association with a halo CME.

Contribution

It provides detailed observational evidence and analysis of a two-step filament eruption, highlighting the role of successive instability zones in the eruption process.

Findings

Filament exhibited a two-step eruption with a 12-hour pause at ~125 Mm altitude.

The eruption was associated with a halo CME and jet activity in the active region.

Decay index analysis suggests multiple instability zones contributed to the eruption.

Abstract

We present here an interesting two-step filament eruption during 14-15 March 2015. The filament was located in NOAA AR 12297 and associated with a halo Coronal Mass Ejection (CME). We use observations from the Atmospheric Imaging Assembly (AIA) and Heliospheric Magnetic Imager (HMI) instruments onboard the Solar Dynamics Observatory (SDO), and from the Solar and Heliospheric Observatory (SOHO) Large Angle and Spectrometric Coronagraph (LASCO). We also use H-alpha data from the Global Oscillation Network Group (GONG) telescope and the Kanzelhoehe Solar Observatory. The filament shows a first step eruption on 14 March 2015 and it stops its rise at a projected altitude ~ 125 Mm on the solar disk. It remains at this height for ~ 12 hrs. Finally it eruptes on 15 March 2015 and produced a halo CME. We also find jet activity in the active region during both days, which could help the filament de-stabilization and eruption. The decay index is calculated to understand this two-step eruption. The eruption could be due to the presence of successive instability-stability-instability zones as the filament is rising.

Figures

a, F4 filament) and there was a slow CME observed in the LASCO C2 field–of–view (FOV) at $\approx$ 13:30 UT. The speed and the angular width of this CME was 208 km s*-1* and 160*∘* respectively.

a represents the modified fragment of the magnetogram taken by the HMI on 14 March 2015 at 15:00 UT, which is used as a boundary condition for the potential magnetic field calculations. The pixel size in HMI magnetograms is 0.5*′′* or 0.36 Mm, which is very small compared with the expected height of a filament $\textgreater$ 10 Mm. To save computational time we apply binning several times and increase the pixel size to $\approx$ 10 Mm. Figure 5b–f shows the distribution of the decay index

Equations

$$n=-\frac{\partial \ln B_{\text{t}}}{\partial \ln h}$$

$$\Delta x=htg{\lambda }_0$$

$$\Delta y=htg{\phi }_0,$$

Full text

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1 Introduction

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S-Intro

Solar filaments (known as prominences, when they appear on the limb) are dense and cool material suspended in the hot solar corona along polarity inversion lines (PILs). They are found in magnetic dip regions. The filaments can be located in quiet as well as in solar active regions. The existence, stability and disappearance of filaments are nicely described in recent reviews (Mackay et al., 2010; Labrosse et al., 2010; Parenti, 2014). There are two main magnetic configurations for the filaments, namely a sheared arcade and a flux rope. In the sheared arcade configuration, the arcade connects the opposite polarities on either sides of a PIL, whereas in the case of the flux rope configuration the magnetic field has helical magnetic structure. Solar filament eruptions are also responsible for Coronal Mass Ejections (CMEs) and hence for geomagnetic activity. Therefore the study of their stability and eruption is very important for space weather prediction.

Active region filaments (for example Chandra et al., 2010) are usually associated more with solar flares in comparison to quiet region filaments (Gosain et al., 2016). It is not necessary that every filament activation results in a CME. The result of the activation of filaments can be a failed eruption (Ji et al., 2003; Török and Kliem, 2005; Alexander, Liu, and Gilbert, 2006; Kuridze et al., 2013; Kushwaha et al., 2015), a partial eruption (Gibson and Fan, 2006; Liu et al., 2014; Kliem et al., 2014) or a full eruption (Chandra et al., 2016). When a filament erupts partially or fully and moves away from the solar surface it becomes a CME. Therefore there is a spectrum from fully confined to fully eruptive filament activations. In the latest studies the Solar Terrestrial Relations Observatory (STEREO) has provided two view-points of filament eruptions. Combining the STEREO data with SDO data, three view-point studies have been done (Filippov, 2013, 2016b).

A flux rope is in equilibrium due to the balance between the upward magnetic hoop–force and the downwards magnetic tension of the overlying coronal magnetic field. If due to some process like reconnection between new and existing magnetic flux the stability of the flux rope is lost, it starts to erupt. Several models have been proposed for solar eruptions (for reviews see Aulanier, 2014; Filippov et al., 2015; Schmieder, Aulanier, and Vršnak, 2015; Vršnak et al., 2014). Catastrophic loss of equilibrium or the torus instability are the important mechanisms for solar eruptions (Forbes and Isenberg, 1991; Kliem and Török, 2006; Démoulin and Aulanier, 2010). In these models, it is assumed that the overlying magnetic field (B${}_{\textnormal{external}}$) decreases with the increase of the height (h) from the photosphere i.e. B${}_{\textnormal{external}}$ $\propto$ h-n. The flux rope becomes unstable when the decay index n at its location becomes less than a critical value. According to simulations this value ranges from 1.3 to 1.75 (Török and Kliem, 2005; Isenberg and Forbes, 2007; Aulanier et al., 2010; Zuccarello et al., 2017). Using different observations including high resolution SDO and multi–view STEREO observations it was found that this value lies between 1 and 1.5 in observed eruptions (Filippov and Den, 2001; Filippov, 2013; Zuccarello et al., 2014; McCauley et al., 2015).

In addition to failed, partial and full filament eruptions, recently two filament eruptions were observed with a quasi-equilibrium state in the middle part of a two-step process (Byrne et al., 2014; Gosain et al., 2016). In these cases the filament starts to erupt and after attaining some height it decelerates, stops and seems to be stable for some time. In case of Byrne et al. (2014) this time was rather short i.e. $\approx$ one hour and for the case of Gosain et al. (2016) the time was 15 hrs. Such cases are very crucial and play an important role in understanding the space weather implications of filament eruptions. In this study, we analyze an active-region-filament eruption on 14–15 March 2015, where we notice that after the initial eruption the filament stays for $\approx$ 12 hrs in the quasi-equilibrium state.

The paper is organized as follows: Section 2 presents the observational data, and the morphology of the filament eruption. The time–distance analysis of the filament eruption is presented in Section 3. The associated CME is described in Section 4. To interpret the quasi–equilibrium of the filament, we present the decay index calculation in Section 5. Finally in Section 6, we discuss our results and conclude.

2 Observations

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obs

The active region, NOAA AR 12297 produced one of the largest geomagnetic storm (D${}_{\textnormal{st}}$ index $\approx$ $-223$ nT) of Solar Cycle 24 on 17 March 2015. This geomagnetic storm was associated with a filament eruption and a Geostationary Operational Environmental Satellite (GOES) C9.1 class flare of 2015 March 15. The active region NOAA AR 12297 was located at S22W25 on 15 March 2015 on the solar disk. Further this filament eruption was associated with a halo CME. The filament eruption on 2015 March 15 was studied by Wang et al. (2016), whileas the geomagnetic storm from this active region was investigated by Liu et al. (2015). The eruption also produced a magnetic cloud (MC) studied by Cho et al. (2017). They calculated the helicity sign in the MC and found it was associated with a positive helicity. Our aim in this study is to investigate the filament activation and eruption of 14–15 March 2015. This filament was disturbed on 14 March 2015 and finally on 15 March 2015, it totally erupted. The event was observed by the Atmospheric Imaging Assembly (AIA, Lemen et al., 2012) onboard the Solar Dynamics Observatory (SDO, Pesnell, Thompson, and Chamberlin, 2012) in different UV and EUV wavelengths. The pixel size and cadence of the data is 0.6 arcsec and 12 s respectively. The event was also observed by the Global Oscillation Network Group (GONG) in the H$\alpha$ line center. The temporal and pixel resolution of GONG H$\alpha$ data are one min and one arcsec respectively. For the magnetic field, we use the data from Helioseismic and Magnetic Imager (HMI, Scherrer et al., 2012) onboard SDO. The cadence of the HMI data is 45 s and the pixel resolution is 0.5 arcsec.

The observational description of the filament activation and eruption on 14–15 March 2015 observed by different instruments is presented in the following sections.

2.1 SDO and H$\alpha$ Observations

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sdo

Figure \ireffig:morpho1 shows the evolution of the filament on 14 March 2015 in AIA 193 Å (first column), 304 Å (second column), and GONG H$\alpha$ (third column). Figure \ireffig:morpho1a is overplotted with HMI magnetic field contours. Before any activity in the filament it has a long sigmoidal shape (see Figure \ireffig:morpho1a, e, f, and also the yellow arrow). We can see the sinistral barbs in GONG H$\alpha$ images. According to Martin (1998), if the barbs in the filament are directed leftwards (rightwards) their chiralities are sinistral (dextral) respectively. The sinistral (dextral) chiralities indicate positive (negative) twist/helicity respectively. In our case the sinistral barbs are represented by blue arrow in Figure \ireffig:morpho1i. This suggests the filament has a positive twist and hence positive helicity. Since the filament is located in the southern hemisphere, this is in conformity with the hemispheric rule of helicity. According to the helicity hemispheric rule the majority of positive/negative helicity solar features located in the southern/northern hemisphere respectively (Pevtsov, Canfield, and Metcalf, 1995).

Around 11:50 UT a jet activity started in the active region, which we name as jet 1 and mark by the white arrow in Figure \ireffig:morpho1b. This jet activity was visible in almost all EUV/UV and H$\alpha$ wavelengths. Due to this jet activity the left lower part of the sigmoidal filament was disturbed. Afterwards a strand of the filament separated from the main body, rose upwards and became stable at the projected altitude $\approx$ 125 Mm. The broken part of the sigmoidal filament is labeled by F1 and indicated by the red arrow in Figure \ireffig:morpho1c, d. At the same time, we observe flare brightening in the active region which was reported by GOES as a C2.6 class flare. The upper–right part of the filament channel, which was not disturbed in this period is shown by black arrows in Figure \ireffig:morpho1k. LASCO C2 at $\approx$ 13:30 UT on March 14 also observed a partial halo CME. Later on this CME interacted with the CME of March 15 (Liu et al., 2015). The CME on March 14 was associated with the small filament in the active region, which is different than the filament studied here. A small filament eruption was associated with this CME as reported by Wang et al. (2016) and is named F4 in their Figure 1a.

An interesting point is that the uplifted broken part F1 from the main sigmoidal filament was stable in that particular location for a period of $\approx$ 12 hrs i.e up to 00:45 UT on 15 March 2015. Around 00:45 UT on 15 March 2015, we again observe the jet/surge activity in the active region towards the west-south direction which interacts with the filament F1 as well as with the big northern filament (indicated by three black arrows). We label this jet as jet 2. After 00:45 UT the filament F1 starts to erupt and finally it leaves the solar surface. The evolution of the erupting filament is shown in Figure \ireffig:morpho2. The left, middle and right column of Figure \ireffig:morpho2 show the development of the erupting filament F1 in AIA 193 Å, 304 Å, and H$\alpha$ wavelengths respectively. The eruption is associated with a GOES 9.1 class flare. The flare has a two–ribbon structure visible in different EUV and H$\alpha$ images. We can also see the ribbon separation as proposed by the CSHKP model (Carmichael, 1964; Sturrock, 1966; Hirayama, 1974; Kopp and Pneuman, 1976). The flare was also observed in hard X-rays by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite and studied by Wang et al. (2016).

The major upper part of the sigmoidal filament channel (indicated by black arrows in Figure \ireffig:morpho2) is also perturbed during the ejection of jet 2. The material of the filament rises up and later on it comes back down to the footpoints of the filaments. In AIA channels it becomes brighter and we can also see its twisted structure. From Figure \ireffig:morpho2d (see also movie in AIA 193 Å), one can infer that the twist is right–handed, which is consistent with the sinistral filament chirality seen in H$\alpha$ data. Therefore, we see here the same sign of twist in the chromosphere, the upper solar atmosphere and in the associated magnetic cloud. It seems that jet 2 injects impulse and heat into the filament at its eastern end. Just after the maximum brightness of the mini-flare in the active region at 00:39 UT, dark and bright features appear in AIA 193 Å images, which move from the flare place along the filament channel (see movie in AIA 193 Å). Obviously the flare happens near the eastern end of the filament and jet 2 propagates along field lines belonging to the flux rope containing the filament. Accelerated and heated plasma of the jet influence significantly the equilibrium of the whole filament. Previously static filament material starts to move along the helical field-lines of the flux rope. Thus the upper parts of the helices become visible as dark and bright (due to heating) threads. We observe intense field-aligned motions within the activated flux rope but it does not change significantly its position, and after the energetic phase of the event the filament is restored to its approximate initial state. We consider arguments for such behavior in Section 5. During the activation the filament becomes less visible in the H$\alpha$ wavelength (see the H$\alpha$ images in the third column of Figure \ireffig:morpho2) most likely for two reasons. The Doppler shift in the moving material can move its H$\alpha$ line out of the filter passband (dynamic disappearance), and the heating of the filament can suppress the absorption of H$\alpha$ radiation (thermal disappearance).

3 Time–Distance Analysis

\ilabel

td To investigate the height–time evolution of the filament eruption during 14–15 March 2015, we select a slit along the direction of the filament eruption in the AIA 193 Å data. The position of the slit is shown by the dashed black line in Figure \ireffig:slicea. The time-distance diagram is given in Figure \ireffig:sliceb. In the time-distance diagram, we can clearly see the two step eruption of the filament. In the first step, the filament starts to rise at $\approx$ 12:00 UT on 14 March 2015 and shifts to a projected altitude of 125 Mm on the disk. Unfortunately we do not have STEREO observations, which could tell us the true height of the eruption. We compute the speed of this eruption and find it to be $\approx$ 40 km s*-1*. After 13:00 UT the filament stops its rise and stays at the same height up to 00:45 UT on 15 March 2015. In the second step after 00:45 UT on 15 March 2015, the filament starts to rise and finally fully erupts. The calculated speed of the second step eruption is 70 km s*-1*.

4 LASCO Observations

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lasco

The CME associated with the filament eruption on 15 March 2015 was observed with the LASCO instrument (Brueckner et al., 1995). As reported in Wang et al. (2016), during the C2.6 class flare of 14 March 2015 a small filament erupted (see their Figure 1a, F4 filament) and there was a slow CME observed in the LASCO C2 field–of–view (FOV) at $\approx$ 13:30 UT. The speed and the angular width of this CME was 208 km s*-1* and 160*∘* respectively.

The F1 filament eruption on 15 March 2015 produced a halo CME, visible in the LASCO C2 FOV at 01:48 UT. The CME was visible up to 27 R*⊙* in the LASCO C3 FOV. The running difference of the C2 and C3 coronagraph images are shown in Figure \ireffig:cme. The white circle represents the solar disk occulted by the coronagraph. In the C2 images, the running difference of SDO/AIA 193 Å images are displayed inside the white circles for the same time. The red and yellow arrows indicate the leading edge of the CME in the LASCO C2 and C3 FOV respectively. The black arrow in the first image of the bottom panel points to the CME from the same active region on 14 March 2015. According to the LASCO Coordinated Data Analysis Workshop (CDAW) Catalog (Gopalswamy et al., 2009) the average CME speed was 719 km s*-1* and the acceleration was $-9.0$ m s*-2*. The mass and kinetic energy of the CME were 3.0$\times 10^{16}$ gram and 7.7 $\times 10^{31}$ ergs respectively. Moreover, Liu et al. (2015) reported the maximum CME speed was 1100 kms*-1*. In the C3 FOV the CMEs of 14 and 15 March 2015 interacted at 02:18 UT. Liu et al. (2015) considered the interaction of these CMEs as the cause of the strong geomagnetic storm of Solar Cycle 24 on 17 March 2015.

5 Decay Index Calculations

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decay

In order to find the reasons why the part F1 of the initial filament erupted after a 12 hr delay in an intermediate state, while the remainder of the filament did not leave its position despite the strong activation, we should analyze the structure of the magnetic field surrounding these parts of the filament. Since the stability of the flux-rope equilibrium depends on the value of the decay index, we need to know the distribution of this parameter in the active region. In principle, the decay index should be calculated for the coronal field external to the flux rope. We can consider the electric current of the flux rope as the major coronal current within the volume of interest, while the surrounding magnetic field is created by currents located below the photosphere. For this part of the coronal field, which is needed for decay index calculations, we can use a potential-field extrapolation of the photospheric field data.

We are interesting in the distribution of the potential magnetic field in the volume around the filament, which is much less than the size of the solar sphere. The bottom boundary of this domain is a part of the photosphere only slightly deviating from the shape of a flat surface. We cut a rectangular area of the photospheric magnetogram below the filament and use it as the boundary condition for the solution of the boundary-value problem in terms of Green’s functions (Filippov and Den, 2001; Filippov, 2013). Doing this we ignore the influence of sources that are located outside the chosen area. In many cases it can be reasonable.

In our case the active region NOAA AR 12297 is the strongest magnetic source on the disk and is rather distant from other active regions. On March 14 and especially on March 15 the active region is at a considerable distance from the central meridian, so we need to take into account the projection effect.

Figure 5a represents the modified fragment of the magnetogram taken by the HMI on 14 March 2015 at 15:00 UT, which is used as a boundary condition for the potential magnetic field calculations. The pixel size in HMI magnetograms is 0.5*′′* or 0.36 Mm, which is very small compared with the expected height of a filament $\textgreater$ 10 Mm. To save computational time we apply binning several times and increase the pixel size to $\approx$ 10 Mm. Figure 5b–f shows the distribution of the decay index

[TABLE]

where B${}_{\textnormal{t}}$ is the horizontal magnetic-field component and h is the height above the photosphere, at different heights above the area shown in the panel (a). The thin lines show isocontours of $\it n$ = 0.5, 1, 1.5, while the thick red lines indicate the positions of PILs at respective heights. Areas where $\it n$ $\textgreater$ 1 are tinted with grey, while regions with n $\textless$ 1 are white. Green contours show the position of the filament taken from the co-aligned Kanzelhoehe H$\alpha$ filtergram transformed in the same way as the magnetogram (Figure \ireffig:decay_hal1). Note that all panels (b)–(f) represent the 2D plots viewed from the normal-to-the-surface direction. Since the filaments are located at some unknown heights (we will consider this problem below) above this surface and the surface is inclined to the line-of-sight, the position of the filament contours does not correspond exactly to the position of magnetic features at any height (the filaments should be somewhat shifted to the north-west in this projection). However, the filament contours show approximately the places of our interest.

A PIL is a favorable place for horizontal equilibrium of a flux rope, because the vertical component of the coronal field vanishes. Any PIL at any height can be considered as a potential location of the flux rope, but it is only a necessary condition. Another necessary (but again not sufficient) condition for stable equilibrium is that the decay index is below the critical value. In fact, flux ropes may be found only in few places where both conditions are fulfilled. In Figure \ireffig:decay, the segments of PILs within white areas (or at least outside of isocontours 1.5) are the places favorable for the occurrence of a stable flux rope. Below 60 Mm (Figure \ireffig:decayc) the segments of the PIL near both green contours are suitable for stable flux ropes. The contour $\it n$ = 1 touches the PIL near both filaments at the height of 75 Mm (Figure \ireffig:decayd), while the contour $\it n$ = 1.5 touches the PIL near the southern filament at the height of 100 Mm (Figure \ireffig:decaye) and near the western filament at the height of 120 Mm (Figure \ireffig:decayf).

Unfortunately, we cannot measure directly the height of the filaments because STEREO is in an unfavorable position. However, we can estimate the heights using the method proposed by Filippov (2016b). It is based on the (confirmed by observations) assumption that the material of filaments is accumulated near coronal magnetic neutral surfaces Br = 0 (Filippov, 2016a). It was found also that the potential approximation for coronal magnetic fields is sufficient for the filament height estimations. Comparison of the 3D shape of the neutral surface, represented in the projection on the plane of the sky as a set of PILs, with the filament shape and position allows us to obtain information about the heights of different parts of the filament including its top, or spine, which is the most reliable indicator of the flux-rope axis.

Figure \ireffig:decay_hal1 shows the fragment of the Kanzelhoehe H$\alpha$ filtergram of the same region as in Figure \ireffig:decay co-aligned with the magnetogram and transformed in the same way. The same PILs as in Figure \ireffig:decayb–f are shown but every PIL is shifted in $\it x$ and $\it y$ coordinates by values

[TABLE]

and

[TABLE]

where $\it h$ is the height of the PIL, $\lambda_{0}$ and $\varphi_{0}$ are the longitude and latitude of the selected area center. Thus they are projected on the plane of the sky in the same way as the filament in the on-disk filtergram. The lowest PIL at the height of 6 Mm is red, while the other is blue. The spine of the western filament follows exactly the PIL at the height of 30 Mm. All of the filament body is located between this line and the red line at the height of 6 Mm. The southern filament does not so strictly follow any PIL, however, its spine is most likely a little bit above the PIL at the height of 78 Mm. For comparison Figure 7 shows the filament and the neutral surface on 14 March at 11 UT before the separation into two parts. The spine of the western section of the filament also follows exactly the PIL at the height of 30 Mm, while the eastern section seems to be higher. The top of the wide part of the eastern section touches the PIL at the height of 54 Mm and the thin thread-like continuation of the spine crosses all PILs.

Returning to Figure \ireffig:decay we establish that the western section of the filament before the separation and the western filament after the separation are relatively low (30 Mm) and are located in the zone of stability within the coronal magnetic field. The eastern section of the filament is less stable because on the one hand it is higher and on the other hand the decay index in this area is also higher. That is why, possibly, the disturbance coming from inner parts of the active region leads to the partial and failed eruption of the eastern section of the filament, which results in the separation of the filament into two parts. The erupted eastern section of the filament obviously finds a new equilibrium position at a greater height. In the new position of the eastern section, this height (about 80 Mm), now considered as the southern filament F1, is within the zone of stability for the decay index threshold $\it n$c = 1.5 and on the edge of stability for the decay index threshold $\it n$c = 1. The next disturbance from the active region easily causes the start of the eruption of the southern filament and this eruption is full because there is no a zone of stability at heights above 100 Mm. So, the eastern section of the filament shows a two–step eruption with a metastable state at a height of 80 Mm for 12 hrs. Possibly it could stay there longer if the strong disturbance did not come from inner parts of the active region. The western filament is deep within the zone of stability and therefore it did not erupt despite the strong activation by the energetic disturbance.

6 Discussion and Conclusion

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dicussion

In this paper, we have presented the two–step filament eruption of 14–15 March 2015 using observations from AIA onboard the SDO satellite and ground–based GONG and Kanzelhoehe Solar Observatory H$\alpha$ data. Our main results are as follows:

• •

The initiation of the filament eruption on 14 March 2015 and its full eruption on 15 March 2015 are associated with the jets in the active region.

• •

The decay index calculation suggests that on 14 March 2015 the filament first enters into the instability zone and after reaching some height it finds itself in the stability zone. Again on 15 March 2015 the filament enters into the instability zone and finally it erupts.

• •

The major part of filament which had not been destroyed on 14 March 2015 was activated on March 15 but could not erupt. Therefore it was a failed eruption. The coronal magnetic field calculation evidences that the decay index at the filament location is below the threshold of the torus instability and hence the filament fails to erupt.

• •

The observation of the same sign of the twist/helicity in the chromosphere, higher solar atmosphere and in the magnetic cloud evidence the conservation property of the helicity.

We find that a big filament located at the periphery of a strong active region undergoes a complicated partial and two-step eruption. The idea of two-step energy release processes came from analyses of two-peak EUV light-curves of some flares (Woods et al., 2011; Su et al., 2012) suggesting that two peaks in light-curves appear due to two stages of a single event associated with the delayed eruption of a CME. Woods et al. (2011) and Su et al. (2012) presented AIA EUV observations of the limb 8 March 2011 event in which a flux rope accelerated in the first stage up to 120 km s*-1*, then the speed decreased to 14 km s*-1*, and in the second stage, started after 2 hrs after the beginning of the event, it accelerated again and became the CME with a speed of $\approx$ 500 km s*-1*. Byrne et al. (2014) also analyzed this event and suggested that either the kink-instability or the torus-instability of the flux rope was the likeliest scenario. Since the event was at the limb and photospheric magnetic-field data were not available for this time, the authors did not make strong conclusions about the magnetic configuration and were not very certain about the supposed torus instability without calculation of the decay index. Gosain et al. (2016) studied a two-step eruption of a quiescent filament on 22 October 2011. It was observed from different viewpoints by SDO, SOHO, and STEREO. The CME associated with the filament eruption and two bright ribbons in the chromosphere both appeared 15 hrs after the start of the event. Computation of the decay index showed that there were zones of stability and instability that alternated in the corona. Below 100 Mm the equilibrium was stable, then the zone of instability followed from 100 to 500 Mm and gave place to a zone of stability again. Above a height of 600 Mm the PIL disappeared, which hinted at the possibility for the flux rope to lose the horizontal equilibrium and erupt. These results showed the possible scenario of the two-step eruption confirmed by observations and calculations. However, the flux rope was not clearly observed in the intermediate position and the magnetic field calculations at great heights, above 400 Mm, were not too reliable.

The event on 14–15 March 2015 we analyze in this paper happens when the initial filament is in positon favorable for observations somewhere between the central meridian and the limb. This allowes us to have reliable photospheric magnetic-field data and to observe the ascending trajectory of the eruptive filament. The disadvantage is the absence of STEREO observations from another point of view, but we use the rather reliable method of measuring of the filament spine height on the disk. Our calculations of the decay index of the coronal magnetic field show that after the first loss of equilibrium a part of the filament finds itself within the zone of stability, but not far from the threshold of instability. The strong disturbance that comes from the inner parts of the active region force the filament to enter into the second step of the eruption.

Wang et al. (2016) studied the filament eruption on 15 March 2015 as the source of the strong geomagnetic storm of Solar Cycle 24. They analyzed the second step of the eruption because it was this event that produced the fast CME that together with another CME started 12 hrs earlier drove the geomagnetic storm. They calculated the decay index $\it n$ in the region using the potential-field source-surface (PFSS) model. They found that n reached the critical value 1.5 for the onset of the torus instability at a height of approximately 118 Mm and concluded that the strapping field was strong enough to prevent any eruption of both the southern and western filaments. If their decay index calculation is averaged over the whole active region it is similar to our result shown in Figure \ireffig:decayf. They related the abrupt acceleration of the southern filament around 01:15 UT to the passage of the filament into the region with open magnetic field, which did not further confine the filament. However, it is difficult to derive the true location of the filament rather high in the corona from images in only one projection.

In our study, we perform the analysis of the filament first-step activation on March 14 and the second step eruption on March 15. We explain this as follows, propogating a scenario based on more accurate magnetic field calculations. Our conclusions are based on the detailed distribution of the decay index over the active region. We define the critical height from values of the decay index in the places where the filament could be located and is really located. The distribution of the decay index provides an opportunity for the two-step eruption. The estimated heights of the filaments show that the western filament is within the zone of stability during all times of observation. That is why it keeps its position despite the strong disturbance and intensive internal motions. The southern filament is close to the threshold of stability during all time before the abrupt acceleration in the second step. Very likely the eastern part of the initial filament becomes slightly unstable at the beginning of the first step. It moves rather slowly in the direction of the zone of stability and is able to find a new position for stable equilibrium there. However, it is also close to the threshold of stability and the next disturbance from the active region causes the full eruption.

Acknowledgments

We thank the anonymous referee for the valuable comments and suggestions. We acknowledge the use of SDO and GONG, and the Kanzelhoehe Solar Observatory data. RC acknowledges the support from SERB–DST project no. SERB/F/7455/ 2017-17. RJ thanks the Department of Science and Technology (DST), Government of India for an INSPIRE fellowship. BS wants to thank the team of the ISSI workshop managed by Nicolas Labrosse on “Nature of prominences” in Bern for fruitful discussion on this event.

Disclosure of Potential Conflicts of Interest The authors declare that they have no conflicts of interest.