# Confined Flares in Solar Active Region 12192 from 2014 October 18 to 29

Huadong Chen11affiliation: Key Laboratory of Solar Activity, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
, Jun Zhang11affiliation: Key Laboratory of Solar Activity, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
, Suli Ma22affiliation: College of Science, China University of Petroleum,
Qingdao 266580, China , Shuhong Yang11affiliation: Key Laboratory of Solar
Activity, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100012, China , Leping Li11affiliation: Key Laboratory of Solar
Activity, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100012, China , Xin Huang11affiliation: Key Laboratory of Solar
Activity, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100012, China , Junmin Xiao11affiliation: Key Laboratory of Solar
Activity, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100012, China<EMAIL_ADDRESS>
###### Abstract

Using the observations from the Atmospheric Imaging Assembly (AIA) and
Helioseismic and Magnetic Imager (HMI) aboard the $Solar\ Dynamics\
Observatory$ ($SDO$), we investigate six X-class and twenty-nine M-class
flares occurring in solar active region (AR) 12192 from October 18 to 29.
Among them, thirty (including six X- and twenty-four M-class) flares
originated from the AR core and the other five M-flares appeared at the AR
periphery. Four of the X-flares exhibited similar flaring structures,
indicating they were homologous flares with analogous triggering mechanism.
The possible scenario is: photospheric motions of emerged magnetic fluxes lead
to shearing of the associated coronal magnetic field, which then yields a
tether-cutting favorable configuration. Among the five periphery M-flares,
four were associated with jet activities. The HMI vertical magnetic field data
show that the photospheric fluxes of opposite magnetic polarities emerged,
converged and canceled with each other at the footpoints of the jets before
the flares. Only one M-flare from the AR periphery was followed by a coronal
mass ejection (CME). From October 20 to 26, the mean decay index of the
horizontal background field within the height range of 40–105 Mm is below the
typical threshold for torus instability onset. This suggests that a strong
confinement from the overlying magnetic field might be responsible for the
poor CME production of AR 12192.

Sun: activity — Sun: coronal mass ejections (CMEs) — Sun: flares — Sun: UV
radiation

##  1 Introduction

As the main sources of solar intense eruptions, including filament eruptions,
major flares, and coronal mass ejections (CMEs), active regions (ARs) have
been extensively explored (e.g., Hagyard et al., 1984; Wang, 1994; Zhang et
al., 2012). Strong flares tend to occur near the prime magnetic polarity
inversion lines (PILs) of ARs where the field gradients are steep and the
horizontal components are highly sheared (e.g., Wang et al., 2002; Deng et
al., 2006; van Driel-Gesztelyi & Culhane, 2009). In many previous works (e.g.,
Wang, 1994; Schrijver et al., 2005; Zhang et al., 2007; Sun et al., 2012),
shear and emergence of magnetic flux were suggested to be an important way to
store the non-potential energy in the coronal field of ARs, which might be
released in the subsequent eruption.

Magnetic reconnection in destabilization processes is considered as a possible
mechanism to trigger solar eruptions (Vršnak, 2008). In the tether-cutting
(TC) model (Moore et al., 2001), the reconnection between the inner legs of
the sheared core field would lead to an unbalanced situation between the
upward magnetic pressure force and downward magnetic tension force. This may
drive the reconnected field connecting the far ends of the core field and the
envelop field to expand outward. Then, another reconnection occurs below the
expanding field and further speeds up the eruption to form the CME (e.g.,
Amari et al., 2014; Chen et al., 2014). Sometimes, the inflating field stops
when reaching a certain height and no obvious CME would be observed in the
wake of the eruption (e.g., Ji et al., 2003). The related flares are called
confined flares (e.g., Wang & Zhang, 2007).

Strong confinement from the overlying magnetic arcades is believed to play an
important role in the failed eruptions (e.g., Török & Kliem, 2005; Guo et al.,
2010; Shen et al., 2011; Netzel et al., 2012; Chen et al., 2013). To
characterize how fast the overlying magnetic field decays, a decay index is
usually defined as $n$ = –$d$ log($B_{h}$)/$d$ log($H$). Here, $B_{h}$ denotes
the horizontal component of the potential field strength; $H$ is the height
above the solar surface. In some earlier studies (Bateman, 1978; Kliem &
Török, 2006; Fan & Gibson, 2007; Aulanier et al., 2010), a typical threshold
of $n$ for torus instability initiation was suggested to be in the range [1.5,
2.0]. When $n$ reaches a larger value at the height of the erupting flux rope,
torus instability would lead to a full eruption of the system.

AR 12192 recently attracted considerable attention (e.g., Thalmann et al.,
2015; Sun et al., 2015) for its large sunspot group and high flare
productivity. According to the $GOES$ observations, while AR 12192 passed
across the visible solar disk, it produced six X-class and twenty-nine M-class
flares from October 18 to 29. However, it is surprising that only one M-flare
was associated with a CME. The data from the Atmospheric Imaging
Assembly/$Solar\ Dynamic\ Observatory$ (AIA/$SDO$; Lemen et al., 2012) show
that some of the flares had similar origin within the AR and common spatial
and timing characters, implying they were homologous flares with analogous
triggering mechanism (e.g., Sui et al., 2004; Yang et al., 2014). To probe the
initiation mechanisms of these homologous flares and causes of the low CME-
association of the major flares, we examined the evolution of the photospheric
magnetic fluxes, the major flares (M- and X-class), and the background
potential field of this AR.

##  2 Data and Observations

The Helioseismic and Magnetic Imager (HMI; Schou et al., 2012) on $\it{SDO}$
produces photospheric vector magnetograms with $\sim$0.$\arcsec$5 plate scale
at 12 minutes cadence (Hoeksema et al., 2014). In the present study, we used
de-projected maps in cylindrical equal area coordinates of the automatically
identified AR (Bobra et al., 2014). The vertical magnetic field component (Bz)
was utilized for the flux estimation and as the lower boundary condition for
potential field modeling. The HMI Bz data show significant errors, especially
in the negative-polarity umbra of the following sunspot. We used an
interpolation method to replace the defective data with fitting values.
According to our calculations, the maximum difference between the fluxes from
the original and corrected data is only $\sim$2%, which does not affect our
conclusions. To better show the similarities of the homologous flares, we de-
rotated the AIA data for four X-flares (XF2–XF5; see Table 1) to the same time
(October 23 15:00 UT).

##  3 Results

###  3.1 Statistics of the Major Flares

The related information of the six X-flares (XF1–XF6) and twenty-nine M-flares
(MF1–MF29) are listed in Table 1. The mean duration (from the start to end
time based on $GOES$ SXR event list111http://hesperia.gsfc.nasa.gov/goes/goes-
event-listings/) of the X-flares is $\sim$69 minutes, which is longer than
that ($\sim$32 minutes) of the M-flares. By checking the AIA data, we find
that not all the flares originated from the AR core. Five M-flares appeared at
two locations (L1 and L2; see Figures 1(a) and (d)) on the AR periphery. MF4
and MF7 occurred at L1; MF11, MF20, and MF25 took place at L2. Among the
thirty-five flares, only MF11 produced a CME. Jet activities were observed in
the four periphery flares MF4, MF7, MF11, and MF20.

###  3.2 Photospheric Magnetic Field Evolution

The HMI Bz maps in Figures 1(a)–(f) present the general evolution of AR 12192
from October 21 to 26. We notice that three pairs of magnetic fluxes (labeled
with “N1P1”, “N2P2”, and “N3P3” in Figure 1) appeared in the AR core. In the
AIA 94 Å image (see Figure 3(d)), it can be seen that some coronal loops
connected N1 (N3) and P1 (P3). The HMI vector magnetic field data (Figure
1(g)) also reveals the connectivity between N2 and P2. Figure 1 shows that the
negative and positive fluxes of N1P1 and N3P3 were respectively located at two
sides of the AR prime PIL. As the AR developed, P1 and P3 moved southwest
along the direction approximately parallel to the AR prime PIL and gradually
decayed. It is apparent that this kind of shearing motions of photospheric
fluxes would result in the shear formation and strengthening of the coronal
field in the AR. In Figure 1(g), we also see that the horizontal field in the
AR core were basically aligned with the AR prime PIL. Different from N1P1 and
N3P3, N2P2 appeared near the prime following sunspot of the AR. During its
emergence, it collided and partly canceled out with the ambient magnetic
field.

###  3.3 Jets Associated with the Flares

Four jets occurred from L1 and L2. Using the AIA 304 Å filtergrams, we display
the four jets and their accompanying flares in Figures 2(a)–(c) (MF4, MF7, and
MF20, respectively) and Figures 3(a)–(c) (MF11). In the AIA 171 Å channel (see
animation 2), both bright and dark features were observed along the open field
or the legs of large-scale coronal loops to form the jets. The maximum
projected lengths of the four jets are $\sim$282, $\sim$281, $\sim$130, and
$>$569 Mm (beyond the FOV of AIA), respectively; their respective mean
velocities (the maximum projected lengths divided by the corresponding
durations) are 361$\pm$1, 360$\pm$3, 309$\pm$6, and 379$\pm$3 km s-1; and they
separately have lifetimes of $\sim$46, $\sim$61, $\sim$74, and $\sim$172
minutes. Compared to the surges or jets studied by Chen et al. (2008), which
also occurred at the AR border but with microflares, the speeds, spatial
scales, and lifetimes found here are evidently greater. The HMI Bz data
clearly show that the magnetic fluxes of different polarities emerged,
converged, and canceled with each other at the base of the jets before the
associated flares. Similar results were also found in earlier studies (e.g.,
Jiang et al., 2007; Chen et al., 2008).

MF11 is the only one followed by a CME, for which
$CACTus$222http://sidc.be/cactus lists a median velocity of $\sim$496 km s-1.
From Figure 3(a), we can see that a small arch filament existed at the flare
source region before the onset of MF11. As the flare occurred, the hot plasma
was ejected southwest at first (as shown by the curved arrows in Figures 3(b)
and (c)) and then spurted out southeast more radially (as indicated by the
straight arrow in Figure 3(c)). The 171 Å filtergrams (see animation 4)
clearly reveal that the ejected plasma moved along one leg of a large-scale
loop at the beginning and then turned to the ambient open field. According to
our measurement, the projected deflection angle of the ejection direction is
$\sim$40$\arcdeg$. After MF11, the arch filament disappeared, indicating its
participation in the ejection. According to Moore et al. (2010), this jet is
very likely a blowout jet, in which the small arch filament underwent a
miniature version of a blowout eruption and produced the subsequent CME (e.g.,
Hong et al., 2011; Pucci et al., 2013).

###  3.4 Tether-cutting Reconnection Triggering the Homologous Confined Flares

Among the thirty flares from the AR core, we mainly focused on the four on-
disk X-flares (XF2–XF5). These flares exhibited similar flaring structures
(see the animation 3), indicating they are likely homologous flares. Coronal
emission associated to three of the homologous flares (XF2–XF4) are shown in
Figures 2(d)–(f) and Figures 2(g)–(i), respectively. The AIA 1600 Å images
clearly display their two-ribbon structure (FR1 and FR2), which show great
similarities concerning spatial distribution and morphology. In comparison
with XF2, the northeastern ends of FR1 in XF3 and XF4 turned to north to
extend, which might be related to the newly emerged N2P2. In the 94 Å images,
sensing hot flare plasma at a characteristic temperature of 6.3 MK, bright
(flare) loops (their apparent projected shape indicated by the dotted lines in
Figures 2(g)-(i)) connecting FR1 and FR2 suggest a complex, non-potential
field geometry, which are different from the usual post-flare loops in the
eruptive flares. This implies that only a little portion of the non-potential
energy was released during these confined flares, which is consistent with the
model results reported by Thalmann et al. (2015) and Sun et al. (2015).

It is very likely that TC reconnection triggered these homologous flares. As
an example, we display the evolution of XF3 in Figures 3(d)–(f) and Figures
3(g)–(i), which correspond to the 94 Å and 304 Å images respectively. In 94 Å,
it can be seen that some sheared magnetic arcades existed in the AR core prior
to the flare. We outline two sheared loop systems (“AB” and “CD”) in Figure
3(d). Figure 1(d) shows the locations of their ends in the photosphere. It is
evident that AB and CD straddled the AR prime PIL and connected the opposite-
polarity field on the two sides. As the flare started and developed, AB
reconnected with CD, which led to the formations of the small flaring loop BC
(Figure 3(e)) and large-scale loop structure AD (Figure 3(f)). Meanwhile, a
jet along CB was also observed not only in the hot 94 Å line (Figure 3(e)) but
also in the cool 304 Å channel (Figure 3(h)), which provides the evidence of
magnetic reconnection. Figure 3(f) shows that the post-flare loops still
retained a highly-sheared topological structure, which made possible the next
homologous energy release. In Figure 3(g), some filament fibrils were almost
aligned with the AR PIL before the flare. However, the detailed 304 Å data
reveal that these fibrils were not affected by the eruption, suggesting a
relatively-high reconnection site in the flare. This is in agreement with what
was suggested by Thalmann et al. (2015), based on the large initial separation
of the associated flare ribbons. Our results strongly support the TC
reconnection mechanism. In addition, the newly emerging flux tubes
reconnecting with pre-existing coronal loops may also play a role as the
enhanced emission of the loops nearby N2P2 was detected before the flare (see
animation 5).

###  3.5 Strong Confinement from the Overlying Background Field

One outstanding feature of AR 12192 is its poor CME production rate, despite
the many major flares observed during its disk passage. According to the
previous studies (e.g., Fan & Gibson, 2007), the confinement from the
overlying background field of AR may play an important role in these confined
flares. Utilizing the HMI Bz maps, the potential field extrapolation of AR
12192 is derived from the Green’s function method (Chiu & Hilton, 1977;
Metcalf et al., 2008). We calculate the decay index $n$ of the horizontal
extrapolated field Bh along a reference line (see Figure 1(c)), the
orientation of which is basically aligned with the AR prime PIL and changes
with the AR evolution. To determine the reference line in a certain Bz map, we
firstly obtain the positions of the maximum positive and negative fluxes.
Then, we connect them and plot the reference line with a fixed length through
the midpoint. The angle we chose between the reference line and connecting
line is 60$\arcdeg$. With this choice, the direction of the AR prime PIL is
outlined best in most of the cases.

Generally, $n$ varies with the height above the photosphere. By checking two
limb flare cases (MF1 and XF1), we find that the height ranges of the erupting
flare loops are respectively $\sim$47–115 Mm and $\sim$78–110 Mm, comparable
to the result of 42–105 Mm suggested by Liu (2008) and Xu et al. (2012). In
this study, we therefore calculate the mean values of $n$ for the height range
$\sim$40–105 Mm above the photosphere at every point along the reference line
firstly and then average them to derive the mean decay index $\overline{n}$,
the time variation of which is displayed in Figure 4(a). We only calculate
$\overline{n}$ from October 20 to 26, during which the longitude of the AR
center was within $\sim$E42–W46. It can be seen that all $\overline{n}$ is
always less than 1.5, the lower limit of the typical threshold for torus
instability onset (Kliem & Török, 2006; Liu, 2008). Even taking the
uncertainties into account, the maximum of $\overline{n}$ is $\sim$1.63 and
does not exceed the upper limit (2.0) of the threshold. From October 20 to 22,
$\overline{n}$ increases from $\sim$1.41 to $\sim$1.50 firstly and then keeps
stable for about 20 hr. After October 22 14:00 UT, $\overline{n}$ begins to
decline and finally reaches a value of $\sim$1.23 at the end of October 26. We
point out that different from previous studies (e.g., Liu, 2008; Xu et al.,
2012; Sun et al., 2015), we firstly calculate and analyze the time evolution
of the mean decay index of an AR horizontal background field during a long
period (7 days).

Figure 4(b) displays the time profiles of the positive (red pluses) and
unsigned negative (blue pluses) vertical fluxes of the whole AR during the
same period. From October 20 to 26, both the positive and unsigned negative
fluxes decrease at first and then are enhanced gradually, which seems to have
an inversed time evolution of $\overline{n}$. Since the background potential
field of AR might be strengthened (weakened) with the emergence (cancelation)
of the photospheric fluxes, this result seems reasonable. The similar
magnitude of the total positive and total unsigned negative flux also suggests
a relatively close coronal field structure of the AR.

Figures 4(c)–(f) show the height profiles of Bh about 1 hr before the start
(blue dashed line) and 1 hr after the end (red dotted line) of XF2–XF5,
respectively. The decay indices $n$ (averaged along the reference line)
derived from Bh are displayed by the green dashed (pre-flare) and purple
dotted (post-flare) curves in the four panels. The strength and height are in
logarithm units. It is apparent that there are little changes of Bh and $n$
during the flares. Correspondingly, the mean decay indices $\overline{n}$
before and after the flares are also similar (see the green and purple values
of $\overline{n}$ in Figures 4(c)–(f)). According to our results,
$\overline{n}$ are $\sim$1.47$\pm$0.14, $\sim$1.37$\pm$0.09,
$\sim$1.32$\pm$0.07, and $\sim$1.27$\pm$0.07 for the four confined X-flares
XF2–XF5, respectively. Within the uncertainty ranges, our results agree with
those of Sun et al. (2015).

##  4 Summary and Discussion

We made a statistics of six X-flares and twenty-nine M-flares in AR 12192 from
October 18 to 29 and performed a detailed investigation to four of the
X-flares and four of the M-flares. Our main results are as follows:

  1. 1.

From October 20 to 26, the background field of AR 12192 remained at a strong
level. The mean decay index $\overline{n}$ of the horizontal potential field
in a vertical plane aligned with the prime PIL and within the height range of
40–105 Mm varied in the range [1.23, 1.50], implying that a strong confinement
from the overlying magnetic field may play an important role in the poor CME
production of the AR. This is in agreement with the findings of Sun et al.
(2015) and Thalmann et al. (2015) for the individual cases XF3 and XF2,
respectively.

  2. 2.

Four periphery M-flares were accompanied by jets. The emergences and
cancelations of the photospheric fluxes with different magnetic polarities
were observed at the roots of the jets, supporting the standard model for
solar coronal jets (e.g., Moore et al., 2010; Chen et al., 2012; Pariat et
al., 2015).

  3. 3.

In HMI Bz maps, the apparent shearing motions of emerged photospheric fluxes
were found in the AR core. This might have established a coronal field
configuration suitable for TC reconnection, which was observed in four
homologous confined X-flares. These observations are well consistent with the
TC model described in Moore et al. (2001).

TC reconnection is a possible way to trigger solar eruptions (e.g., Liu et
al., 2010; Sterling et al., 2011; Amari et al., 2014). Chen et al. (2014)
exhibited a detailed process of TC reconnection during a major event, which
was followed by a halo CME. However, as reported here, CME would not always
appear in the eruptions triggered by TC reconnection (Aulanier et al., 2010).
Several similar observational cases with weak flares have been discussed in
Moore et al. (2001) and Chen et al. (2014). To our knowledge, we firstly
report that successive strong X-flares were triggered by TC reconnection, but
not yielded any partial or full eruptions.

The $SDO$ data are courtesy of NASA, the $SDO$/HMI and AIA science teams. This
work was supported by NSFC (41204124, 11221063, 11203037, and 41331068), the
Project Funded by China Postdoctoral Science Foundation (2015M571126), the
National Basic Research Program of China under grant G2011CB811403, and the
Strategic Priority Research Program—The Emergence of Cosmological Structures
of the Chinese Academy of Sciences (No. XDB09000000).

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Table 1: X- and M-class flares in Solar AR 12192  Event | Date | Start Time | Peak Time | Duration | $\it{GOES}$ | Location | CME | Other
---|---|---|---|---|---|---|---|---
|  | (UT) | (UT) | (minutes) | Level | in AR | Production | Activities
X-class Flares:
XF1 | 19-Oct-2014 | 04:17 | 05:03 | 91 | X1.1 | core | No |
XF2 | 22-Oct-2014 | 14:02 | 14:28 | 48 | X1.6 | core | No |
XF3 | 24-Oct-2014 | 21:07 | 21:41 | 66 | X3.1 | core | No |
XF4 | 25-Oct-2014 | 16:55 | 17:08 | 76 | X1.0 | core | No |
XF5 | 26-Oct-2014 | 10:04 | 10:56 | 74 | X2.0 | core | No |
XF6 | 27-Oct-2014 | 14:12 | 14:47 | 57 | X2.0 | core | No |
M-class Flares:
MF1 | 18-Oct-2014 | 07:02 | 07:58 | 107 | M1.6 | core | No |
MF2 | 20-Oct-2014 | 09:00 | 09:11 | 20 | M3.9 | core | No |
MF3 | 20-Oct-2014 | 16:00 | 16:37 | 55 | M4.5 | core | No |
MF4 | 20-Oct-2014 | 18:55 | 19:02 | 9 | M1.4 | periphery (L1aaMarked by the yellow circle in Figure 1(a).) | No | jet
MF5 | 20-Oct-2014 | 19:53 | 20:04 | 20 | M1.7 | core | No |
MF6 | 20-Oct-2014 | 22:43 | 22:55 | 30 | M1.2 | core | No |
MF7 | 21-Oct-2014 | 13:35 | 13:38 | 5 | M1.2 | periphery (L1) | No | jet
MF8 | 22-Oct-2014 | 01:16 | 01:59 | 72 | M8.7 | core | No |
MF9 | 22-Oct-2014 | 05:11 | 05:17 | 10 | M2.7 | core | No |
MF10 | 23-Oct-2014 | 09:44 | 09:50 | 12 | M1.1 | core | No |
MF11 | 24-Oct-2014 | 07:37 | 07:48 | 16 | M4.0 | periphery (L2bbMarked by the yellow circle in Figure 1(d).) | Yes | jet
MF12 | 26-Oct-2014 | 17:08 | 17:17 | 22 | M1.0 | core | No |
MF13 | 26-Oct-2014 | 18:07 | 18:15 | 13 | M4.2 | core | No |
MF14 | 26-Oct-2014 | 18:43 | 18:49 | 13 | M1.9 | core | No |
MF15 | 26-Oct-2014 | 19:59 | 20:21 | 46 | M2.4 | core | No |
MF16 | 27-Oct-2014 | 00:06 | 00:34 | 38 | M7.1 | core | No |
MF17 | 27-Oct-2014 | 01:44 | 02:02 | 27 | M1.0 | core | No |
MF18 | 27-Oct-2014 | 03:35 | 03:41 | 13 | M1.3 | core | No |
MF19 | 27-Oct-2014 | 09:59 | 10:09 | 27 | M6.7 | core | No |
MF20 | 27-Oct-2014 | 17:33 | 17:40 | 14 | M1.4 | periphery (L2) | No | jet
MF21 | 28-Oct-2014 | 02:15 | 02:42 | 53 | M3.4 | core | No |
MF22 | 28-Oct-2014 | 03:23 | 03:32 | 18 | M6.6 | core | No |
MF23 | 28-Oct-2014 | 13:54 | 14:06 | 29 | M1.6 | core | No |
MF24 | 29-Oct-2014 | 06:03 | 08:20 | 169ccThe unorthodoxly long duration is due to multiple energy releases. | M1.0 | core | No |
MF25 | 29-Oct-2014 | 09:54 | 10:01 | 12 | M1.2 | periphery (L2) | No |
MF26 | 29-Oct-2014 | 14:24 | 14:33 | 27 | M1.4 | core | No |
MF27 | 29-Oct-2014 | 16:06 | 16:20 | 27 | M1.0 | core | No |
MF28 | 29-Oct-2014 | 18:47 | 18:50 | 5 | M1.3 | core | No |
MF29 | 29-Oct-2014 | 21:18 | 21:22 | 7 | M2.3 | core | No |
Figure 1: ((a)–(f)) HMI Bz maps (also see the animation 1); (g) HMI vector
magnetic field map. The blue thick arrows in panels (a) and (b) indicate the
shearing motions of the fluxes P1 and P3. The yellow thin arrow in panel (b)
points to the location of P2. The yellow, blue and red pluses in panel (c)
correspond to the locations of the maximum negative flux, maximum positive
flux, and their midpoint, respectively. The red line in panel (c) is the
reference line along which we calculated the decay index $n$. The circles in
panels (a) and (d) mark the two locations L1 and L2, respectively. The dashed
box in panel (d) indicates the FOV of panel (g). The green and blue curves in
panel (g) indicate the principal shape of the flare ribbons around the peak
time of XF3.  Figure 2: ((a)–(c)) AIA 304 Å images showing the jets associated
with MF4, MF7 and MF11, respectively (also see the animation 2); ((d)–(f)) AIA
1600 Å and ((g)–(i)) AIA 94 Å images displaying the flaring structures of XF2,
XF3, and XF4, respectively (also see the animation 3). The turquoise arrows in
panels (e) and (f) indicate the northward extension of FR1 in XF3 and XF4. The
red dotted curves in panels (g)–(i) outline some apparently sheared and non-
potential flare loops during XF2, XF3, and XF4.  Figure 3: ((a)–(c)) AIA 304 Å
images showing the blowout jet in MF11 (also see the animation 4); The dotted
arrows in panels (b) and (c) indicate the directions of the plasma ejection in
the jet. ((d)–(f)) AIA 94 Å and ((g)–(i)) AIA 304 Å images display the
evolution of XF3 (also see the animation 5).  Figure 4: (a) Time variations of
the mean decay index $\overline{n}$ (plus) with 1$\sigma$ uncertainty (shaded
line) and $\it{GOES}$ soft X-ray (SXR) flux (curve); (b) time profiles of the
positive (red plus) and unsigned negative (blue plus) vertical fluxes of AR
12192; ((c)–(f)) height profiles of Bh with 1$\sigma$ error bars before (blue
dashed line) and after (red dotted line) XF2–XF5; height variations of decay
index $n$ with 1$\sigma$ error bars before (green solid line) and after
(purple dotted line) the four X-flares. Horizontal dotted lines in panels (a)
and (c)–(f) indicate the lower limit ($n$ = 1.5) of the threshold for torus
instability onset. The vertical lines in panel (b) indicate the start times of
XF2–XF5. The orange regions in panels (c)–(f) mark the height range of 40–105
Mm.