is why it kept its position despite the strong disturbance and intensive
internal motions. The southern filament was 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 was also close to the threshold of stability
and the next disturbance (jet) from the AR causes the full eruption. In this
way, a small jet disturbed and triggered the filament to form a complete
eruption. Afterwards the filament follows a CME and becomes the largest
geomagnetic storm of solar cycle 24. In the second case study, a
multi–viewpoint and multi–wavelength analysis of an atypical solar jet based
on the data from SDO, STEREO, and SOHO/LASCO coronagraphs is done. It is
usually believed that the CMEs are developed from the large scale solar
eruptions in the lower atmosphere. However, the kinematical and spatial
evolution of the jet on 2013 April 28 guide us that a jet was clearly
associated with a narrow CME having a width of about 25∘, with an approximate
speed of 450 km s-1. Even the jet speed was lower than the escape speed at the
solar surface, we observed the clear CME associated with the jet by all the
space-borne coronagraphs. The possible mechanism for the jet continuously
accelerating to reach the escape speed and form the narrow CME was that the
falling back material made the upward material of the jet moving faster to
keep the momentum of the whole jet conserved. We concluded that the observed
speed of the CME was containing the speed of the CME center and the expansion
speed, and was much larger than the jet speed, because the different parts of
the erupting structures were being measured. The speed of CME center (the
trajectory followed by the jet) was 220 km s-1 and was equivalent to the speed
of the jet (200 km s-1). This provides a clear view of the jet-CME
association. To better understand the link between the jet and the CME, the
coronal potential field extrapolation was done from the line of sight
magnetogram of the AR. The extrapolations present that the jet eruption
follows exactly the same path of the open magnetic field lines from the source
region which provides the route for the jet material to escape from the solar
surface towards the outer corona. These studies of large scale eruptions
caused by the solar jets gives worth evidence that some jets can escape from
the solar disk towards the solar corona to form a CME, which may contribute to
the solar wind acceleration.

The solar jet study in chapter 5 concerns with the multi wavelength
observations of a jet and mini flare occurring in the AR 12736 around 02:04 UT
on March 22, 2019 (Joshi2020FR). Usually jets contain the hot and cool ejected
plasma that is denser than the solar corona. This chapter explains, how the
twist was injected into a jet, with the AIA, HMI, IRIS observations and
comparison with the MHD simulation of Aulanier2005OHM; Aulanier2005. The IRIS
slit positions were located exactly at the reconnection location and the
nature of the jet reconnection site is characterised using them. The magnetic
history of the AR is followed based on the analysis of the HMI vector magnetic
field computed with the UNNOFIT code. We found that, this AR is the result of
the collapse of two emerging magnetic flux regions overlaid by arch filament
systems. In the magnetic field maps, the evidence suggests a pattern of the
long sigmoidal flux rope along the polarity inversion line between the two
emerging magnetic flux regions, which is the site of the reconnection. Before
the jet, an extension of the FR was present and a part of it was detached and
formed a small bipole with a bald patch region, which dynamically became an
‘X’-current sheet over the dome of one emerging flux region where the
reconnection took place. A comparison with numerical MHD simulations confirms
the existence of the long FR. The cool material follows different paths than
the hot and acts as a wall in front of the hot jet. It resembles the surges
that accompany jets in the MHD simulations. Mini flares in this AR were
observed frequently changing the connectivity at this interface region from a
bald patch region to a current sheet region and vice-versa. The main bipole
was the result of collision between two emerging fluxes. The negative polarity
was sliding, extending towards the South creating a small bipole and cancelled
with the positive polarity. We did not make a non linear force free field
magnetic extrapolation, but preferred to use directly the horizontal vector
magnetic field (vec B) observations to relate the small bipole and the BP to
the origin of the jet (both positioned at the same place). We compared the
observed magnetic field pattern and the values of the electric current density
Jz with synthetic Jz and vec B data from the MHD model of FR (Aulanier2010;
Zuccarello2015) to infer the location of FR. Our detailed observation analyses
suggest that the jet reconnection occurred in a bald patch current sheet and
in the rapidly formed above null point current sheet, driven by the moving
magnetic polarity that carried twist from the remote flux rope and injected it
into the jet. The initial flux rope remains stable during the reconnection
process. We concluded that the reconnection site is heated at all the
temperatures and the hot jet is expelled towards the West side in twisted
field lines.

Chapter LABEL:c7 put on display the spectroscopic analysis of a miniflare and
the associated jet with the IRIS instrument with its high spatial and temporal
resolution, which brings exceptional plasma diagnostics of solar chromospheric
and coronal activity during magnetic reconnection (Joshi2020IRIS). A spatio-
temporal analysis of IRIS spectra observed in the spectral ranges of Mg II, C
II and Si IV ions are proceed and the Doppler velocities from Mg II lines are
computed by using a cloud model technique. Strong asymmetric Mg II and C II
line profiles with extended blue wings observed at the reconnection site are
interpreted by the presence of two chromospheric temperature clouds, one
explosive cloud with blueshifts at 290 km s-1 and one cloud with smaller
Dopplershift (around 36 km s-1). We used the cloud model technique as a simple
diagnostics tool for velocity calculations. Such models are used to derive
true velocities which usually differ from those obtained from Doppler shifts,
and this is the basic idea behind the cloud model. Simultaneously at the same
location (jet base), strong emission of several transition region lines (O IV
and Si IV) and the emission of the Mg II triplet lines of the Balmer-continuum
are observed. Emission at the minimum temperature was detected with AIA 1600 Å
and 1700 Å filters and confirmed the low level heating. Mg II and C II lines
are good diagnostics for detecting plasma at chromospheric temperature (T $<$
20,000 K). We identified the bilateral outflows in the bald patches, and the
bald patch current sheet was transformed to an ‘X’-point current sheet during
the reconnection. The absorption of identified chromospheric lines in Si IV
broad profiles have observed and analysed. In fact Si IV profiles are striped
by absorption lines formed at photospheric temperatures and clearly show the
presence of cool plasma over transition region temperature material in the
reconnection site. This cool plasma is certainly due to the cool clouds,
either the ejected fast cloud feed by trapped material in bald patch or by
surge plasma. All this event is finally embedded in the corona. This
demonstrated the possibility of having successive layers in the atmosphere
with different velocities and temperatures in the current sheet region. With
such observations of IRIS line and continuum emission, we proposed a
stratification model for the white-light mini flare atmosphere with multiple
layers of different temperatures along the line of sight, in a reconnection
current sheet. It was an important result and for the first time that one
could quantify the fast speed (possibly Alfvénic flows) of cool clouds ejected
transverse to the jet direction by using the cloud model technique. It is
concluded that the plasma of ejected clouds could come from the trapped
region, where the cool material was stucked before reconnection between the
two emerging flux regions or be caused by a chromospheric-temperature (cool)
upflow during the magnetic reconnection.

##  Chapter 2 Solar flares and recurrent solar jets from AR NOAA 12035

###  2.1 Introduction

Solar flares are sudden and violent releases of magnetic energy in the solar
atmosphere and can be divided as eruptive flares, when plasma is ejected from
the solar atmosphere, resulting in a CME , and as confined flares when no CME
is associated with the flare (Schmieder2015; Janvier2015). In addition to full
and failed eruptions, there are cases where only a part of the filament is
erupted, such events are defined as partial erupting events. Partial eruption
may or may not be associated with a CME (Gibson2006; Liu2008; Tripathi2013;
Kliem2014; Zhu2014). The most energetic flares are commonly eruptive
(Yashiro2005), even though confined, non-eruptive X-class flares have been
reported (Thalmann2015; Sun2015; Harra2016) as well as CMEs with associated
only C-class flares (Romano2014; Chandra2016).

The CSHKP model (Carmichael1964; Sturrock1966; Hirayama1974; Kopp1976) and its
extension in three-dimensions (Aulanier2012; Janvier2013; Janvier2015) can
explain several observational signatures of the fully (or failed) eruptive
flares, such as the presence of X-ray sigmoids, flare ribbons, and brightening
motions along the ribbons themselves. In particular, Savcheva2015;
Savcheva2016 have shown that the flare ribbons often coincide with the
photospheric signature of quasi-separatrix layers (QSLs, Demoulin1996), i.e.,
thin layers characterized by a sharp gradient in the connectivity of the
magnetic field. The brightening motions along the ribbons have been
interpreted as the signatures of the slipping reconnection of the magnetic
field lines through the QSL (Aulanier2006; Janvier2013; Dudik2016). High
resolution observations and interpretation of the slipping motion of plasma
material in the AR are required to explain the magnetic behaviour of the
region (Zuccarello2017; RJoshi2017).

The morphology and evolution of flare ribbons can also give information on the
overall topology of the system. Masson2009 have shown that circular flare
ribbons are associated with the presence of a null-point topology in the
corona, while parallel ribbons moving away from each other have been
interpreted as an indication of quasi-separator reconnection occurring higher
and higher in the corona (Aulanier2012). Different triggering mechanisms have
been proposed (Forbes1991; Chen2011; Aulanier2014; Filippov2015;
Schmieder2015), but essentially the equilibrium of a magnetic FR embedded in
an overlying magnetic field is determined by two competing effects: the
outward-directed magnetic pressure between the FR and photosphere, and the
inward-directed magnetic tension of the overlying field. In the torus
instability or catastrophic loss of equilibrium model (Forbes1991; Kliem2006;
Demoulin2010; Kliem2014) it is the onset of an ideal MHD instability that
leads to the disruption of this equilibrium, while in the breakout model
(Antiochos1999; Lynch2008; Zuccarello2008; Zuccarello2009; Karpen2012) it is
the onset of a resistive instability. Assuming an overlying external field
$B_{ex}$ that scales with the height $z$ from the photosphere as
$B_{ex}\propto z^{-n}$, in the torus instability model the system becomes
unstable when the apex of the axis of the magnetic FR reaches a critical
height $z_{cr}$ where the decay index $n$ of the external overlying field
$B_{ex}$ becomes larger than a critical value $n_{cr}$. The results of several
MHD simulations place $n_{cr}$ in the range $[1.3-1.75]$ (Torok2005; Fan2007
Torok2007; Isenberg2007; Aulanier2010; Kliem2013; Amari2014; Inoue2015;
Zuccarello2016). Attempt to estimate the decay index at the onset of solar
eruptions have also been made both using limb observations as well as
stereoscopic observations (Filippov2001; Guo2010; Filippov2013;
Zuccarello2014; McCauley2015). Contrary to the torus instability model that
does not require any particular magnetic field topology, the breakout model
requires a multi-flux distribution. The eruption begins when a resistive
instability sets in at the breakout current sheet that exists between the
arcade that confines the FR and the overlying field (Karpen2012). This
reconnection removes the confining flux by transferring it to the neighboring
flux domains. As a result, the magnetic tension of the confining field
decreases resulting in an eruption. For the breakout model to work two
conditions must be satisfied: the presence of a null-point or quasi-separator
in the corona, and the flux of the confining arcade must be larger than the
flux of the overlying field. Due to the nature of the problem, i.e., evidence
of reconnection occurring higher up in the corona, observational studies that
clearly support the breakout model are quite rare (Aulanier2000; Mandrini2006;
Chandra2009; Chen2016). Both models address the triggering of the eruption,
but what determines if the eruption results in a CME or in a failed eruption?
Many questions have to be answered, i.e.: How does the trigger mechanism
affect the eruptive/failed behavior of the flare? How important is the
magnetic environment of the AR?

In some of the studies circular ribbons have been observed at the base of
solar jets (Wang2012). This topology supports the presence of magnetic null-
points above jet locations. However, using photospheric magnetic field
extrapolations, Mandrini1996 and Guo2013 explained the jets by the presence of
bald patch (BP) regions along BP separatrices are regions where magnetic field
lines are not anchored on the photosphere but are tangent between two
different magnetic regions. Flux cancellation at the jet locations is
frequently proposed as the driver of jets (Innes2010; Liu2011; Innes2016;
Adams2014; Young2014; Cheung2015; Chen2015). Zhang2000) proposed such flux
cancellation between oppositely directed magnetic field to explain
macrospicules and microscopic jets. Adams2014 also found magnetic flux
convergence and cancellation along the PIL, where the jets were initiated. In
Guo2013 the cancelling flux occurred at the edge of EMF during its expansion.
Therefore, it is still discussed if the jets are due to the process of flux
emerging or cancelling or both.

In this chapter we present a detail study of the AR NOAA 12035 on April 15-16,
2014 with AIA, HMI space borne instruments and chromospheric observations from
ARIES solar telescope in Hα (Zuccarello2017; RJoshi2017). This study shows the
evolution of key topological structures, such as spines and fans which
determined the eruptive versus non-eruptive behavior of the series of eruptive
flares, followed by confined flares. An interesting slippage of jets from one
location to another is also observed and explained with complex topology of
the region with the presence of a few low-altitude null points and many QSLs,
which could intersect with one another.

###  2.2 Flare and CME observations

The AR NOAA 12035 appeared at the East limb on April 11, 2014 with a $\beta$
magnetic configuration and crossed the West limb on April 23, 2014. During its
disk passage it produced many small–to–medium class solar flares. The AR
turned into a $\beta\gamma$ magnetic configuration on April 13, 2014. During
the disk passage on April 15-16, 2014 the AR (located S15, E20 to E08)
produced eruptive and compact flares, respectively. The description of these
confined and eruptive flares is given in table 2.1.

Table 2.1: Details of compact and eruptive flares. The ‘–’ indicates small
flares that are not reported by GOES, ‘$X$’ indicate CMEs visible in LASCO,
but not associated with the filament activity/eruption.

April 15, 2014
---
Flare No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13
Flare Onset (UT) | 05:56 | 06:15 | 06:59 | 09:15 | 12:37 | 14:37 | 16:56 | 17:53 | 19:22 | 20:55 | 21:39 | 22:48 | 23:40
Flare Class | – | – | – | C8.6 | C3.6 | – | – | C7.3 | – | – | – | – | –
Related CME | No | No | No | 10:24 | 14:00 | No | 14:00 | 18:48 | No | No | No | No | No
April 16, 2014
Flare No. | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26
Flare Onset (UT) | 01:10 | 02:42 | 03:20 | 03:48 | 05:02 | 06:37 | 07:14 | 08:36 | 09:20 | 10:42 | 12:42 | 17:30 | 19:54
Flare Class | C1.9 | – | – | – | – | C1.8 | – | C5.2 | – | – | C7.5 | C2.0 | M1.0
Related CME | No | No | No | No | No | X | No | No | No | No | No | No | X

Figure 2.1: SOHO/LASCO C2 running difference images showing the associated
CMEs for the eruptive flares. The last panel shows that no CME could be
detected for the failed eruption on April 16, 2014.

####  2.2.1 LASCO/CME observations

All the eruptive flares occurred on April 15. The CMEs associated with two of
these eruptive flares are presented in Figures 2.1. The CME associated with
the C8.6 X-ray flare at 09:15 UT is first seen in LASCO C2 coronagraph at
10:36 UT (Figure 2.1 (a)), and is characterized by a narrow angular width of
27∘ and an average speed of 274 km s-1. The CME associated with GOES C7.3
X-ray flare that occurred at 17:53 UT is visible in LASCO C2 field of view
(FOV) at 20:00 UT (Figure 2.1 (b)), and has an angular width of 179∘ and an
average speed of 360 km s-1. On April 16 no CMEs associated with the flares in
the AR are observed. One example of the corona observed two hours after the
flare that occurred at 12:42 UT is presented in Figure 2.1 (c) to show that no
CME is detectable. However, we note that two CMEs are recorded on April 16
(Table 2.1). After a detailed inspection of the LASCO observations we
identified a poor CME around 06:30 UT that it is too early to correspond to
the flare at 06:38 UT, and a narrow CME directly towards the south at 20:00 UT
that is again too early to correspond to the M1.6 flare. These CMEs could
correspond to jet activity that characterize the eastern part of the AR.

Figure 2.2: Two examples of GOES C-class eruptive flares in the AR 12035 on
April 15, 2014 in AIA 304 Å (two top rows) and one example of confined flare
on April 16, 2014 (bottom row).

####  2.2.2 SDO/AIA observations

All the flares of the AR 12035 considered in this study and listed in Table
2.1 were well observed by the AIA instrument on board SDO. Apart from the last
one (flare 26 in Table 2.1), they are all low energy events, and correspond,
for the strongest ones, to C–class flares. During April 15-16, 2014 the AR
produced six eruptive and twenty confined flares. Two of the eruptive flares,
productive of CMEs, that occurred on April 15 are shown in the first two rows
of Figure 2.2 (in AIA 304 Å wavelength).

Figure 2.2 presents the environment of the region around the time of the
flare, and the black box in panel (b) is focused on the AR 12035. A zoom of
its evolution is presented in Figure 2.3. As an example, the image at 09:15 UT
shows a dark north-south oriented filament that has been activated a few
minutes before and, consequently bright arcades are observed around it. The
flare emission reaches its maximum at 09:23 UT while at 09:36 UT a round shape
brightening can also be observed (Figure 2.2). Finally, between 09:39 UT and
10:03 UT dark strips are seen to cross the AR from West to East.

Figure 2.3: Evolution of the filaments in the north part of the AR 12035
between April 15-16 in AIA 304 Å. The FOV corresponds to the black box in
Figure 2.2.

The second flare that we consider here occurred at 17:53 UT, when we see the
activation of the filament that started to be more east-west aligned and with
a second half-circle shaped filament at the north of it (Figure 2.2 (e)).
Observations show that, after a first failed eruption of the southern threads
of the filament, the main body of the filament starts to erupt at 17:51 UT,
when circular bright arcades on the west of the filament are also visible
(Figure 2.2 (e)). During the eruption the filament interacted with the
environment and, similarly to the other eruptive flares, resulted in the
ejection of plasma, visible as dark stripes around 18:32 UT (Figure 2.2 (e)).
These dark, filamentary eruptive structures that can be clearly seen in
Figures 2.2 (c) and 2.2 (f) had a duration of about 45 minutes, and eventually
produced the CMEs. During the two days of observation the filament(s) evolved
from being constituted by two separated filaments on April 15 —one relative-
straight and north-south at 09:15 UT oriented and an upside down U at the
north of the first one well visible at 17:00 UT — to a complete east-west
oriented sigmoidal filament on April 16 at 05:40 UT (Figure 2.3). All failed
eruptions observed on April 16 were initiated by an asymmetric failed eruption
of the southwestern part of the sigmoidal filament.

One example of a compact flare that occurred on April 16 is shown in the
bottom row of Figure 2.2. Around the time of the onset of the flare, i.e., at
12:42 UT, we observe an oval shape of brightening around the AR 12035 with
inside the dark sigmoid and many filamentary structures in its southwestern
end (Figure 2.2 (h) and also Figure 2.3). Until this time the dynamics is
similar to what was observed the day before. However, at 13:00 UT a bright
overlying arcade is seen over the AR 12035 and the dark material inside stops
to rise (Figure 2.2 (h)). The eruption concerned only the southern part of the
sigmoid and did not succeed to drive all the sigmoid to erupt. The two other
failed eruptions, at 10:51 UT and at 20:00 UT, followed the same scenario.
These three events lasted 15 minutes each. The eruption of 10:51 UT is well
observed in Hα and is discussed in detail in the next section.

####  2.2.3 Hα observations

In this subsection we discuss the failed eruption that occurred on April 16 at
10:30 UT and that is well observed in Hα from ARIES, Nainital. The Hα image
taken at 10:34 UT on April 16 (Figure 2.4), shows the S-shaped filament (S) in
the north of the AR, which was formed between April 15-16 (Figure 2.3). Around
10:38 UT, the filament started to be activated, and at around 10:46 UT it
broke in its center. The northern part of the filament remained in its
original condition, while the broken part of it consisted of many threads (T)
that are visible in Hα at 10:48 UT (Figure 2.4), when the filament started to
erupt in the west direction. However, the broken filament’s southern foot
point remained fixed. Eventually, the erupted part of the filament fell back
on the solar surface, resulting in a failed eruption. Together with the
filament eruption close to the breaking location of the filament, we observe
the maximum flare brightening at 10:51 UT corresponding to a C2.0 class flare.
Later on, we observe two flare ribbons (R1, R2) at 10:53 UT. Finally, we note
that the dark Hα structure with a fan-like shape (F) did not expand after
10:58 UT (Figure 2.4).

Figure 2.4: Hα images of the failed filament eruption and of the flare on
April 16, 2014 (from ARIES, Nainital telescope, top two rows). The box in the
left middle image represents the FOV of the images in the top row. In the
bottom row, the corresponding images in AIA 171 Å.

The AIA 171 Å observations confirm the failed eruption (Figure 2.4, bottom
row). The filament is visible in absorption with a S-shaped at 10:47 UT and
with a side-view of the arcade overlying the western part of the filament
during the eruption at 10:54 UT. The ribbons appear as bright structures along
the foot points of the arcades.

Figure 2.5: Distribution of the radial component of the magnetic field (left)
and of the HMI continuum (right). The color scale for the magnetic field is
saturated at $\pm$500 Gauss and black/white indicate negative/positive
magnetic field.

####  2.2.4 Evolution of the magnetic field at flare site

On April 15, the AR had an overall bipolar structure characterized by a
positive leading polarity P1 and a following negative one N1 (Figure 2.5. The
leading polarity appeared to be constituted by a preceding compact flux
distribution P1, coinciding with the umbra of the leading sunspot (Figure 2.5,
right panel), followed by a more disperse polarity P2. The positive polarity
P1 is surrounded by a moat region with frequent bipole flux emergence and
cancellation. Consequently, the positive polarity P1 is surrounded by two
negative flux distributions, indicated as N2 and N3 in Figure 2.5, left panel.
The continuum intensity shows that the sunspot P1 is rotating in the clockwise
direction by an angle of about 35∘ during the two days of observations (and
about 80∘ between April 14-18).

Between April 15-16 we observe the emergence of new magnetic flux between the
dispersed positive flux P2 and the following negative polarity N1. This region
corresponds to the area of an arch filament system (AFS) visible in Figure 2.2
(e). As a result of this process, part of the positive dispersed flux that
constitutes the leading polarity is annihilated and the separation between the
negative N1 and positive P2 flux distribution increases. Furthermore, the
leading polarity is now characterized by two compact distributions of positive
flux that are well separated (P1 and P2 in Figure 2.6 (c)).

Starting from about 19:00 UT on April 15, a succession of bipoles with a
larger negative polarity and a weaker positive one is seen to emerge in the
north of P1 leading to an accumulation of flux in N3. Subsequently, we observe
a northeast migration with a counter clockwise rotation of the newly emerged
flux N3. Therefore, there is a strong shear between the clockwise rotating
polarity P1 and the counterclockwise rotation of N3.

Contemporaneously to this migration, small concentrations of magnetic flux are
seen to spread from the compact leading polarity P1 in all directions. As a
result part of the flux of P1 is canceled with the negative fluxes N3 and N2.
The recurrent jets probably originate from the cancellation of N2 and P1 that
may lead to magnetic reconnection producing the observed jets around the
location of N2. By 10:24 UT on April 16 (Figure 2.6 (c)) the positive polarity
of the AR is constituted of three separate (more or less compact)
distributions of positive flux (P1, P2, P3 in Figure 2.6 (c)) with a negative
intrusion N3 at the north of the leading compact one. The filament that is the
subject of this study is located along the PIL between the compact positive
polarity P1 and the negative flux distribution N3 (arrow in Figure 2.5, left
panel and blue arcades in Figure 2.6).

Figure 2.6: Magnetic field distribution of AR NOAA 12035 together with some
representative potential field lines and QSL maps for April 15-16.

###  2.3 Magnetic field configuration

Here we describe the key topological magnetic structures of the AR between
April 15-16, 2014 i.e., between the time period when the nature of the flares
changed from eruptive to confined.

####  2.3.1 Potential magnetic field extrapolations

To study the connectivity of the different flux domains and their evolution we
computed a potential magnetic field model of the AR (Figure 2.6, left
columns). Potential configurations give robust information on the topological
structures of the coronal field such as separatrices and quasi-separatrices
(section 2.3.2 and Demoulin1996)

Since we are mainly focused on the connectivity of the AR, we perform the
potential extrapolation using a larger FOV provided by the HMI LOS-
magnetograms that includes the neighboring ARs rather then the much smaller
FOV provided by the HMI SHARP data product. To this purpose the HMI LOS-
magnetograms of AR 12035 (and its neighboring ARs) taken at 10:24 UT on April
15-16 have been re-mapped to the disk-center using the mapping software
available through solarsoft. As a result of this process the AR 12035 is
rotated so that its center is located along the central meridian. During this
process we also decreased the resolution of the images from the $\approx
0.5\mbox{$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$}$ of HMI to $\approx
2\mbox{$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$}$. The sub region of the
derotated magnetogram (containing both AR 12035 and the neighboring ARs) is
then inserted at the center of a 8 times larger grid padded with zeros. The
potential field extrapolation is performed by applying the fast Fourier
transform method of Alissandrakis1981 on this larger grid.

As Figure 2.6 (left panels) shows the large scale magnetic field is indeed
bipolar as discussed in section 2.2.4, but the part of the AR that displays an
increased level of activity is characterized by a more complex connectivity.
Essentially, four flux domains are observed: the first connecting the north-
most part of the positive polarity P0 to the negative flux N3 at its south
(green field lines in Figure 2.6 (a)), the second connecting the negative
polarity N3 with the leading compact positive polarity P1 (blue field lines),
the third connecting this latter with the negative flux N2 at the southeast of
it (connecting field lines not shown), and the last one is the large scale
field that connects the positive polarities P0, P1 and P2 to the following
negative one (N1, orange field lines). The anemone-like structure (blue-green
field lines) is embedded in a bipolar field resulting in a breakout-like
magnetic field configuration, and evolves from an northwest-southeast
elongated structure on April 15 to a more circular one on April 16 (Figure
2.6, left panels).

####  2.3.2 Quasi-separatrix layers

Quasi-separatrix layers (QSLs, Demoulin1996) are thin layers characterized by
a finite, but sharp, gradient in the connectivity of the magnetic field, and
are defined as regions where the squashing degree $Q$ is large (Titov2002).
QSLs are also locations where current layers easily develop, where (slip-
running) magnetic reconnection can occur (Aulanier2006; Janvier2013;
Dudik2014), and they often coincide with the position of the flare ribbons
(Savcheva2012; Savcheva2015; Savcheva2016; Zhao2016).

According to Demoulin1996, suppose we integrate in both directions along a
distance ‘s’, the field line crosses a point P$(x,y,z)$ of the solar corona.
Two end points $(x$$\leavevmode\nobreak\
\\!\\!{}^{\prime}$$,y$$\leavevmode\nobreak\
\\!\\!{}^{\prime}$$,z$$\leavevmode\nobreak\ \\!\\!{}^{\prime}$$)$ and
$(x$$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$$,y$$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$$,z$$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$$)$
constitute a vector D$(x,y,z)$={$X_{1},X_{2},X_{3}$} =
{$x\mbox{$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$}-x\mbox{$\leavevmode\nobreak\ \\!\\!{}^{\prime}$}$,
y$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$-y$\leavevmode\nobreak\
\\!\\!{}^{\prime}$, y$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$-y$\leavevmode\nobreak\ \\!\\!{}^{\prime}$}. As the
$QSLs$ are locations of rapid change in field-line linkage, hence for a slight
change in point P$(x,y,z)$, the point D$(x,y,z)$ will shift greatly. To limit
this change into a given value of distance ‘$s$’, the region with drastic
change can be located with a function defined as:

${\bf N}(x,y,z,s)=\sqrt{{\sum\limits_{i=1,2,3}\Bigg{[}{\left(\frac{\partial
X_{i}}{\partial x}\right)^{2}}}+{\left(\frac{\partial X_{i}}{\partial
y}\right)^{2}}+{\left(\frac{\partial X_{i}}{\partial z}\right)^{2}}\Bigg{]}}$
(2.1)

We put a limit on the ‘s’ either with a physical boundary or by the distance
covered by a wave during the magnetic reconnection process, and this
establishes as $z=0$ at the photospheric level from low to high plasma beta,
hence at photospheric level:

${\bf N}(x,y)=\sqrt{{\sum\limits_{i=1,2}\Bigg{[}{\left(\frac{\partial
X_{i}}{\partial x}\right)^{2}}}+{\left(\frac{\partial X_{i}}{\partial
y}\right)^{2}}\Bigg{]}}$ (2.2)

This is the norm evaluated at the boundary. The region with high value of
N(x,y) are the field lines taking part in the QSLs formation. Therefore, by
following these lines, the coronal parts of QSLs can be traced. It has been
reported that the QSLs exist when the field components in the z-direction is
weak compared to the maximum value in x and y directions (Demoulin1996;
Demoulin1997). At the QSLs the breakdown of ideal MHD occurs, which results in
reconnection. A change of connectivity of plasma elements happens even when a
smooth boundary motion is imposed. Because the imposed boundary velocity
values get amplified and the field line velocities exceeds the possible plasma
velocities or Alfvénic speeds and an electric field component is produced in
the layer along the magnetic field with slippinng magnetic field lines. In
this way, concentrated currents are naturally formed at QSLs.

In this work we compute the Q-factor using the latest version of the topology
tracing code (Demoulin1996), where the formula of Pariat2012 is implemented.
To this purpose we define the plane at $z=0.4\leavevmode\nobreak\ $Mm as the
seed plane from which the field lines are traced. On April 15 an elongated
fan-type QSL (arrow Q1, Figure 2.6 (b)) surrounds the negative magnetic field
distribution N3 at the northwest of the compact leading positive polarity P1
and embeds the portion of the PIL where the filament is located. This QSL
essentially encloses and separates the anemone-like structure (blue-green
field lines) from the global/large-scale field (orange field lines) of the AR.
A spine-like QSL that starts from the northwest part of the fan-QSL and
intrudes towards the central part of it is also observed (arrow Q2, Figure 2.6
(b)). Field lines that originate at the north of the spine-QSL connect to the
north-most positive polarity P0 (green lines), while the ones that originate
at the south of it connect to the compact leading positive polarity P1 (blue
lines, Figures 2.7 (a) and 2.7 (b)). These latter are the ones that enclose
the filament that is the object of this study.

Figure 2.7: Distribution of the QSL maps at $z=0.4$ Mm and of the photospheric
magnetic field. The color scale for the magnetic field is saturated at ±300
Gauss and black/white indicates a negative/positive magnetic field.

On April 16 the fan-QSL (arrow Q1, Figure 2.6 (d)) displays a more circular
and less elongated shape, while the spine-QSL (arrow Q2, Figure 2.6 (d)) now
originates from the center of the fan-QSL circle and extends westward. This
magnetic field configuration indicates the presence of an elongated, locally
two-dimensional, hyperbolic flux tube (HFT) that separates the two lobes of
the anemone-like magnetic field configuration from each other and from the
overlying field. This is confirmed by the vertical distribution of $Q$ along
the plane passing through the spine-QSL (Figure 2.8, left panels). The 2D cuts
show that a local ‘null-point like’ configuration is achieved in both cases,
but the two lobes are more symmetric on April 16 than they are on April 15.

A second, less-pronounced, more-complex QSLs system is present around the
region (arrow JR, Figure 2.7) where the recurrent jets are observed. However,
this latter does not intersect the QSL labeled as Q1 suggesting that the jet-
producing region and the flaring region are not directly connected to each
other (although propagating Alfvén waves may still induce a causality
connection between the two parts of the AR).

While QSLs are robust topological features essentially determined by the
connectivity of the magnetic field their exact morphology depends on the
actual magnetic field model used to compute them (Sun2013). To compute the
$Q$-factor we used the simplest magnetic field compatible with the given
boundary, i.e., the current-free magnetic field. Despite this very simple
assumption we note (1) that the computed fan-QSL of the flaring region matches
well the circular flare ribbons, (2) that similarly to the computed fan-QSL
the flare ribbon actually crosses the compact leading polarity, (3) that a
brightening is observed approximately at the location of the spine-QSL, and
(4) that the jet-associated brightening do not cross the flare-associated
ribbons.This evidence suggests that the magnetic field model used is
sufficient to capture the key features of the event.

We note that the discrepancy between the computed fan-QSL (Figure 2.6) and the
circular brightening ribbon (Figure 2.2) is probably also due to the
simplistic magnetic field model used. This can be seen from Figure 10 of
Sun2013 where the QSLs computed using both a potential field and a non-linear
force-free field (NLFFF) are compared. The fan QSL is relatively round in the
potential field model, but displays a more sigmoidal shape in the NLFFF model
that actually accounts for the shear present in the configuration. This is
compatible with our configuration where the counterclockwise motion of the
polarity N3 and the clockwise rotation of the sunspot P1 definitely introduced
a degree of shear that the potential field model does not capture.

####  2.3.3 Decay index estimation

A parameter that allows the estimation of the stability of a given magnetic
field configuration is the decay index. Briefly, a magnetic FR embedded in an
external magnetic field ($B_{\text{ex}}$) is unstable to perturbations if the
axis of the FR has an height $z$ above the photosphere where the decay index
of the external magnetic field (Filippov2009):

$n=-\frac{d\ln B_{\text{ex}}}{d\ln z},$ (2.3)

is larger than a critical value $n_{\text{cr}}$, that depends on the
morphology of the FR (Demoulin2010; Zuccarello2015), and is in the range
$n_{\text{cr}}\simeq 1.1-1.75$.

To evaluate the stability of the magnetic field configuration we computed the
decay index (using only the tangential component of the computed potential
magnetic field) in all the volume above the flaring region. A vertical cut of
decay index along a plane passing through the approximate position of the HFT
is shown in Figure 2.8 (right panels). The first conclusion that can be drawn
from the figure is that in the proximity of the HFT the decay index changes
sign becoming negative (and reaching very large, negative values) as already
shown by Torok2007 and as expected from its definition (Equation 2.3).

Figure 2.8: Projected 2D view of the squashing degree $Q$ (left panels) and of
the decay index (gray color scale, right panels). The green, cyan, and red
contours on the right panels indicate isocontours of decay index n = 0.5, 1,
and 1.5, respectively. The yellow contour indicates the polarity inversion
line.

A second conclusion is that the large scale stability of the magnetic field
(away from the HFT) does not change significantly between April 15-16. This
can be deduced by comparing the height at which the decay index is larger than
the “nominal” $n=1.5$ critical value. The decay index for both days shows an
initial increase with altitude (i.e., the system is more prone to erupt),
followed by a decrease at even larger altitudes (i.e., the system is torus
stable).

As previously discussed, both the circular-shaped photospheric-QSL (Q1, Figure
2.6) and the fan-spine-like distribution of $Q$ (2D vertical cuts of Figure
2.8) indicate the presence of a null-point topology in the corona. At the
null-point the decay index (Equation 2.3) has a singularity and its validity
is limited in this region. The distinction between torus instability or
breakout-type reconnection as trigger mechanism for the eruption in this
configuration is not at all straightforward (Kliem2014). Furthermore, in
configurations with a vertical magnetic field (Figure 2.7, right columns), the
verticality of the field lines itself prevents any tension-related confinement
even in a uniform field where the decay index is zero. Therefore, for this
complex magnetic field topology the analysis of the decay index does not
provide a useful criterion for eruptivity.

For configuration that displays a coronal null point, the breakout scenario is
a valuable mechanism to trigger the eruption. In this scenario the eruption is
triggered by the onset of magnetic reconnection, and the efficiency of it also
depends on the mutual orientation of the reconnecting fields. Galsgaard2007
performed a series of MHD simulations of a dynamical flux emergence experiment
aimed to study the role of the mutual orientation between the emerging FR and
the overlying field. The authors have shown that when the two system are
(nearly) anti-parallel substantial reconnection is observed, while this is not
the case when the flux systems are (nearly) parallel. More recent simulations
of dynamical emergence have shown that interaction of (nearly) anti-parallel
flux systems leads to FR-like eruptions, while this is not the case for
(nearly) parallel systems (Archontis2012; Leake2014).

###  2.4 Recurrent solar jets

The AR NOAA 12035 produced many solar jets during April 15-16, 2014 towards
the south direction. We have selected eleven clearly visible jets for our
investigation. Their description is given in Table 2.2. These jets were
observed by the AIA onboard SDO in different EUV and UV wavebands. On April
16, 2014 two jets, that we will name jet J5 and J′5 in the next section, were
observed in Hα by the 15 cm Coudé telescope operating at ARIES, Nainital,
India (Figure 2.10). The pixel size and cadence are 0.58$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$ and 1 minute respectively. For consistency, we have
alligned all the images at April 16, 2014 10:30 UT. For identifying the onset
and peak time of the jets, we look into the temporal evolution of intensity at
the jet foot-point. We create a box containing the bright jet base and
calculate the total intensity inside it. Then this total intensity is
normalized by the intensity of the quiet region.

Table 2.2: Different physical parameters derived from SDO/AIA data for jets on April 15-16, 2014. Jet |  Start/ | Speed at different | Height | Width | Lifetime
---|---|---|---|---|---
number | end |  wavelengths ($\lambda$) in km s-1 | (Mm) | (Mm) | (minutes)
| (UT) | 304Å 211Å 193Å 171Å 131Å 94Å |  |  |
J1 |  14:55/ | 205 295 257 249 268 206 | 145 | 4.4 | 15
| 15:10 |  (252) |  |  |
J2 |  18:01/ | 234 177 199 232 221 235 | 124 | 5.2 | 08
| 18:09 |  (196) |  |  |
J3 |  06:33/ | 137 140 132 153 148 163 | 202 | 4.3 | 23
| 06:56 |  (126) |  |  |
J′3 |  06:10/ | 113 121 109 110 105 100 | 108 | 3.5 | 15
| 06:34 |  (100) |  |  |
J4 |  07:13/ | 136 139 147 133 164 138 | 95 | 2.6 | 11
| 07:23 |  (147) |  |  |
J′4 |  07:12/ | 305 295 325 300 296 303 | 116 | 4.5 | 06
| 07:18 |  (322) |  |  |
J5 |  10:36/ | 183 202 174 185 184 182 | 217 | 6.0 | 24
| 10:50 |  (174) |  |  |
J′5 |  10:33/ | 275 343 364 291 316 241 | 87 | 3.6 | 10
| 10:43 |  (357) |  |  |
J6 |  14:41/ | 197 177 192 156 170 171 | 94 | 3.0 | 15
| 14:55 |  (187) |  |  |
J′6 |  14:47/ | 343 326 340 323 307 304 | 152 | 4.0 | 16
| 14:59 |  (335) |  |  |
J7 |  16:59/ | 183 174 154 187 184 217 | 145 | 5.1 | 14
| 17:13 |  (154) |  |  |
Figure 2.9: Recurrent jets in AR 12035 on 15 and 16 April 2014. The top,
middle, and bottom panels show images of AIA filters at 304 Å 193 Å and 94 Å
respectively. The arrows indicate the bright emission of the jets in the two
different locations. Figure 2.10: Jets J5 and J′5 from site 1 and site 2, from
left to right in Hα, observed in ARIES Nainital, in 304 Å and in 171 Å
observed with SDO/AIA. Figure 2.11: Evolution of jet J1 initiated in site 1
observed by AIA 211 Å. The contours on the first image are HMI longitudinal
magnetic field with yellow and cyan colors for positive and negative
polarities.

The eleven selected jets during April 15-16, 2014 are named as J1–J7 and J′3–
J′6 respectively. Out of eleven jets, the first two jets J1 and J2 occur on
April 15 and the remaining nine jets are on April 16, 2014. These jets
originated from two locations in the south part of the AR NOAA 12035. One
location is at position [X,Y] = [-220${}^{{}^{\prime\prime}}$,
-215${}^{{}^{\prime\prime}}$] and the other is at
[-205${}^{{}^{\prime\prime}}$, -215${}^{{}^{\prime\prime}}$] (Figure 2.10 left
panel). Here, we will refer them as site 1 jets (J) and site 2 jets (J′)
respectively. The two sites are at a distance of 15$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$ from each other ($\approx$ 11 Mm). Figure 2.9
displays images of the eleven jets observed with the AIA filters at 304 Å
(top), 193 Å (middle) and 94 Å (bottom) during their peak phase. Almost all
the jets are visible in all EUV channels, which indicates the multi-thermal
nature of the jets. The onset and end time of each jet are summarized in Table
2.2.

Figure 2.12: Evolution of jets J5 and J′5 from site 1 and site 2 (indicated by
white arrows) observed by AIA 211 Å. Yellow and cyan colors are for positive
and negative polarities respectively.

Jet J1 started on April 15, 2014 with a bright base at site 1. The zoomed view
of evolution of jet J1 in AIA 211 Å is shown in Figure 2.11. Together with the
ejection of bright material, we have also observed the ejection of cool and
dark material in 211 Å (Figure 2.11c). The dark jet is due to the presence of
cool material absorbing the coronal emission. The bright and cool jet material
were rotating clockwise. After the onset of $\approx$ 2 minutes it started to
rotate anti-clockwise. This indicates the untwisting of the system to relax to
a lower energy state by propagating twist outwards. The jet J2 started also
with a bright base similar to J1 from the same location. This jet was also
showing untwisting like as in the case of J1. However, its base was less
bright and less broader than J1. On April 16, 2014 J3 and J′3 started from
site 1 and site 2 respectively. The base of J′3 was like a circular ribbon and
broader than J3. Jet J′4 is bigger than J4. Jet J4 peaks almost simultaneously
in all EUV wavelengths around 07:17 UT. The peak time for J′4 is five minutes
later than J4, around 07:21 UT in all wavebands. One difference between these
jets and J1–J′3 was that they have no rotation. The evolution of jets J5 and
J′5 is presented in Figure 2.12 in AIA 211 Å. In contrast to the other jets,
the peak time for jet J5 and J′5 is different for different wavebands. The
peak time for J5 at 304 Å is 10:38:30 UT, and at 94 Å is 10:41 UT. For the
case of J′5, the peak time in 304 Å is 10:37:30 and at 94 Å is 10:38 UT.

Figure 2.13: Intensity profile of jet J5 at base location. Different colors
represent different SDO/AIA wavelengths. The peak of the cooler component is
earlier than the peak of the hotter component. Figure 2.14: Sigmoidal
orientation of the loops in AIA 193 Å filter and in the difference image.

For these jets, the peak for cool plasma (longer wavelength 304 Å) appears
earlier than the hot plasma material (shorter wavelength 94 Å). The temporal
evolution of flux at the base of jet J5 is shown in Figure 2.13. This behavior
is contrary to other jets reported in the literature where hotter plasma
appears before cooler plasma, suggesting some mechanism of cooling versus time
(Alexander1999). These are the largest jets among the ones discussed in this
study. As the event progress, interestingly part of jet J′5 was detached from
it and moved towards site 1 and finally merged with jet J5. We have estimated
the speed of J′5 towards J5 as $\approx$ 45 km s-1. Merging of the broken part
of J′5 with J5 made it bigger as it was ejected in the south as well as in the
north direction at the same time. We have also noticed the circular ribbon at
the base of J′5, shown in Figure 2.12 (e). Looking at the evolution of the J′5
jet, we found that the jet follows a sigmoidal-shape loop path visible in AIA
193 Å (Figure 2.14). These loops are originating from the sunspot and going
towards the south with a sigmoid-shape. The sigmoidal-shape of these loops
could be due the the clockwise rotation of big positive polarity spot. We have
observed the clockwise rotation in jet J5 and the calculated rotation speed in
four wavelengths 171 Å , 193Å , 211 Å and in 304 Å. The speed varies from 90
km s-1 to 130 km s-1. Jet J6 was small and of weak intensity whereas J′6 had a
strong intensity and was very bright, wide and had a circular base. J′6
started to move towards site 1, but like in the case of J′5, it could not
reach up to J6 location. We did not find any rotation in this jet. Jet J7
started from site 1 location and also showed clockwise rotation. In a
nutshell, we have found that all jets from site 1 have similar morphology.
Jets from site 2 also have similar morphology, but this is different from the
morphology of jets ejected from site 1. One common feature in all jets of site
2 on 16 April was that after their trigger they all have a tendency to move
towards site 1 before or during the ejections. It seems that for the case of
J5 and J′5, there is a connection between these two. Another common feature of
jets originated from site 2 is that they all follow the sigmoidal loops
visible in different AIA wavebands. The jets from site 2 occur before or
almost simultaneously (in the case of J′4) with the jets from site 1. This is
true apart from the jet J6. The main difference is that J6 is quite weak among
all of the coupled jets. We have noticed that jets observed in 193 Å are
thinner than in 304 Å. All jets started with a bright base, similar to common
X-ray jet observations.

####  2.4.1 Hα observations

Two jets– jet J5 and J′5 were also observed in the Hα line center (6563 Å) by
the solar tower telescope at ARIES, as a bright ejecta. Hα jets from both jets
sites started at $\approx$ 10:35 UT, one minute later than in the EUV
wavebands and they faded away at $\approx$ 10:50 UT. We also observed the dark
material ejection surge between the bright jets from the two sites site 1 and
site 2 respectively. To compare the spatial location of Hα with EUV images, we
have over-plotted the contours of Hα in AIA 304 Å and 171 Å . We found that Hα
jets are coaligned with the EUV jets. However, the position of the Hα jet is
only at the origin of the EUV jets. It may be because the Hα jets are in the
chromosphere and have less height than the EUV jets. The bright ejections in
Hα are followed by dark material ejections. It could be the cooler part of the
jet. This cooler part is spatially shifted towards the west side from the
bright jets.

####  2.4.2 Height-time analysis of the jets with two different methods

Figure 2.15: Time-slice analysis of jet J1 on April 15, 2014. Left: position
of slit along the jet, right: velocity comparison at different wavelengths.
Figure 2.16: An example of a height–time plot for Jet J1 derived using the
leading edge procedure.

To understand the kinematics and dynamics of the observed jets, we have made a
time-distance analysis in different AIA/EUV channels i.e. 94, 131, 171, 193,
211, and 304 Å. To perform this analysis, we adopted two methods, one is the
time–slice technique and the other is tracking of the leading edge of the
jets. For the time–slice technique, we fixed a slit at the center of the jets
and observed the motion of plasma along the slit. An example of this
time–slice analysis of jet J1 on April 15, 2014 is presented in Figure 2.15.
In the figure, the left image shows the location of the slit (drawn as a black
dashed line) and the right denotes the height-distance maps at different EUV
wavelengths. Using this time–slice technique, we have computed the heights and
projected speeds for the different structures of all jets at different
wavelengths, shown in the right panel of the figures. For the same jet of
April 15, 2014 at 193 Å, the height–time plot using the leading edge procedure
is presented in Figure 2.16. The curve has an exponential behavior with two
acceleration phases. We decided to fit linearly the beginning of the expansion
and then the later phase in order to compared the values with those of the
other methods. Two speed values are derived. The first is 117 km s-1 which is
nearly half of the speed derived after the acceleration phase (252 km s-1).
The error is around 10 km s-1 according to the points chosen for the fits.

The time–slice technique indicates that every jet has multi-speed structures
and the speeds of the jets are different in different EUV wavelengths. The
average speed by the time–slice technique varies in different wavelengths for
J1: 205 – 295 km s-1, J2: 177–235 km s-1, J3: 132–163 km s-1, J′3: 100 –121 km
s-1, J4: 133 –164 km s-1, J′4: 295 –325 km s-1, J5: 174 –202 km s-1, J′5: 275
–364 km s-1, J6: 156 –197 km s-1 J′6: 304 –343 km s-1, and for J7: 154 –217 km
s-1 respectively. The dispersion of the values for one jet according to the
different considered wavelengths is between 10$\%$ to 50$\%$. It is difficult
to understand if it is just the range of the uncertainties of the measurements
or if it really corresponds to the existence of multi-components in the jet
with multi-temperatures and speeds or if the slit of the time distance diagram
is crossing different components of the jets. We have compared these results
with the speed derived by the leading edge procedure. We found that the fast
speed fits with the time-distance derived velocity. The time-distance
technique with a straight slit ignores the first phase of the jets. The values
of speed derived by both methods are presented in Table 2.2.

We have also computed the lifetimes, widths, and the maximum heights of each
jet. The lifetimes vary from 6 to 24 minutes. J5 has the maximum lifetime (24
minutes), whereas J′4 has the minimum (6 minutes) lifetime. In general, we
found the narrow and long life–time jets achieved more height than the wide
and short lifetime jets. We have also noticed that the lifetimes of jets are
longer in 304 Å and in 171 Å than in 94 Å. The width ranges from 2.6–6 Mm. The
maximum height was attained by J5 and it was 217 Mm.

Figure 2.17: Magnetic field evolution of AR NOAA 12035. The two jet locations
(site 1 between N2 and p, site 2 at the edge of the supergranule indicated by
the black contour) are indicated by white arrows. Figure 2.18: Evolution of
magnetic field at the site 1 location. The flux cancellation at site 1 between
the negative polarity and the positive polarity (p) is shown by a red arrow.
Figure 2.19: Evolution of magnetic field at the site 2 location. The positive
(negative) flux emergence is shown by green (cyan) arrows respectively. The
roundish black curve indicate supergranule cell. Figure 2.20: Magnetic field
evolution along the slice shown in Figure 2.17 at site 1. Two vertical lines
in the image indicate the time of jet activity.

####  2.4.3 Photospheric magnetic field at the jet base

Figure 2.17 presents the magnetic field evolution of the AR near the jet
source region observed by SDO/HMI during April 15-16, 2014. The AR consists of
two large positive polarity sunspots P1 and P2 followed by the negative
polarity spot N1. The positive polarity P1 behaves like a decaying sunspot
with a “moat region” around it. When the sunspot is close to its decay stage,
it loses its polarity by dispersing in all directions. This dispersed positive
polarity cancels a part of the negative magnetic polarity left at the site of
the jet location. The origin of jet activity lies between the two leading
positive polarities and the whole AR shows clockwise rotation. Together with
the rotation of the whole AR, the western big spot P1 also shows a rotation in
the same direction as the AR. The sunspot rotation makes the AR sheared and
the loops connecting the preceding positive polarity and the following
negative polarity become sigmoidal (Figure 2.14). The jets are ejected in the
south-east direction instead of south direction probably because of the upper
part of the sigmoidal loops.

To investigate the magnetic field evolution at the jet’s origin, we have
carefully analyzed the development of different polarities. On April 15, we
observed the positive polarity P1 and in its south a bunch of negative
polarity N2 and a positive polarity p (Figure 2.17). Site 1 of the jet’s
origin is located between N2 and p. Site 2 is located to the west of site 1.
The zoomed view of magnetic flux evolution at site 1 is shown in Figure 2.18.
In the figure, we have noticed several patches of emerging flux of positive
and negative polarities. In addition to this emerging flux, we have
interestingly found that the negative polarity N2 and the positive polarity p
came closer and cancelled each other. The jet’s cancelling location is
represented by the red arrow. To examine the flux cancellation at the jet site
1, we made a time-slice diagram along the slit shown in Figure 2.18 as the
yellow line. The result is presented in Figure 2.20. The positive and negative
flux approached each other and cancelled afterwards. We have drawn the start
and end time of the jets from site 1 and this is shown in the figure by
vertical red lines. We noticed that the jet activity from site 1 was between
this flux cancellation site. Further, we did quantitative measurements in the
box at jet site 1 drawn in Figure 2.17 (top, middle panel). The positive, and
negative flux variation as a function of time calculated over the box is shown
in Figure 2.21(a). On April 15 the flux is constantly emerging even with some
cancellation around 16:00 UT, on April 16 the flux decreases due to
cancellation.

For site 2, the enlarged version of magnetic field evolution is shown in
Figure 2.19. The emergence of different positive and negative patches is shown
by green and cyan arrows respectively. Around the site 2 location, we have
observed positive polarities surrounded by a kind of supergranule cell. Inside
this positive polarity supergranule, small bipoles with mainly negative
polarities are continuously emerging. For the quantitative evolution of the
positive, and negative magnetic flux at the site 2 location, we have also
calculated the magnetic flux as a function of time inside the red box (top,
middle) of Figure 2.17. The variation of magnetic flux with time is shown in
Figure 2.21(b). We have noticed that the emergence of magnetic field is
continuously followed by the cancellation. At site 2, all the four jets are
present on April 16 and we have drawn the onset and end time of these jets.
The jet duration over site 2 is denoted by the green dashed lines in Figure
2.21(b). We found that the jets from site 2 were lying in between the
emergence and the cancellation site.

Figure 2.21: Magnetic flux as a function of time calculated over the red box
of Figure 2.17 for the site 1 (a) and site 2 (b) location. Red and blue curves
are for positive and negative magnetic flux. Figure 2.22: Magnetic field
configuration of AR 12035. Panel (a): two leading positive and following
negative polarity. Panels (b-c): contours of the magnetic field overlaid with
the footprints of the QSL.

###  2.5 Magnetic null points formation at the jet base

The longitudinal magnetic field maps observed by HMI show a strong complexity
of the polarity pattern and a fast evolution (Figures 2.17, 2.18, 2.19) in the
two sites where the two series of jets are initiated. FRom the AIA
observations, we have detected a shift of the jets from site 2 to site 1 and
never from site 1 to site 2. It is important to understand why there is a
slippage of the magnetic field lines. Slippage reconnection has been observed
in many flares (Priest1992; Berlicki2004; Aulanier2005; Dudik2012). Commonly
it is due to the slippage of magnetic field lines anchored along QSL
structures. The slippage occurs when and where the squashing degree is high
enough along the QSL to force the reconnection. Demoulin1996 and Demoulin1998
has shown, theoretically and observationally, how it can be produced.
Dalmasse2015 demonstrated that the QSLs are robust structures and can be
computed in potential configurations. Qualitatively the results are very good
with this approach and there is a relatively good fit between the location of
QSL footprints with the observed flare ribbons (Aulanier2005). However when
the magnetic configuration is too complex, the QSL footprints do not fit
perfectly and a one to one comparison is increasingly difficult with smaller
and smaller scale polarities (Dalmasse2015). The benefit of using linear
force–free field (LFFF) extrapolation can be weak since QSLs are robust to
parameter changes. In the present case, LFFF extrapolation would perhaps help
to follow the path of the jets which shows some curvature at their bases
(mentioned as a sigmoidal shape) but at the expense of the geometry of loops
at large heights. However, the magnetic field strength is really fragmented in
the jet regions. Pre-processing the data would smear electric currents in
their moving weak polarities, so it will not help to derive better QSLs.
Therefore to investigate the magnetic topology of the jet producing regions,
we use the same potential magnetic field extrapolation of AR 12035 calculated
in Zuccarello2017. This method is based on the fast Fourier transform method
of Alissandrakis1981 and the extrapolation is performed by using a large
field-of-view that includes at its center the AR 12035. This allows us to
identify the key topological structures of the AR (Figure 2.22). Maps of the
squashing degree Q at the photospheric plane were calculated using the
topology tracing code topotr (Priest1995, Demoulin1996, Pariat2012 for more
details). The locations of the largest values of Q define the footprints of
the QSLs (Demoulin1996; Aulanier2005) and they correspond to regions where
electric current layers can easily develop. We have found two QSLs: the first
one (Q1 in Figure 2.22 (b) and (c)) encircling the positive polarity P1 and
separating the magnetic flux system from the external field and a second one
(Q2 in Figure 2.22 (b) and 2.22 (c)) highlighting the spine of a high-altitude
coronal null-point similarly to what is seen in Masson2009. The flares
occurred mainly at the north-west edge of the large QSL (Q1). Since the fan-
like QSL (Q1) encircling the flare region was separated from the complex QSL
system around the jet producing region (at the south of P1), we have argued
that the jet activity and the flares were not really linked to each other,
even if their timings seem to be related (Zuccarello2017).

Figure 2.23: Zoom of the jet region inside the red box of April 16 (panel (c)
in Figure 2.22). Q1 and Q2 indicate the QSLs related to the flares, Q3 and Q4
to the site 1 and site 2.

On April 15 the jets are initiated in site 1 and we find a well defined QSL
surrounding the region of the jet. On April 16 the configuration is much more
complicated with many QSLs which are in the site region of both jets. The zoom
of the Q map of April 16 around the jet producing region (red box of Figure
2.22 (c)) is shown in Figure 2.23. We find that the two sites of the jets,
site 1 and site 2, are respectively inside the QSLs Q3 and Q4, and that both
were embedded in a larger QSL, labeled as Q0 in the figure. We also identified
several quasi photospheric null points, that are indicated by yellow circles.
The QSL map is very complex, and difficult to analyze and compare in detail
with the observations due to the small scale of the events and fast motion of
the small polarities, both the moving p polarity in site 1 and the emergence
of small bipoles in site 2. Since it looks quite possible that the 2 QSLs (Q3
and Q4) intersect or touch each other, we conjecture that field line foot
points could move from site 2 and site 1 by a sequence of reconnections across
QSLs as in Dalmasse2015. This could produce the transfer/or tendency of
movement of jets from site 2 to site 1, as we have observed for jets J5 and
J′5 for example (Figure 2.12). In the case of the other jets from site 2, they
also show a tendency of slippage towards site 1.

###  2.6 Results and conclusion

The study of the transition from eruptive to confined flares and the recurrent
solar jets in active region NOAA 12035 is done in this chapter. The transition
occurred between 2014 April 15 and April 16. On April 15, four of the 13
flares observed resulted in a CME, while none of the 13 flares recorded on
April 16 resulted in a measurable CME. The slippage of the jets from one
reconnection site to other is explained by the complex topology of the region
and the intersection of many QSLs. The main results of this study are as
follows:

Eruptive to confined behavior of the flares can be attributed to the change of
orientation of the magnetic field below the fan with respect to the
orientation of the overlaying spine, rather than an overall change in the
stability of the large scale field. We found that a closed fan-like QSL exists
around the location of the filament on both days. The presence of circular,
closed fan QSLs indicate the presence of a (quasi-)separator in the corona.
The presence of a null-point topology in the corona, the presence of shear
motions that reduced the mutual inclination between the two flux systems
achieving a configuration less favorable for reconnection, as well as the non
significant change in the theoretical stability (with respect to the torus
instability scenario), leads us to the conclusion that the breakout scenario
seems the more probable scenario to describe the observed behavior. The
discerning element between fully and failed eruption behavior being determined
by the mutual inclination of the flux systems involved in the process, namely
the erupting flux and the overlying field.

We found two sites for the different jet’s activity. On April 15 the jets
originated from site 1 and we measure a large increase of emerging flux and
small cancellation. On April 16 site 1 and site 2 are associated with
continuous emerging magnetic flux followed by cancellation at the jet time.
The kinematics of jets at different EUV wavebands revealed that the speeds,
widths, heights and lifetimes of jets are slightly different at different
wavelengths. This can be interpreted as the multi-temperature and multi-
velocity structure of solar jets. In addition to this, most of the jets showed
clockwise rotation, which indicates untwisting. As a result of this
untwisting, the twist/helicity was injected in the upper solar atmosphere
(Pariat2015). The injected helicity in the jets may be part of the global
emergence of twisted magnetic fields. During the rotation like in the case of
jet J1, we observed the rotating jet material contains bright as well as dark
material. This result is consistent with simulations done by Fang2014. In
their simulation, they found the simulated jet consists of untwisted field
lines, with a mixture of cold and hot plasma.

We observed the slippage of jets at site 2 namely J′3–J′6 towards the eastern
site (site 1) and never the reverse movement. Along with the movement of jets
towards site 1, we found, in the case of jet J′5 that a part detached from it
and moved towards the site 1 location and finally merge into jet J5. On April
16 both jet sites are associated with the QSLs. The possible intersection of
the two QSLs encircling each site could explain the slip reconnection
occurring along the QSLs which favor the translation of jets from site 2 to
site 1. The coronal jets may be due to the eruption of mini filaments
(Sterling2015; Panesar2018). According to this hypothesis, the spire of the
jets moves away from the jet base bright point. Our observation of the motion
of the broken part of J′5 is away from the jet base. This supports the
findings of Savcheva2009 and the interpretation proposed by Sterling2015. We
have observed the flux emergence followed by flux cancellation at site 1 on 15
April 2014. Moreover, on 16 April 2014, flux emergence and cancellation are
recurrent in both jet sites. The observation of cool and hot material in our
study supports the hypothesis of small filament eruption and a universal
mechanism for eruptions at different scales (Sterling2015; Wyper2017). The
observations with high spatial resolution instruments, e.g. IRIS, will be very
useful to explain the jet mechanism with the another scenario of magnetic flux
emergence MHD models.

##  Chapter 3 Multi temperature coronal jets for emerging flux MHD models

###  3.1 Introduction

Hot coronal jets are a basic observed feature of the solar atmosphere whose
physical origin is still actively debated. Here, we found a series of jets
observed in the hot EUV channels of SDO/AIA as well as in cool temperatures
with IRIS slit–jaw images. The jets were ejected from the AR NOAA 12644 on
April 4, 2017; on that date, the region was located at the west limb (N13W91)
(Figure 3.1). When passing through the central meridian, this region had shown
high jet activity alongside episodes of emerging magnetic flux (Ruan2019). The
AIA filters allow us to study the temperature and the emission measure of the
jets using the filter ratio method. We studied the pre-jet phases by analysing
the intensity oscillations at the base of the jets with the wavelet technique.
A fine co-alignment of the AIA and IRIS data shows that the jets are initiated
at the top of a canopy-like double-chambered structure with cool emission on
one and hot emission on the other side. The hot jets are collimated in the hot
temperature filters, have high velocities (around 250 km s-1) and are
accompanied by the cool surges and ejected kernels that both move at about 45
km s-1. In the pre-phase of the jets, we find quasi-periodic intensity
oscillations at their base that are in phase with small ejections; they have a
period of between 2 and 6 minutes, and are reminiscent of acoustic or MHD
waves. This series of jets and surges provides a good case study for test the
2D and 3D MHD models that result from magnetic flux emergence. The
double–chambered structure found in the observations corresponds to the cold
and hot loop regions found in the models beneath the current sheet that
contains the reconnection site. The cool surge with kernels is comparable with
the cool ejection and plasmoids that naturally appears in the models. The
location of the AR at the limb in the present observations allows us to
visualize the structure of the brightenings from the side and thus facilitates
the comparison with the MHD jet models, which motivates for this present
study.

We present the multi wavelength EUV observations and the pre-jet oscillations
and conclude that this series of jet and surge observations obtained with a
high spatial and temporal resolution match important aspects of the expected
behaviour predicted by the MHD models of emerging flux. We could identify a
candidate location for the current sheet and reconnection site and follow the
evolution of the cool surge and hot jets with individual blob ejections. This
is a clear case-study for the emerging flux MHD jet models (Joshi2020MHD).

###  3.2 Multi-temperature coronal jets

####  3.2.1 Multi-instrument observations

In this study, we select six jet eruptions occurring in the AR NOAA 12644 at
the western solar limb on April 4, 2017. We use data from the AIA and IRIS
instruments. The IRIS target was pointed towards the AR NOAA 12644 at the
western limb with a field of view of 126$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$ x 119$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$
between 11:05:38 UT and 17:58:35 UT. For our current study, we use the SJIs in
the C II and Mg II k bandpasses obtained with a cadence of 16s. The SJIs
picture the chromospheric plasma around 104 K.

Figure 3.1: Full disk image of the Sun on April 4, 2017. The solar jets were
ejected from the AR NOAA 12644 shown by the white circle at the west limb.
Figure 3.2: Six solar jets (Jet1–Jet6) in AIA 131 Å filter. The red square in
each panel shows the position at which the pre–jet oscillations are measured.

####  3.2.2 Characteristics of the coronal jets

On April 4, 2017, AR jets were observed at the limb between 02:30–17:10 UT
with AIA. The observations in different wavelengths of AIA (131 Å, 171 Å, and
304 Å) reveal that there are two sites of plasma ejections (jets) along the
limb. First, there is a northern site (921$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$, 264$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$),
where the jets are straight and have their base located behind the limb.
Second, there is a site in the south of the field of view
(931$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$, 255$\leavevmode\nobreak\
\\!\\!{}^{\prime\prime}$) in which the jets have their base over the limb.
Therefore we study in the present chapter the six main jets originated in the
southern site occurring after 10:00 UT. Five of them were also observed by
IRIS, whereas the first of them occurred before the IRIS observations. These
jets reach an altitude between 30 and 70 Mm; their recurrence period is around
80 minutes, with the exception of two jets which were separated by only 15
minutes. We also noticed many small jets reaching less than 10 Mm height both
before and in between the main jets. The observed jets in AIA 131 Å are shown
in Figure 3.2 (a–f). The first main jet, Jet1, reaches its peak at $\approx$
10:22 UT with an average speed of 210 km s-1 (panel a). Jet2 (panel b) starts
at 11:45 UT and reaches its maximum extent at $\approx$ 11:47 UT. We note a
large filament eruption located in the northern site of the jets which erupts
$\approx$ 13:30 UT and falls back after reaching its height. Moreover, we
could see that the jet and the filament are not associated with each other.

Jet3 and Jet4 (panel b and c, respectively) reach their maximum altitude at
13:55 UT and 14:15 UT respectively. Jet5 (panel e) erupts with a broader base
and reaches its maximum height at $\approx$ 15:25 UT. We see a fast lateral
extension of the jet base along a bright loop. Jet6 (panel f) is ejected at
$\approx$ 16:57 UT. A second instance of filament eruption is observed during
the peak phase of Jet6 starting again at the same location of the first one.
In this case the erupted filament material seems to merge later with the jet
material and is ejected in the same direction. However, here the jet is not
launched by the filament eruption, because it is not at the jet footpoint.

Figure 3.3: An example of timeslice analysis of the jet 1, used for velocity
and height calculations in AIA 131 Å. In panel (a) the solid black line is the
slit location, which we use to make the height–time. Figure 3.4: IRIS
observation of the the AR from 11:05 UT to 17:58 UT. It covers five jets in
our present analysis in CII (top) and MgII k (bottom) lines.

We have computed various physical parameters, namely, height, width, lifetime,
speed of these jets using the AIA 131 Å data. For the velocity calculation, we
calibrated height–time of each jet in AIA 131 Å fixing a slit in the middle of
the jet plasma flow and calculating the average speed in the flow direction.
An example of height–time calculation is shown in Figure 3.3 for Jet2. All
computed physical parameters are listed in Table 3.1. The maximum height,
average speed, width, and lifetime of the observed jets vary in the ranges
$\approx$ 30–80 Mm, 200–270 km s-1, 1–7 Mm, and 2–10 minutes respectively.

Jet2–Jet6 were also observed by IRIS in two wavelength, namely, CII (top row
of Figure 3.4) and MgII k (bottom row). The high spatial resolution of IRIS
allowed us to make a clear identification of what looks like a null–point
structure at a height of $\approx$ 6 Mm. In the CII filter we see bright loops
above a bright half dome in the northern site of the jet footpoints. In the Mg
II filter, the northern part of the dome is also bright. We find jet strands
all over the northern side of the dome, like a collection of sheets. We will
discuss about these jet strands, which are infact cool jets/surges with a
lower velocity in section 3.2.4. In AIA 131 Å we see clearly, for all the
jets, a bright area which could correspond to a current sheet (CS), possibly
containing a null point, with underlying bright loops shaping a dome (Figure
3.2). However we notice that the bright dome and loops are located on the
southern side of the tentative current sheet, whereas the bright loops in IRIS
C II are rather on its northern side. In the following, for simplicity, when
referring to observations of this candidate current sheet and possible null
point we will sometimes call them ‘the null point’ even though there is
clearly no way in which one could detect a zero of the magnetic field (nor the
intensity of the electric current) in those temperatures with present
observational means.

Figure 3.5: Top: Two maps of the AR Jet2, at two different temperatures (log
T= 5.8 and 6.3). Bottom: In panel (c) the red line shows the temperature at
the location of the blue box in panel (a) before the first jet ejection on
April 4, 2017 and the black line shows the temperature of solar AR jet at
11:45 UT.

Moreover in all the hot channels of AIA (131 Å 193 Å, 171 Å, 211 Å) and IRIS C
II and Mg II SJIs the jets have an anemone (“Eiffel–Tower” or “inverted–Y”)
structure, with a loop at the base and elongated jet arms (Figures 3.2 and
3.4) as reported in previous events (Nistico2009; Schmieder2013; Liu2016).

In AIA 131 Å we could also see that between the first and the last jet
eruption, the tentative current sheet and the jet spine move towards the
south–west direction (Figure 3.2). More precisely, by following the motion of
the point with maximum intensity, we determined a drift of 5
$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$ in less than 6 hours.

####  3.2.3 Temperature and emission measure analysis

We have investigated the distribution of the temperature and emission measure
(EM) at the jet spire for all jet events. We performed the differential
emission measure (DEM) analysis with the regularized inversion method
introduced by Hannah2012 using six AIA channels (94 Å, 131 Å, 171 Å, 193 Å,
211 Å, and 335 Å). After this process we find the regularized DEM maps as a
function of temperature. We use a temperature range from log T(K) = 5.5 to 7
with 15 different bins of width $\Delta$ log T = 0.1. We calculated the EM and
lower limit of electron density in the jet spire using ne = $\sqrt{EM/h}$,
with $h$ the jet width, assuming that the filling factor equals unity. These
EM values were obtained by integrating the DEM values over the temperature
range log T(K) = 5.8 to 6.7. We chose a square box to measure the EM and
density at the jet spire and at the same location before the jet activity for
each jet. The example for DEM analysis of Jet2 is presented in Figure 3.5,
which represents the DEM maps at two different temperatures, namely log T (K)
= 5.8 (panel a) and 6.3 (panel b), at 11:45 UT. We investigate the temperature
variation at the jet spire during the jet and pre–jet phase. During the
pre–jet phase for Jet2 the log EM and the electron density values were 27.3
and 2 x 109 cm-3, whereas for the jet phase the values were 28.1 and 8.6 x 109
cm-3 respectively. Thus, during the jet evolution the EM value increased by
over one order of magnitude and the electron density increased by a factor
three at the jet spire. We find that the EM and density values increased
during the jet phase in all six jets. The values for all jets are listed in
Table 3.1.

Figure 3.6: Example of Jet2 at 11:45 UT observed with IRIS in panel a,b and
AIA 193 Å in panel c. Cool bright dome in the northern side of the null point
is shown with a white arrow in panel a. Table 3.1: Physical parameters of six
studied hot jets from AR NOAA 12644.
Jet | Jet start | Jet peak | Max | Average | T | EM | Oscillation
---|---|---|---|---|---|---|---
no. | time | time | height | speed |  | (1028 | period
| (UT) | (UT) | (Mm) | (km s-1) | (MK) | cm${}^{-5})$ | (min)
1 | 10:15 | 10:22 | 80 | 210 | 1.4 | 1.4 | 6.0
2 | 11:46 | 11:47 | 50 | 245 | 1.8 | 1.9 | 1.5
3 | 13:54 | 13:55 | 40 | 265 | 1.4 | 1.5 | 2.5
4 | 14:12 | 14:15 | 50 | 250 | 1.8 | 1.1 | 2.0
5 | 15:23 | 15:25 | 55 | 235 | 1.8 | 1.3 | 4.0
6 | 16:57 | 17:00 | 70 | 220 | 1.8 | 2.0 | 2.5

####  3.2.4  Identification of observed structural elements

In Section 3.2.2 we have discussed the morphology of the jets observed with
AIA and IRIS. The region below the jet, as seen in different wavelengths, has
a remarkably clear structure, resembling those discussed in theoretical models
of the past years. For identification with previous theoretical work, in
Figure 3.6 several structural elements are indicated for the case of the Jet2
observations. In IRIS C II (Figure 3.6, panel a) the brightenings below the
jet delineate a double–chambered vault structure, with the main brightening
being located in the northern part of the base of the jet. Only narrow loops
are seen above the southern part of the vault in this wavelength. In the other
chromospheric line, IRIS Mg II, we see (panel b) roughly the same scenario,
although the general picture is rather fuzzier. The jet, in particular, is no
longer narrow but formed by parallel strands issuing from the edge of the
northern part of the vault, similar to a comb (Figure 3.6 panel b).

The assumption of a double-vault structure below the jet is reinforced when
checking both the hot-plasma observations (AIA 193 Å, panel c) and the
temperature map obtained through the DEM analysis explained in the previous
section (panel d). In those two panels, the southern loops are shown to be
bright and hot structures, and the same applies to the point right at the base
of the jet, where the temperature reaches $10^{6}$ K. Additionally, we observe
bright kernels moving from time to time along the jets and more clearly
visible in Jet4, Jet5, and Jet6. An example of kernels of brightening moving
along the Jet6 in IRIS CII is presented in Figure 3.7. We have computed the
velocities of the kernels and find that they are comparable to the mean
velocities of the cool jet. The time between the ejection of two kernels is
less than 2 minutes.

Figure 3.7: Kernels of brightening moving along the Jet6 observed in the IRIS
SJI in CII wavelength range (white arrows). The kernels could correspond to
untwisted plasmoids.

The foregoing structural elements seem to correspond to various prominent
features in the numerical 3D models of Moreno2008; Moreno2013, or in the more
recent 2D models of Nobrega2016; Nobrega2018, all of which study in detail the
consequences in the atmosphere of the emergence of magnetized plasma from
below the photosphere. One can identify the bright and hot plasma apparent in
the observations at the base of the jet with the null point and CS structures
resulting in those simulations (the scheme in Figure 3.11, right panel): the
collision of the emerging magnetized plasma with the preexisting coronal
magnetic system leads, when the mutual orientation of the magnetic field is
sufficiently different, to the formation of an elongated CS harboring a null
point and to reconnection. As a next step in the pattern identification, the
hot plasma loops apparent in the southern vault in the AIA 193 Å image and the
temperature panels of Figure 3.6 should correspond to the hot post-
reconnection loop system in the numerical models (as apparent in Figures 3 and
4 of the paper by Moreno2008, or along the paper by Moreno2013. On the other
hand, the northern vault appears dark in AIA 193 Å, and has lower temperatures
in the DEM analysis. This region could then correspond to the emerged plasma
vault underlying the CS in the numerical models: the magnetized plasma in that
region is gradually brought toward the CS where the magnetic field is
reconnected with the coronal field. Additional features in the observation
that fit in the foregoing identification are:

Figure 3.8:  The evolution of cool plasma material along both sides of the hot
jet (Jet2) in IRIS MgII wavelength. The red star shows the leading edge of the
cool material ejecting with an average speed of 45 km s-1. Figure 3.9:
Intensity distribution during pre–phase of recurrent jets at the base of each
jet in AIA 131 Å. The location of the base of the each jet is displayed in
Figure 3.2 (red squares).

  1. 1.

As time proceeds the northern chamber decreases in size while the southern
chamber grows. In our observations in the beginning phase of the jets (for
instance; jet2 at 11:30 UT) the area of the northern and southern vaults is
1.4 x 1018 and 1.16 x 1018 cm2, respectively, and during the jet phase (11:47
UT), they become $1.05\times 10^{18}$ and $2.2\times 10^{18}$ cm2,
respectively. This suggests that while the reconnection is occurring, the
emerging volume is decreasing whereas the reconnected loop domain grows in
size, as in the emerging flux models (Moreno2008; Moreno2013; Nobrega2016).

  2. 2.

A major item for the identification of the observation with the flux emergence
models is the possibility that we also observe a wide, cool and dense plasma
surge ejected in the neighborhood of the vault and jet complex. This wide
laminar jet is observedin the Mg II IRIS filter as an absorption sheet
parallel to the hot jet in AIA 193 Å. The evolution of the cool material along
both sides of the hot jet in the IRIS Mg II channel is presented in Figure 3.8
and the leading edge of the cool part is indicated by red stars. The cool
ejection is generally less collimated than the hot jet and is seen to first
rise and then fall, similarly to classical Hα surges. The velocities measured
along the cool sheet of plasma in Mg II are $\approx$ 45 km s-1. The ejection
of cool material next to the hot jets is a robust feature in different flux
emergence models (Yokoyama1996; Moreno2008; Nishizuka2008; Moreno2013;
MacTaggart2015; Nobrega2017; Nobrega2018). The cool plasma in the models is
constituted by matter that has gone over from the emerged plasma domain to the
system of reconnected open coronal field lines without passing near the
reconnection site, that is, just by flowing, because of flux freezing,
alongside the magnetic lines that are being reconnected at a higher level in
the corona. All those models report velocities which match very well the
observed value quoted above.

  3. 3.

The observed kernels in Figure 3.7 could be plasmoids created in the CS during
the reconnection process. In some of the flux emergence models just discussed,
plasmoids are created in the CS domain (see, for example Moreno2013), and they
are hurled out of the sheet probably via the melon-seed instability
(Nobrega2016), even though they are not seen to reach the jet region.
Observational evidences of the formation of plasmoids in this kind of scenario
have been found by Rouppe2017. On the other hand, in the 2D jet model by
Ni2017, plasmoids are created in the reconnection site that maintain their
identity when rising along the jet spire, possibly because of the higher
resolution afforded by the Advanced Mesh Refinement used in the model; this is
in agreement with the behavior noted in the present observations as well as in
the previous observations of Zhang_Ji_2014 and Zhang2016 mentioned in the
introduction. Plasmoids are also generated in the model by Wyper2016, which is
a result of footpoint driving of the coronal field rather than flux emergence
from the interior. On the other hand, the formation of the kernels could
follow the development of the Kelvin–Helmholtz instability (KHI). The KHI can
be produced when two neighboring fluids flow in same direction with different
speed (Chandrasekhar1961). This instability may develop following the shear
between the jet and its surroundings (Zhelyazkov2019).

  4. 4.

The main brightening at the top of the two vaults seems to be changing
position systematically in the observations. There is a shift in the
south–west direction as time advances, and the same displacement is apparent
in AIA 131 Å (Figures 3.2 and 3.4), possibly marking the motion of the
reconnection site. Such type of observations are also reported in the study of
Filippov2009. This shift may be used to compare with the drift of the null
point position detected in the MHD models.

  5. 5.

We also notice a significant rise of the brighter point (null point) between
different jet events. The rise of the reconnection site as the jet evolution
advances has been found in the MHD emerging flux models of Yokoyama1995;
Torok2009. In the present case, it may be because during each jet event the
reconnection process causes a displacement of the null point and jet spine. In
this way the next jet event occurs in a displaced location as compared with
the previous jet. This could indicate that the magnetic field configuration
has some reminiscences of the earlier reconnection and behaving in the same
manner afterwards. Another possible reason for this shifting could be as a
result of the interaction between different QSLs as suggested by Joshi2017.
However, in the present case because of the limb location of the AR, we could
not compute the QSL locations.

###  3.3 Prejet intensity oscillations

In Section 3.2.2 we mentioned that before and in between the six main jets we
also observed many small jet-like ejections, with length less than $10$ Mm.
Also, in the AIA 131 Å observations we clearly see many episodic brightenings
related to the small jets. In the present section we would like to investigate
different properties, like the periodicity, of these features. To that end, we
select a square of size $4\times 4$ arcsec at the base of the jets where the
intensity is maximum, in the AIA 131 Å data, as shown in Figure 3.2 and
calculate the mean intensity inside the square in the AIA 131 Å channel. We
compute the relative intensity variation in the base, after normalization by
the quiet region intensity. We find that the oscillations start at the jet
base some 5–40 minutes before the main jet activity.

Figure 3.9 shows the intensity distribution at the jet base for all the jets
before and during the jet eruption and the pre–jet phase is shown in between
two vertical red dashed lines. The right red dashed lines indicate the
starting time of the main jets. The blue arrows indicate the time of the
maximum elongation of the main jets. We note that the maximum of the
brightening at the jet base does not always coincide exactly with the start of
the jet neither with the maximum extension time. In most of the cases the
maximum brightening occurs before the peak time of the jets by a few minutes.
For the smaller jets it is nearly impossible to compute the delay between
brightenings and jets. They appear to be in phase with the accuracy of the
measurements.

To calculate the time period of these pre–jet oscillations, we apply a wavelet
analysis technique. For the significance of time periods in the wavelet
spectra, we take a significance test into account and the levels higher than
or equal to 95% are labeled as real. The significance test and the wavelet
analysis technique is well described by Torrence1998. The cone of influence
(COI) regions make an important background for the edge effect at the start
and end point of the time range (Tian2008; Luna2017).

The wavelet analysis of the intensity fluctuation at the jet base shows that
the oscillation period for these pre–jet intensity varies between 1.5 minutes
and 6 min; the current values obtained are presented in the last column of
Table 3.1. An example of wavelet spectrum for the pre–jet activity for Jet2 is
presented in Figure 3.10 (a). The COI region is the outer area of the white
parabolic curve.The global wavelet spectrum in panel (b) shows the
distribution of power spectra over time. Bagashvili2018 investigated the
intensity at the base of several jets issued in a coronal hole and obtained
similar results concerning the periodicity and duration of the oscillations.

Figure 3.10: An example of wavelet spectrum for the pre–jet intensity
oscillations for Jet2. The solid thick white contours are the regions with the
value of wavelet function larger than the 95% of its maximum value. Figure
3.11: Schematic view of the 3D jet showing the location of the null point, the
cool surge and the hot loops. Panel (a): Schematic view of the 3D jet derived
from Moreno2008. Panel (b): Temperature map from the numerical experiments by
Nobrega2017; Nobrega2018.

###  3.4 Results and conclusion

This chapter presents observations concerning the structure, kinematics, and
pre-jet intensity oscillations of six major jets that occurred on April 4,
2017 in active region NOAA 12644. The discussion is based on the observational
data from AIA and IRIS. The conclusion of our main results is as follows:

A first significant finding of this study is the observation of pre–jet
activity, in particular in the form of oscillatory behavior. Earlier authors
had studied the pre–jet activity of quiet region jets observed in the hot AIA
filters (Bagashvili2018). The jets studied by those authors had their origin
in coronal bright points and the bright points showed oscillatory behavior
before the onset of jet activity. They reported periods for the pre–jet
oscillations of around 3 minutes. Our study deals with AR jets, instead, also
observed in the hot filters of AIA and we find an oscillatory behavior of the
intensity in a time interval of 5–40 minutes prior to the onset of the jet.
The period of the intensity oscillation is in the range 1.5–6 minutes. These
values are consistent with the results reported by Bagashvili2018. They are
also close to typical periods of acoustic waves in the magnetized solar
atmosphere. This indicates that acoustic waves may be responsible for these
observed periods in the occurrence of jets (Nakarikov2005). Quasi-oscillatory
variations of intensity can also be the signature of MHD wave excitation
processes which are generated by very rapid dynamical changes of velocity,
temperature and other parameters manifesting the apparent non-equilibrium
state of the medium where the oscillations are sustained (Shergelashvili2005;
Shergelashvili2007; Zaqarashvili2002). In 3D reconnection regions like the
quasi-separatrix layers, a sharp velocity gradient is likely to be present.
The impulsiveness of the jets could lead to such MHD wave excitation. The
observed brightness fluctuations could also be due to the oscillatory
character of the reconnection processes that lead to the launching of the
small jets. Oscillatory reconnection has been found in theoretical contexts in
two dimensions (Craig1991; McLaughlin2009; Murray2009). The latter authors, in
particular, studied the emergence of a magnetic FR into the solar atmosphere
endowed with a vertical magnetic field. As the process advances, reconnection
occurs in the form of bursts with reversals of the sense of reconnection,
whereby the inflow and outflow magnetic fields of one burst become the outflow
and inflow fields, respectively, in the following one. The period of the
oscillation covers a large range, 1.5 to 32 minutes. However, this model is
two-dimensional and it is not clear if the oscillatory nature of the
reconnection can also be found in general 3D environments.

A second significant point in our study is the comparison of the observations
of the structures and time evolution of the jet complex with numerical
experiments of the launching of jets following flux emergence episodes from
the solar interior. Structures like the double-vault dome with a bright point
at the top where the jets are initiated as seen in the hot AIA channels and
also in the high-resolution IRIS images mimic the structures found in the
numerical simulations of Moreno2008 and Moreno2013, who solved the MHD
equations in three dimensions to study the launching of coronal jets following
the emergence of magnetic flux from the solar interior into the atmosphere;
they also have similarities with the more recent experiments, in two
dimensions, of Nobrega2016, obtained with the radiation-MHD Bifrost code
(Gudiksen2011). In the 3D models, the jet is launched along open coronal field
lines that result from the reconnection of the emerged field with the
preexisting ambient coronal field. Underneath the jet, two vault structures
are formed, one containing the emerging cool plasma and the other a set of
hot, closed coronal loops resulting from the reconnection. Overlying the two
vaults one finds a flattened CS of Syrovatskii type, which contains hot plasma
and where the reconnection is occurring. The field in the sheet has a complex
structure with a variety of null points; in fact, in its interior, plasmoids,
with the shape of tightly wound solenoids, are seen to be formed. The
reconnection is of the 3D type, in broad terms of the kind described in the
paper by Archontis2005. A vertical cut of the 3D structure, as in Figure 4 of
the paper by Moreno2008, clearly shows the two vaults with the overlying CS
containing the reconnection site and with the jet issuing upwards from it. The
figures in that paper contained values for the variables as obtained solving
the physical equations; a scheme of the general structure is provided here as
well (Figure 3.11, left panel). As the reconnection process advances, the hot-
loop vault grows in size whereas the emerged-plasma region decreases, very
much as observed in the present study.

An interesting feature in the observations is the tentative detection of a
surge-like episode next to the jet apparent in the IRIS Mg-II time series in a
region that appears dark, in absorption, in the AIA 193 Å observations. This
ejection of dense and cool plasma next to the hot jet, with the cool matter
rising and falling, like in an Hα surge, also occurs naturally both in the 3D
and 2D numerical models cited above (and was already introduced by
Yokoyama1995 in an early 2D model). The phenomenon has been studied in depth
by Nobrega2017; Nobrega2018 using the realistic material properties and
radiative transfer provided by the Bifrost code, which, in particular,
facilitate the study of plasma at cool chromospheric temperatures. A snapshot
of one of the experiments by those authors showing a temperature map and with
indication of some major features is given in Figure 3.11 (right panel). In
their model, the magnetic field can accelerate the plasma with accelerations
up to $100$ times the solar gravity for very brief periods of time after going
through the reconnection site because of the high field line curvature and
associated large Lorentz force. In the advanced phase of the surge, instead,
the cool plasma basically falls with free-fall speed, just driven by gravity,
as had been tentatively concluded in observations (nelson2013). The velocities
obtained from the observations in the present chapter broadly agree with those
obtained in the numerical models.

##  Chapter 4 Role of solar jets as a driver of large scale coronal
disturbances

###  4.1 Introduction

Solar jets are occasionally associated with the large scale solar filament
eruptions (Janvier2014a; Chandra2017). Solar filaments are dense and cool
material suspended in the hot solar corona along PILs. They are found to be in
magnetic dip regions. There are two main magnetic configurations for filaments
namely sheared arcade and FR. In the sheared arcade configuration, the arcade
connects the opposite polarities on either sides of a PIL, whereas in the case
of the FR configuration the magnetic field has helical magnetic structure.
Several models have been proposed for the solar eruptions (Aulanier2014;
Vrsnak2014; Filippov2015; Schmieder2015). Catastrophic loss of equilibrium or
torus instability is the important mechanism for the solar eruptions
(Forbes1991; Kliem2006; Demoulin2010). In these models, it is assumed that the
overlaying magnetic field (Bex) decreases with the increase of the height (z)
from the photosphere i.e. Bex $\propto$ z-n. The FR 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 (Torok2005; Isenberg2007;
Aulanier2010; Zuccarello2017). Using different observations including high
resolution SDO data and multi–view STEREO observations it was found that this
value lies between 1 and 1.5 in observed eruptions (Filippov2001;
Filippov2013; Zuccarello2014; McCauley2015). In addition to failed, partial
and full filament eruptions, recently two filament eruptions were observed
with the quasi-equilibrium state in the middle part of a two-step process
(Byrne2014; Gosain2016). 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 Byrne2014 this time was rather short i.e. $\sim$ one hour and
for the case of Gosain2016 the time was 15 hrs. Such cases are very crucial
and play an important role in understanding the Sun–Earth connections.

CMEs have attracted the solar physicists greatly as they are playing a
significant role in affecting the Earth’s space environment. Usually CMEs are
associated with large scale solar eruptions, i.e., two–ribbon flares
(NJoshi2016; Zuccarello2017), filament eruptions (Schmieder2013;
RChandra2017), and occasionally with small scale solar eruptions, i.e., solar
jets (Shen2012; Jiajia2015; Zheng2016; Sterling2018). Shen2012 reported two
simultaneous CMEs associated with a blowout jet. One of the two CMEs was
bubble-like and the other was jet–like. The authors suggested that the
external magnetic reconnection produced the jet–like CME and also led to the
rise of a small filament underneath the jet base. Further, they explained that
the bubble–like CME is due to the internal reconnection of the magnetic field
lines. Jiajia2015 observed a coronal jet event which led to a high-speed CME
(1000 km s-1), suggesting that large–scale eruptions could be triggered by a
small–scale jet. Zheng2016 reported another similar event as a case study of
solar jet activity which developed into a CME eruption. However, the number of
such jet–CME associated cases are very less reported in the literature to
understand the mechanism and kinematic processes behind the phenomenon.

Solar jets are small scale plasma eruptions due to magnetic reconnection and
act as a driver of large scale eruptions i.e. solar filament eruptions and
CMEs. In this chapter two different cases are analysed for the large scale
eruptions triggered by a solar jet. In the first case study a two step
filament eruption from the AR NOAA 12297 on March 14-15, 2015 is studied. This
filament eruption starts to erupt after triggered from the jet which initiates
from the same AR and afterwards the filament remains in a meta-stable stage
for more than 10 hours. Again a jet hits the meta stable filament and the
filament finally erupts from the solar surface followed by the largest
geomagnetic storm of solar cycle 24. In the second case study a jet event is
analysed followed by a CME on April 28, 2013 which provides evidence of clear
association of the jet and the CME. The jet erupted with an initial speed of
$\approx$ 200 km s-1 and developed into a CME of speed $\approx$ 450 km s-1
together with the ambient coronal structures.

###  4.2 Two-step filament eruption triggered by jets

The AR NOAA 12297 produced the largest geomagnetic storm (Dst index $\sim$
-223 nT) of solar cycle 24 on March 17, 2015. This geomagnetic storm was
associated with a GOES C9.1 class flare of March 15, 2015 and a filament
eruption, which was triggered and derived by solar jets from the same AR. The
AR NOAA 12297 was located at S22W25 on March 15, 2015. Further the filament
eruption was associated with a halo CME. This filament was disturbed on March
14, 2015 by a small solar jet and finally totally erupted with a further push
by an another solar jet on March 15, 2015. The event was observed by AIA
onboard SDO in different UV and EUV wavelengths. The event was also observed
by the Global Oscillation Network Group (GONG) in Hα line center. For the
magnetic field, we have used the data from the HMI onboard SDO. The
observational description of the filament activation and eruption on 2015
March 14-15 observed by different instruments is presented in following
Section 4.2.1.

Figure 4.1: Evolution of the filament on March 14, 2015. Left column : AIA 193
Å, middle column: AIA 304 Å, and right column: Hα observations. The position
of jet 1 is shown by the white arrow.

####  4.2.1 Morphology of the two step filament eruption

Figure 4.1 shows the evolution of the filament on March 14, 2015 in AIA 193 Å
(first column), 304 Å (second column), and GONG Hα (third column). Before any
activity in the filament it has a long sigmoidal shape (Figure 4.1 a, e, f,
and also yellow arrow). We can see the sinistral barbs in GONG Hα images
(Figure 4.1 (i)). This suggests the filament have a positive twist and hence
the 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 majority of positive/negative
helicity solar features are located in the southern /northern hemisphere
respectively (Pevtsov1995). Around 11:50 UT a jet activity started in the
active region, we name it as jet 1 and mark by the white arrow in Figure
4.1(b). This jet activity was visible almost in all EUV/UV and Hα wavelengths.
Due to this jet activity the left southern part of the sigmoidal filament was
disturbed. Afterwards a strand of the filament separated from the main body,
rose upwards and became stable after a displacement of $\approx$ 125 Mm. The
broken part of the sigmoidal filament is labeled by F1 and indicated by the
red arrow in Figure 4.1 (c). At the same time, we have observed flare
brightening in the AR as a GOES C2.6 class flare. The upper–right part of the
filament channel, which did not disturb in this period is shown by blue arrows
in Figure 4.1(c).

Figure 4.2: Evolution of the filament on March 15, 2015. Left column : AIA 193
Å, middle column: AIA 304 Å, and right column: Hα observations. The position
of jet 2 is shown by the white arrow.

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 upto 00:45 UT on
March 15, 2015. Around 00:45 UT on March 15, 2015 we again observed the
jet/surge activity in the AR towards the west-south direction and it
interacted with the filament F1 as well as with the big northern filament
(indicated by three blue arrows). We label this jet as jet 2. After 00:45 UT
the filament F1 started to erupt and finally it went away from the solar
surface. The evolution of the erupting filament is shown in Figure 4.2. The
left, middle and right columns of Figure 4.2 show the development of the
erupting filament F1 in AIA 193 Å, 304 Å, and Hα wavelengths respectively. The
eruption was associated with the C9.1 class GOES flare. The flare has two
ribbon structure visible in different EUV and Hα images. We can also see the
ribbon separation as proposed by CSHKP model. The flare was also observed in
hard X-rays by the RHESSI satellite and studied by Wang2016.

The major upper part of the sigmoidal filament channel (indicated by blue
arrows in Figure 4.2) was also perturbed during the ejection of jet 2. The
material of the filament rose–up and later–on it came back to the foot–points
of the filaments. In AIA channels it becomes brighter and we can also see its
twisted structure. From Figure 4.2(d), one can infer that the twist is
right–handed, which is consistent with the sinistral filament chirality seen
in Hα data. Therefore, we see here the same sign of twist in the chromosphere,
the upper solar atmosphere and in the associated MC. It seems that Jet 2
injects impulse and heat into the filament at its eastern end. Previously
static filament material comes in motion along helical field-lines of the FR.
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 FR but it does not change significantly its position, and after the
energetic phase of the event the filament restores to its approximately
initial state. During the activation the filament becomes less visible in the
Hα wavelength (Hα images in the third column of Figure 4.2) most likely for
two reasons. The Doppler shift in the moving material can remove its Hα line
out of the filter passband (dynamic disappearance), and the heating of the
filament can suppress the absorption of Hα radiation (thermal disappearance).

####  4.2.2 Evolution of the filament eruption

To investigate the height-time evolution of the filament eruption during March
14-15, 2015 we have selected a slit along the direction of the filament
eruption in AIA 193 Å data. The position of the slit is shown by the dashed
black line in Figure 4.3 (a). The time-distance diagram is given in Figure 4.3
(b). In the time-distance diagram, we can clearly see the two step eruption of
filament. In first step, the filament starts to at rise at $\sim$ 12:00 UT on
March 14, 2015 and attains a projected height of 125 Mm, as also discussed in
Section 4.2.1). Due to the projection effect, this is the minimum value of
height. The real height must be of larger value. Unfortunately we do not have
STEREO observations, which could tell about the true height of the eruption.
We computed the speed of this eruption and it was found $\sim$ 40 kms-1. After
13:00 UT the filament stops to rise and stays at the same height upto 00:45 UT
on March 15, 2015. In the second step after March 15, 2015 00:45 UT, the
filament starts to rise and finally fully erupts. The calculated speed of the
second step eruption was 70 kms-1.

Figure 4.3: (a) AIA 193 Å image showing the location of a slit select for the
time–slice analysis. (b)Time-slice image of the eruption during March 14-15,
2015. Figure 4.4: Development of CME on March 15, 2015 observed by LASCO C2
(top panel, red arrows) and C3 (bottom panel, yellow arrows). The black arrow
indicates the CME of March 14, 2015.

####  4.2.3 CME observation associated with the filament eruption

The CME associated with the filament eruption on March 15, 2015 was observed
with the LASCO instrument. As reported in Wang2016, during the C2.6 class
flare of March 14, 2015 a small filament erupted (their Figure 1 (a), F4
filament) and there was a slow CME observed in LASCO C2 field–of–view (FOV) at
$\sim$ 13:30 UT. The speed and the angular width of this CME was 208 kms-1 and
160∘ respectively. By the push from jet 1, the F1 filament eruption on March
15, 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 4.4. 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 AR on March 14, 2015.
According to the LASCO CDAW Catalog (Gopalswamy2009) the average CME speed was
719 kms-1 and the acceleration was -9.0 ms-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, Liu2015 reported the maximum CME speed was 1100 kms-1.
In C3 the FOV the CME of March 14-15, 2015 interacted at 02:18 UT. Liu2015
considered the interaction of these CMEs as the cause of the largest
geomagnetic storm of solar cycle 24 on March 17, 2015.

####  4.2.4 Decay index distribution for the jet driven filament eruption

In order to find the reasons why the part F1 of the initial filament erupted
after 12 hrs delay in an intermediate state, while the remainder of the
filament does 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 AR. In principle, the decay index should be calculated for the coronal
field external to the FR. It is reasonable to assume that major coronal
currents in the volume of interest are contained within the FR. For the
magnetic field of currents below the photosphere, the coronal potential field
is a rather good approximation.

We need the potential magnetic field distribution in the corona at heights of
prominences, which are much less than a solar radius. Therefore, we can use a
restricted area of a photospheric magnetogram as the boundary of the
calculation domain and neglect its sphericity considering as a part of a flat
surface and use the well-known solution for half-space with a plane boundary
in terms of Green’s functions (Filippov2001; Filippov2013). When we cut out a
rectangular area around the filaments under study from the full disk
magnetogram, we ignore the contribution of the magnetic sources outside of it.
Such simplification is reasonable if the main sources of the field lie within
the cut-out area. In our case the AR NOAA 12297 is the strongest magnetic
source on the disk and is rather distant from other ARs. On March 14 and
especially on March 15 the AR is at a considerable distance from the central
meridian, so we need to take into account the projection effect. We construct
for the boundary condition the data array with the equal angular size of
pixels and assume the projection of the line-of-sight-field on the normal as
the radial component. Thus we obtain the rectangular area of the magnetogram
that looks as if the region were located at the center of the disk.

Figure 4.5 (a) represents the modified fragment of the magnetogram taken by
the HMI on March 14, 2015 at 15:00 UT, which was used as a boundary condition
for the potential magnetic field calculations. The pixel-size in HMI
magnetograms is $\sim$ 0.5$\leavevmode\nobreak\ \\!\\!{}^{\prime\prime}$ or
$\sim$ 0.36 Mm, which is very small compared with the expected height of a
filament > 10 Mm. To save computational time we applied binning several times
and increased pixel-size up to $\sim$ 10 Mm. Figure 4.5(b)–(f) show the
distribution of the decay index from equation 2.3, where Bex is the horizontal
magnetic-field component and z (or h) is the height above the photosphere, at
different heights above the area shown in the panel (a). The thin lines show
isocontours of n = 0.5, 1, 1.5, while the thick red lines indicate the
positions of PILs at respective heights. Areas where n > 1 are shadowed. Green
contours show the position of the filament taken from the co-aligned
Kanzelhoehe Hα filtergram transformed in the same way as the magnetogram
(Figure 4.6). 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).

Figure 4.5: (a) HMI magnetogram of the selected area OF THE AR. Distribution
of the decay index ‘n’ at different heights above the area shown in panel (a).
Red line indicate the position of the PILs.

A PIL is a favorable place for horizontal equilibrium of a FR, because the
vertical component of the coronal field vanishes. Any PIL at any height can be
considered as a potential location of the FR, but it is only a necessary
condition. Another necessary (but again not sufficient) condition for the
stable equilibrium is the quantity of the decay index below the critical
value. In fact, FRs may be found only in few places where both conditions are
fulfilled. In Figure 4.5, the segments of PILs within white areas (or at least
outside of isocontours 1.5) are the places favorable for the flux-rope stable
occurrence. Below 60 Mm (Figure 4.5 (c)) the segments of the PIL near both
green contours are suitable for stable FRs. The contour n = 1 touches the PIL
near both filaments at the height of 75 Mm (Figure 4.5 (d)), while the contour
n = 1.5 touches the PIL near the southern filament at the height of 100 Mm
(Figure 4.5 (e)) and near the western filament at the height of 120 Mm (Figure
4.5 (f)).

Unfortunately, we cannot measure directly the height of the filaments because
STEREO was in an unfavorable position. However, we can estimate the heights
using the method proposed by Filippov2016. It is based on the confirmed by
observations assumption that the material of filaments is accumulated near
coronal magnetic neutral surfaces Br = 0 (Filippov2016b). 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 heights of different parts of the filament including its top, or spine,
which is the most reliable indicator of the flux-rope axis.

Figure 4.6: Kanzelhoehe Hα filtergram of the same region as in Figure 4.5 (a)
taken at the same time with superposed PILs at different heights.

Figure 4.6 shows the fragment of the Kanzelhoehe Hα filtergram of the same
region as in Figure 4.5 co-aligned with the magnetogram and transformed in the
same way. The same PILs as in Figure 4.5 (b)-(f) are shown but every PIL is
shifted in x and y coordinates by values (Filippov1999; Filippov2009;
Chandra2017):

$\Delta x=htg\lambda_{0}\leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ and\leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \Delta y=htg\varphi_{0}$ (4.1)

where, h is the height of the PIL, $\lambda_{0}$ and $\varphi_{0}$ are
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 are
blue. The spine of the western filament follows exactly the PIL at the height
of 30 Mm. All 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 4.6 shows the filament and the neutral surface on
March 14 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.

We found that a big filament located at the periphery of a strong AR undergo 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
(Woods2011; Su2012) suggested that two peaks in light-curves appear due to two
stages of a single event associated with the delayed eruption of a CME. They
presented AIA EUV observations of the limb March 8, 2011 event in which a FR
accelerates in the first stage up to 120 km s-1, then the speed decreases to
14 km s-1, and in the second stage, started after 2 hrs after the beginning of
the event, it accelerates again and becomes the CME with a speed of $\sim$ 500
km s-1. Byrne2014 also analysed this event and suggested that either the kink-
instability or torus-instability of the FR may be 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
magnetic configuration and were not very certain with the supposed torus
instability without calculations of the decay index. Gosain2016 studied two-
step eruption of a quiescent filament on October 22, 2011. It was observed
from different viewpoint by SDO, SOHO, and STEREO. The CME associated with the
filament eruption and two bright ribbons in the chromosphere both appear 15
hrs after the start of the event. Computation of the decay index showed that
there were zones of stability and instability that alternate in the corona.
Below 100 Mm the equilibrium was stable, then the zone of instability follows
from 100 to 500 Mm that gave place to the zone of stability again. Above a
height of 600 Mm the PIL disappeared, which hinted on the possibility for the
FR 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 FR was not clearly observed in the intermediate
position and magnetic field calculations at great heights, above 400 Mm, were
not too reliable.

###  4.3 Cause and kinematics of a jet–like CME

For the jet-CME relationn, this case study presents a jet event followed by a
CME on April 28, 2013 which provides evidence of clear association of the jet
and the CME. The jet erupted with an initial speed of $\approx$ 200 km s-1 and
developed into a CME together with the ambient coronal structures.

####  4.3.1 Observational analysis of jet and narrow CME

The observational data for the jet eruption and the CME is taken from SDO,
STEREO, and SOHO/ LASCO. For the multi-thermal jet structure, we analysed the
AIA data in 131 Å, 171 Å, 193 Å, 211 Å, and in 304 Å. For a better contrast of
the hot and cool counterparts of the jet, we create the base and running
difference images of the AIA data. To probe the jet and CME from multiple
perspectives the EUV images taken by SECCHI are analysed. For our current
analysis of the jet, we use the EUV images of _STEREO_ –B in 304 Å with a
cadence of 10 minutes and pixel size of 1 arcsec. _STEREO_ –A and B were
separated by 83∘ on April 28, 2013. The CME is well observed with SOHO/LASCO
and _STEREO_ /COR coronagraphs. With the multi-point observations from LASCO
and COR, we employ the Graduated Cylindrical Shell (GCS) model to obtain the
three-dimensional height and direction of the CME (section 4.3.3). We further
analyse the photospheric magnetic field using the line-of-sight magnetograms
from HMI instrument. For a closer and clear view of the jet source region, we
use HMI SHARP data set with a cadence of 12 minutes.

Figure 4.7: The observed jet (a1-a2) and height–time analysis (b1-b3) with AIA
304 Å on April 28, 2013. Jet material falls back in the direction of S2 into
the source region with a speed of $\approx$ 60 km s-1.

####  4.3.2 Kinematics of the jet

The jet started to erupt $\approx$ 20:53 UT with a circular base, towards the
northern direction from the AR NOAA 11731 (N09E23) and observed in all six AIA
channels (94 Å, 131 Å, 171 Å, 193 Å, 211 Å, and 304 Å). After reaching to some
height at about 80 Mm, the jet material was deflected from its original
direction of propagation and revolved around the north–east direction. The jet
was initially bright (Figure 4.7 (a2), and afterwards followed with dark
material (Figure 4.7 (a1)), suggesting impulsively strong heating at the
initial phase. The following dark material was only visible in AIA 304 Å and
not observed in hot channels, i.e. 171 Å. The propagation of the whole jet in
AIA 304 Å is shown in Figure 4.7 (a1) along with the red curve C1, which
indicates the deflection of the jet from north direction to north–east
direction towards the solar limb. The initiation of the jet from the source
region is shown in panel (a2). We also observed a small jet ejection at about
21:24 UT in the eastern neighbourhood of the source region, and this jet
material merged with the big jet. Panel (b1) is the height–time plot of the
jet along the slit C1. The jet speed shows a two–stage profile. The speed in
the later stage is about 80 km s-1 towards the north–east direction (red
dotted line). For the velocity in the initial stage, we set two slits S1 and
S2 (panel (a2) of 10 pixel width in two different directions, and found that
the speed in the S1 direction is 200 km s-1 and that the other direction S2 is
about 160 km s-1 (as presented in panel (b2) and (b3)). In addition to this,
we found that a portion of the jet material falls back to the source region
around 21:51 UT with a speed of $\approx$ 60 km s-1, clearly appeared in
height–time plot along S2 direction in panel (b3).

Figure 4.8: The leading edge of the jet material in AIA 304 Å (a) and in
_STEREO_ –B EUV 304 Å (b). The $+$ sign shows the location of the leading edge
of the jet obtained from the SCC-MEASURE technique.

From $\approx$ 21:16 UT, _STEREO_ –B observed the cool counterpart of a jet in
304 Å above the western limb. The full-disk image of AIA 304 Å and _STEREO_ –B
EUV 304 Å is presented in Figure 4.8. The highest visible peak of the jet is
indicated with a circle at the solar limb which is used to get the read jet
speed. Figure 4.9 (panel (c)) showed the locations of _STEREO_ satellite, the
Earth and the Sun. With the aid of SCC-MEASURE procedure, we get the real
speed and propagation direction of the jet by clicking on the same feature in
AIA 304 Å and in _STEREO_ –B 304 Å image. The real jet-speed was 200 km s-1
towards the north–east (longitude = -18∘, latitude = 19∘) direction. However,
this correction can be only applied to the second stage of the jet when it was
propagating towards the north–east direction, because we do not have the
stereoscopic observations for the early stage of the jet.

Figure 4.9: CME associated with the jet is observed by LASCO and _STEREO_
coronographs. The direction of the slit for this height–time analysis is shown
in panel (a) with red dashed line. Figure 4.10: CME associated with the jet
eruption analysed with GCS model, which indicates the direction of propagation
of the CME in _STEREO_ COR2, and LASCO C2 with a speed of 450 km s-1.

####  4.3.3 Kinematics of the CME

The associated CME was well observed with SOHO/LASCO and _STEREO_ –B COR1 and
COR2 coronographs, as shown in Figure 4.9. The CME is not a typical one. It is
narrow (width $\approx$ 25∘), and likes a giant jet in the corona, no matter
from which perspective the CME was viewed. The jet–CME association is very
much evident in _STEREO_ –B observations (Figure 4.9 (e)). For the continuous
tracking of the solar jet in EUV channel (304 Å) and the CME in coronagraphs,
we put a slit in the jet–CME direction in _STEREO_ –B EUV 304 Å, COR1 and
COR2. The direction of the slit is shown in Figure 4.9 (a). The continuous
spatial and temporal correlation between the jet and the CME is presented in
Figure 4.9 (e). The front of the CME is much higher than the jet front and the
separation between them is due to the expansion of the CME, causing the speeds
of their fronts are different. If extrapolating them back to the solar
surface, they almost originated from the same time.

To reduce the projection effect, we use the GCS model to get the real
kinematic properties of the CME. The GCS model is developed to represent the