# Evolutionary stages and triggering process of a complex eruptive flare with
circular and parallel ribbons

Navin Chandra Joshi,1,2 Bhuwan Joshi,1 and Prabir K. Mitra1,3
1Udaipur Solar Observatory, Physical Research Laboratory, Udaipur 313 001,
India
2Department of Physics, SRM University, Delhi-NCR, Sonepat-131029, Haryana,
India<EMAIL_ADDRESS>
3Department of Physics, Gujarat University, Ahmedabad 380 009, India E-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted 2020 November 2. Received 2020 October 23; in original form 2020
March 21)

###### Abstract

We report multi–wavelength study of a complex M–class solar eruptive flare
that consists of three different sets of flare ribbons, viz. circular,
parallel, and remote ribbons. Magnetic field modeling of source active region
NOAA 12242 exhibits the presence of 3D null–point magnetic topology which
encompasses an inner bipolar region. The event initiates with the faint
signatures of the circular ribbon along with remote brightening right from the
pre–flare phase which points toward the ongoing slow yet persistent null–point
reconnection. We first detected flux cancellation and an associated
brightening, which are likely signatures of tether-cutting reconnection that
builds the flux rope near the polarity inversion line (PIL) of the inner
bipolar region. In the next stage, with the onset of M8.7 flare, there is a
substantial enhancement in the brightening of circular ribbon which
essentially suggests an increase in the rate of ongoing null–point
reconnection. Finally, the eruption of underlying flux rope triggers “standard
flare reconnection" beneath it producing an abrupt rise in the intensity of
the parallel ribbons as well as enhancing the rate of null–point reconnection
by external forcing. We show that within the the fan dome, the region with
magnetic decay index n>1.5 borders the null-point QSL. Our analysis suggests
that both the torus instability and the breakout model have played role toward
the triggering mechanism for the eruptive flare. This event is a nice example
of the dynamical evolution of a flux rope initially confined in a null-point
topology, that subsequently activates and erupts with the progression of the
circular–cum– parallel ribbon flare.

###### keywords:

Sun:flare – Sun:activity – Sun:X–rays, gamma rays – Sun:magnetic fields –
Sun:coronal mass ejections (CMEs)

††pubyear: 2020††pagerange: Evolutionary stages and triggering process of a
complex eruptive flare with circular and parallel ribbons–LABEL:lastpage

##  1 Introduction

Solar flares occur due to transient and explosive release of magnetic energy
in the solar corona. This magnetic energy is stored in the highly sheared and
twisted magnetic field associated with active regions (ARs). The released
energy is converted to heat the plasma as well as to accelerate the electrons
and other particles (Benz, 2008; Shibata & Magara, 2011).

Various theories/models have been proposed to explain solar flares and
associated eruptions (Forbes, 2000; Lin et al., 2003; Schmieder et al., 2013).
In the well known two–dimensional (2D) “CSHKP" model of eruptive solar flares
(Carmichael, 1964; Sturrock, 1966; Hirayama, 1974; Kopp & Pneuman, 1976), the
reconnection occurs underneath the erupting filament or the flux rope in a
vertical current sheet. The eruption of the filament or the flux rope proceeds
to give a coronal mass ejection (CME). The flare arcades form underneath the
vertical current sheet. This model also successfully explains the formation of
parallel flare ribbons at chromospheric heights along either side of polarity
inversion line (PIL).

The standard flare model does not explain how the eruption is triggered in the
first place. Further, the explanations for various three–dimensional (3D)
aspects of the eruptive flares are beyond the scope of the standard flare
model, such as shear in the flare loops (e.g., Aulanier et al., 2012),
converging motions of flare ribbons and X-ray footpoint sources (e.g., Joshi
et al., 2009; Joshi et al., 2017a) and, J–shaped ribbons (e.g., Chandra et
al., 2009; Joshi et al., 2017a). To incorporate these complex observational
features Aulanier et al. (2012); Janvier et al. (2013) further described a 3D
model based on numerical simulation. This is a magnetohydrodynamics (MHD)
model which considers a flux rope that lies in a sigmoidal AR (Savcheva et
al., 2012). During the build–up phase of the flux rope, the current sheet
forms underneath it. The flux rope undergoes eruption due to the torus
instability (e.g., Kliem & Török, 2006; Aulanier et al., 2010). The magnetic
reconnection occurs in the current sheet beneath the erupting flux rope. The
current layers are associated with the quasi–separatrix layers (QSLs; Titov &
Démoulin, 1999), which are the regions where the magnetic connectivity has
strong gradients. The nature of the reconnection within the QSLs is of a
slipping type where the magnetic field lines continuously exchange their
connectivity with the neighboring field lines. As a result, the apparent
slipping motions of the field lines are observed (e.g., Dudík et al., 2016).

Circular ribbon flares occur in a 3D magnetic configuration and consist of
ribbons that present circular or semi–circular morphology (e.g., Masson et
al., 2009; Reid et al., 2012; Wang et al., 2012; Jiang et al., 2013; Sun et
al., 2013; Vemareddy & Wiegelmann, 2014; Joshi et al., 2015, 2017b; Hernandez-
Perez et al., 2017; Xu et al., 2017; Li et al., 2018; Zhong et al., 2019).
Circular ribbon flares exist because of the reconnection in a 3D null–point
topology (e.g., Török et al., 2009; Masson et al., 2009; Wang et al., 2012;
Sun et al., 2013; Joshi et al., 2017b). The photospheric magnetogram
observations for such a null–point topology show a central compact polarity
surrounded by a polarity of opposite sign (e.g., Sun et al., 2013; Joshi et
al., 2017b, 2018b). In corona, it involves a set of closed field lines (i.e.,
the lines enclosed below the fan) connecting the central compact polarity to
the surrounding polarity. In this configuration, we further recognize field
lines over the fan, which join the surrounding polarity to the far away remote
region of polarity with the same sign as that of central compact polarity. In
this topology, the fan itself is a separatrix surface and the spine is a
singular line that intersects the fan at the null–point. Reconnection can
occur between the magnetic fluxes below and above the fan surface. When
magnetic fields reconnect at null–point, they pass through the fan separatrix
surface and jump from the inner to the outer connectivity domain. Particles
accelerated at the reconnection site (i.e., the null–point) propagate along
the fan field lines which are anchored close to the fan surface, hence the
formation of the circular ribbon. Numerical simulations of this type of 3D
reconnection and circular ribbon flares have also been explored in some of the
studies (e.g., Masson et al., 2009; Pariat et al., 2009; Török et al., 2009;
Jiang et al., 2013; Nayak et al., 2019). Here, we also highlight some
interesting examples of the null–point reconnection that involves external
forcing below the null point e.g., filament and/or the flux rope eruption from
inside the fan–dome (Jiang et al., 2013, 2014; Sun et al., 2013; Liu et al.,
2015; Joshi et al., 2015, 2017b, 2018a); shearing of the dome field lines
(e.g., Vemareddy & Wiegelmann, 2014; Xu et al., 2017; Li et al., 2017).

The solar flares which are associated with the eruption of the filaments
and/or flux ropes are known as eruptive solar flares. Two representative
models – tether–cutting and breakout – invoke magnetic reconnection as the
triggering mechanism of the eruption of the flux rope. The tether–cutting
scenario has been suggested long back (Sturrock et al., 1984; Moore &
Roumeliotis, 1992) and extended later on by Moore et al. (2001). According to
this model, the initial low lying tether–cutting magnetic reconnection at the
PIL is responsible for the formation of the flux rope as well as its
subsequent destabilization. Several observational studies provide substantial
support for the tether cutting model to explain the flux rope eruptions (e.g.,
Yurchyshyn et al., 2006; Chifor et al., 2007; Raftery et al., 2010; Fan, 2012;
Liu et al., 2013; Joshi et al., 2017b, 2018a; Mitra et al., 2020a). The
investigations of temporal and spatial evolution of the X-ray emission during
the precursor phase together with the activation of underlying flux rope
structure (e.g., filament and hot channel) are considered as important
signatures for the tether-cutting magnetic reconnection (e.g., Chifor et al.,
2007; Kim et al., 2008; Joshi et al., 2011, 2013b; Mitra & Joshi, 2019; Sahu
et al., 2020). The magnetic reconnection associated with the growth and
evolution of flux rope along with associated flare loops during an eruptive
flare has been substantiated in the standard flare model in 3D (Aulanier et
al., 2012, 2013; Janvier et al., 2013). Here the current sheet forms inside
the sheared arcade and magnetic reconnection builds–up the flux rope. As the
flux rope forms and rises, the current sheet extends due to the elongation of
the flux rope. Thus the role of magnetic reconnection forming the flux rope in
3D model can be considered similar to the tether–cutting process.

Breakout model of the solar eruption was proposed by Antiochos et al. (1999)
and it relies on resistive instability. They began with quadrupolar magnetic
configuration having a single null point in 2.5 dimensional (2.5D)
axisymmetric spherical geometry. The model recognizes that the early
reconnection (i.e., breakout process) at the magnetic null, lying well above
the core field region, can trigger the eruption of core fields. The breakout
model was further manifested in 3D null point configuration (Lynch et al.,
2008, 2009; Wyper et al., 2017). The 3D configuration typically consists of a
fan separatrix surface between two different flux system, spine line and a 3D
magnetic null point (e.g., Lynch et al., 2008, 2009). The reconnection occurs
at 3D magnetic null point (e.g., Aulanier et al., 2000; Sun et al., 2013; Liu
et al., 2015; Xu et al., 2017; Li et al., 2018; Wyper et al., 2017).
Observational evidences for the breakout model has been identified in various
studies (e.g., Sterling & Moore, 2001; Manoharan & Kundu, 2003; Gary & Moore,
2004; Sterling & Moore, 2004; Deng et al., 2005; Pohjolainen et al., 2005;
Joshi et al., 2007; Aurass et al., 2011; Chen et al., 2016; Mitra et al.,
2018). Aulanier et al. (2000) observed a typical fan–spine type magnetic
configuration with a 3D null–point and interpreted the reconnection at the
magnetic null–point to be a “magnetic breakout" process. Sun et al. (2013) and
Xu et al. (2017) conducted multiwavelength studies of circular ribbon flares
and compared the flare morphology with that obtained from magnetic field
extrapolation. Those studies identified null-point reconnection, suggesting
that the triggering mechanism of the eruption may be the breakout.

The contemporary studies recognize the eruption of twisted flux ropes by ideal
instabilities, viz., kink (e.g., Török et al., 2004) and torus (e.g., Török &
Kliem, 2007) instabilities. In the context of present study, we briefly
discuss the latter one. Torus instability occurs when the flux rope reaches a
region where the decay index is greater than 1.5 i.e., the critical value of
decay index (e.g., Török & Kliem, 2007; Aulanier et al., 2010). However, some
studies point toward a range in the decay index rather than a single critical
value, such as, 1.5–1.75 (e.g., Liu, 2008; Kliem et al., 2013) and 1.3–1.5
(e.g., Zuccarello et al., 2015).

Recently, few cases of typical flares that consist of two sets of ribbons –
two parallel and one circular ribbon – have also been reported (Joshi et al.,
2015; Carley et al., 2016; Joshi et al., 2017b; Devi et al., 2020). The first
observation of this kind was reported by Joshi et al. (2015) where they
proposed a scenario in which two stages of magnetic reconnection explained the
formation of two different sets of flare ribbons. Later on, Carley et al.
(2016) studied the same event using Nançay radioheliograph radio data and
supported the scenario. These types of events occurred in a typical 3D
null–point magnetic configuration with multiple steps in the activation and
eruption of the flux rope (Joshi et al., 2015, 2017b). In all these cases, we
find that the flux rope eruption and associated standard reconnection occur
prior to the null–point reconnection. Regardless of the timing in the
evolution of circular and parallel flare ribbons, the topology is almost
always the same: a flux rope is enclosed below the fan surface of a null–point
topology. In the present work, we study a complex circular ribbon flare during
which parallel ribbons are also formed within the extension of the circular
ribbon after an interval of about 30 min. Further, the circular ribbon flare
was eruptive in nature with clear signatures of flux rope activation and
eruption in the source region which eventually resulted into a CME. The event
under investigation occurs in the AR NOAA 12242 on 2014 December 17. The event
further gives us an opportunity to explore the triggering mechanism of the
eruption in the light of contemporary theoretical understandings. The overall
organization of the paper is as follows. Section 2 shows the description of
the observational data set and the related instruments used for this work. The
magnetic field configuration over the AR and the changes of the magnetic field
near the inner PIL are discussed in Section 3. Section 4 describes the
multi–wavelength analysis of this event including the temporal evolution of
flare (Section 4.1), the characterization of various phases of the event and
the discussion of associated CME (Section 4.2), and the analysis of RHESSI
X–ray data (Section 4.3). The main results and discussions are presented in
Section 5 and conclusions in Section 6.

##  2 Observational Data Set

Multi–wavelength data set is used to analyze this flare event. We mainly use
data from Atmospheric Imaging Assembly (AIA; Lemen et al., 2012), Helioseismic
and Magnetic Imager (HMI; Schou et al., 2012), the Geostationary Operational
Environmental Satellite (GOES), and the Reuven Ramaty High Energy Solar
Spectroscopic Imager (RHESSI; Lin et al., 2002) instruments. AIA observes the
Sun in seven Extreme Ultraviolet (EUV) (i.e., 304, 131, 171, 193, 211, 335,
and 94 Å), two Ultraviolet (UV) (1600 and 1700 Å), and one white light
wavelengths. It has a temporal cadence of 12 s for EUV images, 24 s for UV
images and 1 hr for white light images with the pixel size of $\rm
0.6\arcsec$. AIA 131 Å data is used to study the pre–eruptive phase, while the
AIA 94 Å data is used to study the eruption dynamics of the event. AIA 1600
and 304 Å wavelength images are utilized to investigate the flare ribbons and
remote brightening dynamics (RB). The line–of–sight photospheric magnetogram
having the temporal cadence of 45 s with the pixel size of $\rm 0.5\arcsec$ is
observed by HMI. Both AIA and HMI are the instruments on–board the Solar
Dynamics Observatory (SDO; Pesnell et al., 2012). Integrated full disk X–ray
flux at 1.0–8.0 Å and 0.5–4.0 Å wavelength bands are observed by GOES. X–ray
observations at energy bands ranging from 3 keV to 50 keV are obtained from
RHESSI. The image reconstruction is done with the CLEAN algorithm using front
detector segments only. Out of 9 detector segments, segments 3–8 (excluding 7)
are taken into account. To study the morphology of the associated CME we use
the Large Angle and Spectrometric Coronagraph (LASCO; Brueckner et al., 1995)
on board the Solar and Heliospheric Observatory (SOHO; Domingo et al., 1995).

To investigate the coronal magnetic field topology over the AR, we use
potential–field source–surface (PFSS, Wang & Sheeley, 1992; Schrijver & De
Rosa, 2003) as well as the optimization based non–linear force free field
(NLFFF, Wiegelmann et al., 2006, 2012) extrapolation methods. PFSS is an
IDL–based algorithm which is available in the SolarSoftWare package
(SSW111http://www.lmsal.com/solarsoft/). As boundary condition for the NLFFF
extrapolation, we used photospheric vector magnetograms from the
hmi.sharp_cea_720s series of SDO/HMI which were preprocessed as described in
Wiegelmann et al. (2006). The input parameters for preprocessing i.e., $\nu$,
$w_{los}$, $w_{trans}$, $\mu_{1}$, $\mu_{2}$, $\mu_{3}$, $\mu_{4}$ (see
Section 4.2.1 in Mitra et al., 2020b), were chosen to be 0.01, 1,
$\frac{B_{trans}}{max(B_{trans})}$, 1, 1, 0.001 and 0.01, respectively. The
extrapolations were done in a Cartesian volume of $510\times 180\times 180$
pixels with resolution 2$\arcsec$ which translates to a physical volume of
$\sim$740$\times 260\times 260$ Mm3. For visualization of the NLFFF lines, we
use Visualization and Analysis Platform for Ocean, Atmosphere, and Solar
Researchers software (VAPOR222https://www.vapor.ucar.edu, Clyne et al., 2007).
Using the extrapolated magnetic field, we calculated the net Lorentz force
($|\vec{J}\times\vec{B}|$), current-weighted angle between the modelled
magnetic field and electric current density, $\theta_{J}$, and the volume-
averaged fractional flux, $<|f_{i}|>$ (DeRosa et al., 2015) which can be
considered to assess the quality of the NLFFF extrapolation. The corresponding
values333For a perfectly solenoidal and force free magnetic field, the values
of the parameters assessing the quality of the extrapolation, such as,
$|\vec{J}\times\vec{B}|$, $\theta_{J}$, $<|f_{i}|>$ should be 0. However,
since the code essentially works on numerical calculations using real
magnetogram observations, non-zero finite values of these parameters are
expected. In general, NLFFF solutions returning the values
$|\vec{J}\times\vec{B}|\lesssim 10\times 10^{-3}$, $\theta_{J}\lesssim
10^{\circ}$, $<|f_{i}|>~{}\lesssim 20\times 10^{-4}$, are considered as good
NLFFF solutions (see, e.g., DeRosa et al., 2015; Thalmann et al., 2019). were
found to be $5.54\times 10^{-3}$, $8.98^{\circ}$ and $3.92\times 10^{-4}$. The
Quas–Separatrix Layer (QSL) is calculated within the extrapolation volume by
employing the code developed by Liu et al. (2016).

##  3 Evolution and configuration of magnetic field in AR 12242

Figure 1: (a) Full disk SDO/HMI line–of–sight photospheric magnetogram at
00:00:04 UT on 2014 December 17 with magnetic field lines obtained from PFSS
extrapolation method. (b) SDO/HMI line–of–sight photospheric magnetogram on
2014 December 17 at 03:00:24 UT. The red box over the panel (b) represents the
field–of–view of Figure 2(a). (c) SDO/AIA 4500 Å image at 03:00:07 UT on 2014
December 17. (d) SDO/AIA 304 Å image on 2014 December 17 at 03:00:07 UT,
showing the region of flaring activity. White box shows the area used to
calculate the SDO/AIA intensity profiles shown in Figure 4(b).

On 2014 December 17, AR NOAA 12242 was located at the south–west quadrant of
the Sun with heliographic coordinates S19W02. Figure 1(a), shows the full disk
SDO/HMI magnetogram at 00:00:04 UT on 2014 December 17 with PFSS extrapolated
field lines over the AR 12242. The zoomed image of the line–of–sight (LOS)
photospheric magnetogram corresponding to the box in Figure 1(a) is shown in
Figure 1(b). The magnetic configuration of the AR is very complex and
classified as $\rm\beta\gamma\delta$. The AR 12242 mainly consists of two
large (indicated by arrows in Figure 1(c)) and several small sunspots. The
northern and southern sunspots in AR 12242 correspond to the negative and
positive polarities, respectively (cf. Figures 1(b) and 1(c)). The AR
structure in the SDO/AIA 304 Å wavelength at 03:30:07 UT on 2014 December 17
can be seen in Figure 1(d). We note the existence of a large filament on the
west side of the AR (shown by the arrow in Figure 1(d)).

Figure 2: (a) SDO/HMI line–of–sight photospheric magnetogram at 04:00:24 UT on
2014 December 17. The central positive polarity and the surrounding negative
polarity regions are represented by the green and white ellipse, respectively.
The flux rope formation and remote brightening regions are marked by the red
box and yellow ellipse, respectively. ((b)–(d)) Zoomed view of the coronal
field lines showing the null–point topology in three different projections.
The yellow and red lines represent the inner dome and outer dome lines,
respectively. The cyan patch lying in between the yellow and red field lines
in panels (b)–(d) represents an isosurface of 4 Gauss that consists a magnetic
null–point.

Figure 3: ((a)–(c)) SDO/HMI line–of–sight photospheric magnetograms showing
the magnetic field changes near the inner polarity inversion line (PIL) region
(shown by the yellow circles). (d) The field lines obtained from the NLFFF
extrapolation method. The low–lying sheared field lines and the high–lying
less sheared field lines are shown by the purple and blue colors,
respectively. A set of field lines with a relatively higher twist are
represented by orange color lines. It is likely that the low lying sheared
field lines would form the flux rope due to magnetic field changes at the
inner PIL.

Detailed structures of the photospheric and overlying coronal magnetic field
configuration of AR are shown in Figure 2. Figure 2(a) represents the SDO/HMI
LOS photospheric magnetogram at 04:00:24 UT on 2014 December 17. It can be
observed that the AR consists of a compact patch of positive polarity (shown
by the green oval) surrounded by negative polarity region (shown by the white
oval). This type of photospheric magnetic field configuration is suggestive of
a 3D null–point magnetic topology in the corona (see e.g., Joshi et al., 2015,
2017b, 2018a). The field lines enclosed below the fan should connect the
central compact positive polarity to the surrounding negative polarity. There
also exists a bipolar type magnetic field configuration in between the central
compact positive polarity and the outer negative polarity with a sharply
defined PIL that resembles with an inverted S–letter (see the region enclosed
by the red box in Figure 2(a)). Hereafter, we call this inverted S–shaped PIL
as inner PIL. It can be anticipated that the field lines from the outer
negative polarity field region (shown by the white oval in Figure 2(a)) should
connect to the far south–westward positive polarity region (shown by the
yellow oval Figure 2(a)).

Figure 4: (a) GOES and RHESSI X–ray temporal profiles at different energy
channels from $\approx$03:30 UT to $\approx$07:00 UT on 2014 December 17. The
black solid and dotted lines represent the GOES X–ray flux profiles at 1.0–8.0
and 0.5-4.0 Å, respectively. The pink, red, green, and blue lines show the
RHESSI X–ray profiles at 3–6, 6–12, 12–25, and 25–50 keV energy bands,
respectively. Data gaps between $\approx$04:10 UT–$\approx$04:40 UT and
$\approx$05:45 UT–$\approx$06:19 UT are due to the night time and/or South
Atlantic Anomaly (SAA) period of the spacecraft. (b) SDO/AIA intensity
profiles from $\approx$03:30 UT to $\approx$06:30 UT on 2014 December 17. The
red, green, blue, and orange curves represent the AIA intensity profiles at
94, 131, 304, and $\rm 1600~{}\AA,$ respectively. The GOES X–ray profiles at
1.0–8.0 Å (solid black) and 0.5–4.0 Å (dotted black) are overplotted for
comparison.

In order to formalize the coronal magnetic topology of AR 12242, PFSS and
NLFFF extrapolation methods have been used. Both the extrapolation methods
show a closed 3D null–point topology over the AR (see PFSS and NLFFF results
in Figures 1(a) and 2(b)–(d), respectively). The NLFFF analysis reveals that
the central positive polarity region is connected with the outer negative
polarity regions by a set of closed field lines (shown by the yellow color in
Figures 2(b)–(d)). The outer negative polarity regions are also connected with
the far south–westward positive polarity region (i.e., the region co–spatial
with remote brightening (RB), described in Section 4) by another set of closed
field lines (shown by red color in Figures 2(b)–(d)). The null–point lies in a
region between the inner yellow and outer red field lines, over the central
compact polarity (shown by a cyan isosurface in Figures 2(b)–(d)). This
isosurface represents the magnetic field of 4 Gauss and situated at a height
of $\approx$36$\pm$1 Mm (shown by the arrow in Figure 2(d)).

Magnetic field near the inner PIL (shown inside the red box in Figure 2(a))
persistently experienced small–scale yet significant changes including
converging motions and moving magnetic features. The areas showing these
changes are marked by the three yellow circles (see Figures 3(a)–(c)). In the
middle circle, we clearly see the disappearance of few negative polarity
patches. Within the right side yellow circle, we see flux emergence as well as
the westward–moving magnetic features. We also observed similar small flux
changes within the left yellow circle. All these changes can be seen clearly
in the SDO/HMI animation attached with Figure 3. These magnetic changes (flux
cancellation, emergence, and moving magnetic features) close to the PIL
indicate that some magnetic stress and energy are injected in the AR through
the photospheric layer. More importantly, the NLFFF extrapolation result
demonstrates the presence of an extended set of low–lying sheared field lines
along the inner PIL which are shown by the purple–colored lines in Figure
3(d). We also obtained a few relatively highly sheared field lines which are
represented by orange color in Figure 3(d). The observed changes in the
magnetic field at the inner PIL play a crucial role in the formation process
of the flux rope via tether–cutting reconnection involving the low–lying
sheared arcades (see Subsection 4.2.1 and Figure 5). The converging motion of
the magnetic flux elements toward the PIL and flux cancellation are considered
to be the key ingredients of the tether–cutting process (Moore & Roumeliotis,
1992; Moore et al., 2001). Several earlier works confirm the role of these
observed processes during the formation and evolution of the flux rope (e.g.,
van Ballegooijen & Martens, 1989; Joshi et al., 2017a; Yardley et al., 2018;
Joshi et al., 2020).

##  4 Multi–wavelength observations of the eruptive flare

###  4.1 Flux profiles of GOES, RHESSI, and AIA

The temporal evolutions of X–ray flux (from GOES and RHESSI) and (E)UV
intensity (from AIA) during the flare are shown in Figure 4. The flare has
been classified as an M8.7 class flare in soft X–ray (Figure 4(a)). The soft
X–ray flux in 1.0–8.0 Å and 0.5-4.0 Å wavelengths undergo monotonic increase
from $\approx$04:18 UT, implying the onset of the flare. The flare emission
peaked at $\approx$04:51 UT in GOES 1.0–8.0 Å channel. It consists of a long
decay phase that lasts up to $\approx$07:00 UT. RHESSI X–ray flux profiles at
different energy bands (3–50 keV) are also overplotted in Figure 4(a). RHESSI
observed this flare event during the pre–flare phase, i.e., from
$\approx$03:40 UT to $\approx$04:10 UT, as well as, most of the peak phase
from $\approx$04:40 UT to $\approx$05:45 UT. There are two gaps in RHESSI
observations: during the rise and part of the peak phase of the flare from
$\approx$04:10 UT to $\approx$04:40 UT as well as from $\approx$05:45 UT to
$\approx$06:19 UT during the decay phase.

Figure 4(b) represents the AIA light curves at four wavelengths, viz. 94, 131,
304 and 1600 Å. We have estimated the average intensity within the region of
interest (shown by the white rectangle in Figure 1(d)) to get the intensity
flux. All intensity profiles show build–up of corresponding fluxes at around
$\approx$04:18 UT. The 1600 and 304 Å profiles show the corresponding peaks
during the impulsive rise of the GOES soft X–ray flux at $\approx$04:33 UT and
$\approx$04:35 UT, respectively. The AIA 131 and 94 Å profiles, on the other
hand, show the peak during the decline phase of the GOES soft X–ray light
curves at $\approx$05:00 UT, implying hot thermal emission from flare arcades.

Figure 5: ((a)–(e)) Sequence of selected AIA 131 Å images from 03:53:08 UT to
04:10:08 UT, showing the formation and evolution of the flux rope. The white
circles in panel (a) show the region of compact brightening. White and red
contours in the panels (b)–(c) are the RHESSI X–ray contours of 3–6 and 6–12
keV energy bands, respectively. The contours levels are 45%, 60%, 80%, and 95%
of the peak intensity. (d) SDO/AIA 131 Å images at $\approx$04:05 UT with
NLFFF extrapolated field lines. (f) SDO/HMI photospheric magnetogram at
04:10:09 UT on 2014 December 17. The red dashed curved lines in panels (c) and
(f) outline the expanding twisted loop system at 04:04:08 which presumably
represents a flux rope.

###  4.2 Dynamical evolution of the flux rope, associated flare and CME

####  4.2.1 Pre-flare processes and possible scenario of flux rope formation

Figure 6: Normalized intensity profiles of the circular ribbon (a), remote
brightening region (b) and parallel ribbons (c), respectively at 304 (solid
line) and 1600 (dotted line) Å wavelength channels. The red and black vertical
dashed lines represent the start ($\approx$03:45 UT) and the end time
($\approx$04:18 UT) time of the pre–flare phase, respectively. The verticle
blue line represent the start time of another phase at $\approx$04:28 UT. (d)
SDO/AIA 304 Å image at 04:30:07 UT on 2014 December 17. Yellow, white and
green boxes represent the area used for intensity measurements for circular
ribbon, parallel ribbons, and remote brightening region, respectively.

Pre–eruptive phase starts at $\approx$03:40 UT and lasts till $\approx$04:15
UT. Figure 5 shows the selected images during this phase at AIA 131 Å
wavelength channel. The compact brightening appears to start at $\approx$03:44
UT near the inner PIL (see the area shown by the red box in Figure 2(a)). This
compact brightening region is shown in Figure 5(a) by white circle. Along with
this compact brightening, we also see the appearance of loop–like structures
(shown by the arrows in Figures 5(b)–(e)) connecting the westward positive
polarity to the eastward negative polarity regions (cf. dotted curved lines in
Figures 5(c) and 5(f)). The successive formation of these channel–like twisted
loop structures and corresponding footpoint brightenings, provide indirect
evidence for the build–up of a flux rope, probably due to the tether–cutting
reconnection (see also the animations of AIA 131 and 94 Å associated with
Figure 5). It is also important to note that the formation process of flux
rope occurs inside the fan–dome (see Figure 5(d)). However, from AIA images we
could not gather any robust observational structure in support of a flux rope
(such as sigmoid, filament or mini-filament) inside the fan-dome during the
pre-flare phase. On the other hand, as discussed in Section 4.2.4, the
eruption began from underneath the dome during the flare’s impulsive phase
which supports the idea of in-situ formation of the flux rope.

Figure 7: ((a)–(f)) SDO/AIA 94 Å running difference images showing the
eruptions during the event. The red and green dashed curves represent the
eruption of the erupting loops and the flux rope, respectively. The white
circle in panels (e) and (f) shows the remote brightening region. The vertical
yellow dashed lines in panels (b) and (e) represent the chosen trajectories
along which the height measurements for eruptions are made (see height–time
plot in Figure 10(a)).

####  4.2.2 Temporal evolution of circular and parallel ribbons

A careful examination of AIA 304 Å image sequence clearly shows that the
circular ribbon formation started well before the impulsive phase of the flare
while the development of parallel ribbons initiated during the impulsive
phase. In order to critically distinguish the timing of the brightenings in
the circular ribbon and the parallel ribbons, we precisely compute the
intensity profiles of the flare ribbons which are presented in Figure
6(a)–6(c). To plot these profiles, we have estimated the intensity of the
respective regions (see Figure 6(d)) from $\approx$03:30 UT onward using
series of AIA 304 and 1600 Å images (see solid and dotted lines for the two
channels, respectively). To estimate the normalized intensity, we first
subtract the background intensity from the intensity of the selected region
and then divide the resulting value by the background intensity again. Here,
the background intensity is calculated by taking average of all the intensity
values of the images from $\approx$03:30 UT to $\approx$03:45 UT, much before
the initiation of the pre–flare phase during which the intensity was observed
to be almost constant.

Time profile of the circular flare ribbon (Figure 6(a)) readily reveals that
its formation started as early as $\approx$03:45 UT and the emission from the
circular ribbon gradually rose till 04:18 UT (indicated by the vertical red
dashed line). The time profile of the remote ribbon (Figure 6(b)) reveals that
its temporal evolution to be very similar to the circular ribbon: both slowly
evolve during $\approx$03:45–04:18 UT, before entering into the phase of
impulsive brightening, which is expected. On the other hand, the parallel
ribbons developed about more than 30 minutes later, after $\approx$04:18 UT,
with the onset of the impulsive phase (Figure 6(c)). The distinct and
simultaneous appearance of the circular ribbon along with the remote ribbon
prior to the flare’s impulsive phase is indicative of the null–point
reconnection.

Figure 8: ((a)–(f)) Sequence of SDO/AIA 304 Å images showing the evolution of
different sets of flare ribbons. The big white circles in the panels (a) to
(f) show the remote brightening (RB) regions. The blue and green contours in
panel (c) are the SDO/HMI magnetogram contours representing the negative and
positive polarity regions, respectively. The contour levels are $\pm$150
Gauss. (d) SDO/AIA 304 Å image at $\sim$04:35 UT overplotted with the NLFFF
extrapolated field lines. The green and yellow contours in panels (e) and (f)
represent the RHESSI X–ray contours at 10–15 and 25–50 keV energy bands.
Contour levels are 20%, 40%, 60%, 80%, and 95% of the peak intensity for 10–15
keV sources and 35%, 60%, 80%, and 95% for the 25–50 keV sources.

####  4.2.3 Field line restructuring and eruption

Figure 9: ((a)–(f)) Sequence of SDO/AIA 1600 Å images showing the evolution of
different sets of flare ribbons. The blue and green contours in panel (e) are
the SDO/HMI magnetogram contours representing the negative and positive
polarity regions, respectively. The contour levels are $\pm$150 Gauss.

The flare undergoes a transition into the impulsive phase starting from
$\approx$04:18 UT with the outward expansion of hot erupting loops (Figure 7)
and rapid rise in the intensity of circular and parallel ribbons (see Figures
8 and 9). The erupting loops are observed in AIA 94 Å images which means that
these are hot loops ($\sim$6 MK). However, we note that the erupting loops is
a visual fact which has been observed in the running difference images of AIA
94 Å (see Figures 7(a)–(c) and associated animation). This phase is
characterized by the onset of restructuring of magnetic field lines over and
under the fan structure involving the closed 3D null–point magnetic
configuration. The erupting loops are observed until $\approx$04:25 UT (shown
by arrows in Figures 7(a)–(c)). These eruptive loops appear to move southward
against the on–disk projection (see red dotted curved lines in Figures
7(a)–(c)). The erupting loops are more likely those field lines that reconnect
continuously in the QSL–halo surrounding the null–point. After reconnection at
the magnetic null, some of the accelerated electrons and particles would
travel downward along the fan–dome lines, thereby heating the chromospheric
region and forming the circular ribbon structure. The accelerated electrons
traveling along the field lines surrounding the outer spine would produce RB
at their footpoints.

The height–time profile showing the eruption of overlying loops, observed in
the AIA 94 Å image (Figures 7(a)–(c)), is shown by the red curve in Figure 10.
It is observed that the eruption of restructured and overlying loops started
at $\approx$04:18 UT. The projected height of the erupting structure is
estimated along the trajectory shown in Figure 7(b) by the yellow dashed line.
For the purpose, we carefully trace the front of the erupting leading edge
along the chosen trajectory. The starting point of the trajectory is used as
the reference point (shown by the cross symbol on the yellow dashed line in
Figure 7(b)) for height estimation. We have made three repeated measurements
of the height to estimate the uncertainty in the height estimation. The linear
speed of the erupting structure comes out to be $\approx$370 $\rm
km~{}s^{-1}$.

We would like to emphasize that the onset of the eruption of overlying loops
temporally matches with the significant and progressive enhancement in the
brightening of the parallel, circular and remote ribbons at $\approx$04:18 UT,
as evident from the SDO/AIA 304 and 1600 Å images (see Figures 8(a)–(b),
9(a)–(b), 10, and associated animations). Furthermore, this stage marks the
onset of flare’s impulsive phase as recorded in GOES X–ray measurements (see
Figure 4).

Figure 10: Projected height–time plots of the erupting loops (I) and flux rope
(II) eruptions are shown by the red and green lines, respectively. The GOES
soft X–ray flux profiles at 1.0–8.0 Å (solid black line) and 0.5–4.0 Å (dotted
black line) are also over–plotted for the comparison. The trajectories along
which the height measurements for the erupting coronal loops and flux rope
eruptions have been made are shown in Figures 7(b) and 7(e) by yellow dashed
lines, respectively. Since the erupting features were very faint, we prefer
the conventional height–time plot based on the eye judgement over the
time–slice diagram.

####  4.2.4 Flux rope eruption and CME initiation

The appearance of parallel ribbons and the flux rope eruption are the most
prominent features of the impulsive phase of the flare (starting from 04:18
UT), which imply the start of the standard flare reconnection. The AIA imaging
at 304 Å (Figure 8) along with corresponding light curve (Figure 6(c)) show an
impulsive rise in the brightness of the parallel ribbons from $\approx$04:18
UT and remain brightened until the late decay phase. The appearance of the
parallel ribbons at $\approx$04:18 UT suggest that the flux rope eruption
initiated at that time. The AIA 94 Å images clearly show the eruption of hot
EUV channel (i.e., flux rope) whose motion can be deduced from the running
difference images between $\approx$04:25 UT and $\approx$04:35 UT (see dashed
green line in Figures 7(d)–(f)). The height–time plot of the flux rope (shown
by the green plot in Figure 10) along a chosen trajectory (indicated by the
yellow dashed line in Figure 7(e)) gives the speed of the flux rope to be
$\approx$560 $\rm km~{}s^{-1}$.

Figure 11: LASCO C2 ((a)–(b)) and C3 (c) coronograph white light images of the
CME associated with the eruptive flare event. The difference images have been
downloaded from https://cdaw.gsfc.nasa.gov/CME_list/. The arrows represent the
two parts of the leading edge of the CME.

The dynamic evolution of the circular and parallel ribbons can be seen in the
AIA 304 and 1600 Å images (see Figures 8(b)–(f) and 9(b)–(f), respectively).
It is noteworthy that by $\approx$04:33 UT the strong emission from parallel
ribbons overtakes the emission coming from larger circular ribbon structure
(Figures 8(c), and 9(d)). These parallel ribbons appear to grow in size and
also to separate away from each other (see Figures 8(e)–(f) and 9(e)–(f) and
associated animations). Simultaneous to the growth of parallel ribbons, the
circular flare ribbons continue to exhibit enhanced emission. Also, the RB
remains prominent during this phase while it slowly extends westward with time
as well (see Figures 8(c)–(f), Figure 9(d)–(f) and associated animation). This
observational feature can also be infered from the intensity plot. At
$\approx$04:28 UT, we see another stage of intensity inhancement (shown by the
vertical blue bashed line in Figures 6(a)–(c)) in all the the circular,
parallel and, remote brightening regions. This is due to the fast eruption of
flux rope, which intensify the reconnection (both null-point and standard) and
hence the intensity of circlar, parallel and, remote ribbons.

The eruptions from the AR eventually produce a halo CME which is observed by
LASCO on–board the SOHO (Figure 11). The CME is first observed by LASCO C2 at
a height of 3.25 $\rm R_{\odot}$ at $\approx$05:00 UT. We note that the CME
exhibits a complex structure with the clear appearance of two distinct yet
connected leading edges (shown by the arrows in Figure 11). According to the
LASCO CME catalog
444$https://cdaw.gsfc.nasa.gov/CME\\_list/UNIVERSAL/2014\\_12/htpng/20141217.050005.p162g.htp.html$
the CME propagates within LASCO C2 and C3 field–of–view with a linear speed of
$\rm\approx$587 $\rm km~{}s^{-1}$.

In order to determine whether the torus instability is the triggering
mechanism of the flux rope eruption, we have calculated the distribution of
magnetic decay index over the AR volume (i.e., $\rm 510\times 180\times 180$
pixels) using potential magnetic field extrapolation (see Figure 12). Decay
index (n) is calculated using the relation: $\rm n=-d[log(B_{ex})/d[log(h)]$;
where $\rm B_{ex}$ and h are potential external field and height, respectively
(Bateman, 1978; Kliem & Török, 2006). Figure 12(a) represents closed 3D
null–point magnetic configuration over the AIA 304 Å image with iso–surfaces
of n=1.5 shown by yellow color. As the image suggests, there are two regions
in the AR volume where the value of decay index is greater than 1.5: inside
the fan-dome (within the closed iso–surface) and in the high coronal altitude
(the open iso–surface at the top of the figure). While the open iso–surface at
the top is rather standard, the closed surface inside the dome is important
and useful in our case. It suggests us that the majority of the upper region
within the fan-dome was subjected to torus instability. In Figure 12(b), we
have drawn a vertical

surface that passes through the parallel ribbons, where the distribution of
decay index along the surface is plotted. The black curves on the vertical
surface indicate n=1.5. For further clarification, we have separately plotted
the surface in Figure 12(c). We have approximated the locations of the flare
ribbons by the two solid brown boxes near the bottom boundary of the plot. The
average values of decay index (along this surface) as a function of height
within the two vertical dotted lines are shown in Figure 12(d). From this
panel, we find that the decay index reached the value of 1.5 at a height of
$\approx$30 Mm.

We would like to emphasize that the n=1.5 region inside the dome directly
borders the fan surface. To explore this further, we calculated the QSL in the
flaring region which also includes the fan-dome and depicted the high
Q-regions (log (Q)=5) by blue iso-surface (Figure 12(a)). Our analysis readily
suggest that the flux rope activation by the torus instability would
immediately lead to reconnection at the null point.

###  4.3 RHESSI X–ray observations

Figure 12: (a)–(d) Distribution of decay index over the active region NOAA
12242. In panel (a) we plot an isosurface of n=1.5 by yellow color. For
comparison, we have also indicated the region of the null-point in brown
color. Two regions (inside and outside the fan dome) have been observed with
decay index value equal or greater than 1.5. The blue coloured iso-surface
shows the QSL (log(Q)=5), which represents the fan surface. (b) Distribution
of decay index along the vertical surface that passes through the parallel
ribbons. The black curves on the vertical surface indicate n=1.5. For further
clarification, we have separately plotted the surface in the panel (c). We
have approximated the locations of the flare ribbons by the two solid brown
boxes near the bottom boundary of the plot (see panel (c)). The average values
of decay index (along this surface) as a function of height within the two
vertical dotted lines are plotted in the bottom panel (d). From this panel, we
find that the decay index reached the value of 1.5 at a height of $\approx$30
Mm.

The RHESSI observations are available during some part of the peak and decay
phases of the M–class flare while it completely missed its rise phase (Figure
4(a)). We also find useful RHESSI observations during a part of the
pre–eruptive phase. Some of the RHESSI imaging observations during the
pre–eruptive phase are shown in Figures 5(b)–(c) where the background
corresponds to the AIA 131 Å images. It is noteworthy that RHESSI’s attenuator
state was A0 during this phase, i.e., RHESSI observed with its highest
sensitivity at low energies. This has enabled us to examine the X–ray sources
associated with the weak pre–flare emission down to 3 keV energy. We note that
the earliest X–ray emission at 3–6 keV and 6–12 keV energy bands originates
from the location of pre–flare brightening (Figure 5(b)). At this time, the
main source presents a broad structure while secondary sources, situated south
of the main source, are also noticeable. In the later stages of the
pre–eruptive phase, the X–ray sources converge toward the bright loop–like
structure which is clearly noticeable in the background EUV images (Figure
5(b)–(c)). The RHESSI observations reveal that the pre–flare X–ray emission is
persistent and spatially not so–localized. From the comparison of X–ray and
EUV images along with the corresponding magnetogram, we infer that the
pre–flare brightening is suggestive of the slow evolution of a bundle of field
lines that continues to emit enhanced hot emission while undergoing upward
expansion. Based on temporal and spatial characteristics of pre–flare emission
over a wide range of energy scales, we argue that it is related to the slow
magnetic reconnection, presumably of tether–cutting category.

Figure 13: Representative RHESSI X–ray images overplotted on AIA 94 Å images.
The red, green, blue and yellow contours represent the RHESSI X–ray contours
at 5–10, 10–15, 15–25, and 25–50 keV energy bands, respectively. Contour
levels are 35%, 60%, 80%, and 95% of the peak intensity for 5–10 keV, 15–25
keV, and 25–50 keV sources. To examine the extent of hot plasma emission, we
set the contour levels as 20%, 40%, 60%, 80%, and 95% of the peak intensity
for 10–15 keV sources. Arrows represent the edge of the circular structure.

In Figure 13 we show the evolution of X–ray sources with respect to EUV 94 Å
flaring image in four representative energy bands, namely, 5-10, 10-15, 15-25,
and 25-50 keV. The X–ray source in $\lesssim$15 keV are mostly dominated by
the thermal emission from the hot flaring loops while at higher energies
($\gtrsim$20 keV) the non–thermal component from foot–point regions becomes
predominant. Notably, during this whole phase the centroids of X–ray sources
at lower and higher energies are almost co–spatial, thus indicating the
presence of multi–thermal plasma within a confined environment. Further, at
times, the X–ray emitting sources exhibit very extended structures (see panels
(a), (b), (d) and (e) of Figure 13), mainly at 10–15 keV energy band. We also
emphasize that, in contrast to the standard flare scenario, the X–ray sources
here do not undergo much spatial evolution. Comparison of X–ray and EUV images
reveals that the broad X–ray sources likely indicate the composite thermal
emission caused by the reconnection of magnetic field lines spread in a larger
yet confined region i.e., the region is delineated by a 3D null–point magnetic
topology. In Figures 8(e)–(f), we compare the spatial distribution of EUV and
X–ray sources in the light of the formation of parallel ribbons. From the
co–spatial images, it is evident that the compact non-thermal source (i.e.
25-50 keV emission) originated mainly from the location of southern flare
ribbon and the region in-between the parallel ribbons. This suggests asymmetry
in the evolution of HXR footpoint sources. Thus, the spatial structures
associated with 25-50 keV sources suggest that the non-thermal emission
observed during this circular flare came from the footpoints of short loops
lying within the inner PIL (Figure 2(a)) by the standard flare reconnection.
On a whole, the structure and evolution of X–ray sources present a complex
situation associated with the release of the magnetic energy by the
reconnection in 3D null as well as standard flare reconnection in the
underlying magnetic configurations.

Figure 14: Schematic representation of the different phases of the eruptive
flare event. The field lines enclosed below and over the fan are represented
by the blue and red colors, respectively. The remote brightening (RB) is
represented by the blue color structure in panels (b) and (c). Reconnection
regions are marked by the cyan color stars in panels (b) and (c). The circular
and parallel flare ribbons are shown by the solid purple lines in panels
(b)–(c). Flux rope is shown by the black line in panels (b)–(c).

##  5 Results and Discussion

Table 1: Observational Sequence of the Event Time | Observational features
---|---
$\approx$03:45 UT | Appearance of circular ribbon in 304 Å images along with remote brightening.
| -Starting of compact brightening at the inner PIL region.
$\approx$04:18 UT | Start of flare’s impulsive phase; formation of parallel ribbons started;
| Circular ribbon continued to appear with impulsive increase in intensity.
| -Onset of the eruption of overlying loops observed in hot 94 Å channel.
$\approx$04:25 UT | Onset of the inner field lines (either flux rope of sheared arcades) observed in hot 94 Å channel.
$\approx$04:51 UT | Peak phase of the flare observed from GOES X-ray flux profile.
$\approx$05:00 UT | First appearance of CME observed in LASCO-C2 field of view.

In Figure 14, we provide schematic diagrams to explain and interpret the
multi–phase evolution of the complex circular ribbon flare exhibiting distinct
parallel conjugate ribbons within the periphery of the circular ribbon. For
the convenience, we summarize the chronology of the various evolutionary
phases of the event in Table 1. The magnetic topology over the AR is of closed
3D null–point topology where a bipolar region lies inside the fan dome (cf.
Figures 14(a) and 2). This type of magnetic configuration consists of field
lines enclosed below the fan and over the fan (shown by blue and red lines,
respectively in Figure 14(a)) with a magnetic null and a distinct region
showing RB (e.g., Sun et al., 2013; Joshi et al., 2017b). A flux rope evolving
inside the fan–dome (Figure 5) is likely formed due to the tether–cutting
reconnection caused by the magnetic flux changes at the inner PIL (see Figure
3). In this context, we would like to refer some studies which suggest that
the mechanism responsible for such pre–flare brightenings for the formation of
flux ropes and flare arcades are the result of magnetic reconnection at the
hyperbolic flux tube (HFT) which is the topological element below a forming
flux rope by assuming that the observed structure is a flux rope (see e.g.,
Aulanier et al., 2010; Janvier et al., 2013). We propose that the slowly
evolving flux rope pushed the lines enclosed below the fan lines toward the
magnetic null and trigger the null–point reconnection. In this scenario, the
reconnection region would lie between the inner blue fan lines and the outer
red fan lines which is depicted in Figure 14(b), where the location of the
null–point reconnection is shown by sky blue colored star in Figures
14(b)–(c). As a consequence of null point reconnection, erupting loops are
observed (cf. Figures 14(b) and 7(a)–(c)) which likely represent newly formed
loop system moving away from the null-point. Thus, the null point reconnection
would facilitate the eruption of the underlying flux rope lying within the fan
dome. The next phase starts with the onset of flux rope eruption and standard
reconnection occurs underneath it (cf. Figures 14(c) and 7(d)–(e)). This
reconnection enhances the brightness of two parallel ribbons that form on both
sides of the inner PIL inside the fan dome (cf. Figures 14(c), 8(a)–(f), and
9(a)–(f)). In the 3D model for the flux rope eruption, the standard
reconnection corresponds to magnetic reconnection in the HFT behind the
erupting flux rope (see Aulanier et al., 2010; Janvier et al., 2013). The
null–point reconnection continues with the eruption of the underlying flux
rope until null–point topology gets partially disrupted. The configuration
just after the eruption is shown in Figure 14(d). Later on, the system gets
back to a potential stage with 3D null–point magnetic configuration, which is
similar to the initial configuration (Figure 14(a)).

Recently, Joshi et al. (2015) and Joshi et al. (2017b) studied flares that
show two different sets of flare ribbons viz. parallel and circular in an AR
with a 3D null–point magnetic topology. They observed that the parallel
ribbons form before the circular ribbon. They suggested two stages of magnetic
reconnection to explain their observations like: initial standard followed by
later null–point reconnection. In this paper, we present a reverse case in
which the signatures of circular ribbon comes first in the pre–flare phase.
The parallel ribbon starts to form in the implusive phase. Both kinds of
ribbons underwent rapid intensity enhancements as the flux rope activated
towards eruption.

Flares that consist of a circular ribbon are usually found to occur in a
typical 3D null–point topology via the null–point reconnection (Aulanier et
al., 2000; Jiang et al., 2014; Sun et al., 2013; Joshi et al., 2015, 2017b).
In this work, we provide further insights of the different reconnection stages
possible in the null–point topology by carefully analyzing the temporal
aspects in the developments of circular and parallel ribbon flares. We
observed a slow rise in the brightness of the circular ribbon area at
$\approx$03:45 UT in AIA 304 Å images (see Figure 6(a)). The apparent eruption
of overlying loops started at $\approx$04:18 UT (Figures 7(a)–(c), 10), which
is co–temporal with the onset of sharp enhancement in the circular ribbon
brightening and RB (see Figures 8(a)–(b) and animations associated with
Figures 8 and 9). Circular morphology of the flare ribbon observed in the
early phase and magnetic configuration inferred from NLFFF extrapolation
signify magnetic reconnection in the null point topology. As a consequence of
this reconnection, two distinct flux systems below and above the fan
separatrix would reconnect (see schematic shown in Figure 14(b)). This would
create a newly reconnected overlying hot coronal erupting loops (Figures 7, 10
and 14). According to our understanding the erupting (overlying) loops
observed from $\sim$04:10 UT to $\sim$04:25 UT (Figure 7(a)-(c) and
corresponding measurements in Figure 10) presumably trace the newly formed hot
loops moving away from the null point. The eruptive expansion of overlying
loops caused due to the null-point reconnection imply removal of the
constraining flux that envelop the flux rope. This proceeds toward decreasing
the downward tension of the restraining fields and hence ease the eruption
process of the underlying flux rope. Afterwards, the field lines continue to
reconnect across the QSL–halo surrounding the outer spine. The illustration
showing the distribution of QSL along with torus unstable region within the
fan-dome (Figure 12(a)) further clarifies the eruption scenario. The fact that
the torus unstable region (i.e., region with n=1.5) inside the dome directly
borders the fan surface (having large Q-values) confirms that any instability
of the flux rope would immediately trigger reconnection at the fan-QSL leading
the circular ribbon brightening. After the reconnection, the field lines may
appear to slip within the same dome and hence the sequential circular
brightening (Sun et al., 2013; Joshi et al., 2015, 2017b). In our case, we
observed counterclockwise sequential movement of brightening in a circular
manner (see animation associated with Figure 9), which provide evidence of the
reconnection at QSL.

We would like to elaborate that during the evolution of the present event, the
role of null–point reconnection toward the eruption of the underlying flux
rope in null–point topology (evident from the initial circular ribbon
brightening) seems to match with the null–point reconnection in the breakout
model of solar eruption Aulanier et al. (2000); Sun et al. (2013); Liu et al.
(2015); Xu et al. (2017); Li et al. (2018). However, we also state that the
null–point reconnection alone may not be able to explain the eruption of
underlying quasi–stable flux rope. The NLFFF analysis suggests the location of
null–point to be at $\rm\approx 36~{}Mm$ which implies that the null–point
reconnection occurred at lower coronal heights. This interpretation is also
supported by the fact that (1) the mild yet persistent circular brightening
during the pre–flare phase (see Figure 6 and animation associated with Figures
8 and 9); (2) cotemporality between the eruption of overlying loops and sharp
enhancement of circular as well as RB (cf. Figures 8(a)–(b), 9(a)–(b) and
Figure 10); (3) the time delay ($\approx$7 min) between the onset of eruption
of the underlying flux rope ($\approx$04:24 UT; Figure 10) and the overlying
filed lines ($\approx$04:17 UT; Figure 10; see Figure 7 and associated
animation). This fact is supported by the observations that a sharp increase
in the brightness of the circular ribbon (a proxy for the increase in the rate
of null-point reconnection) occurred simultaneously with the observed eruption
of overlying loops (cf. Figures 6(a), 7 and 10). We suggest that the transfer
of flux across the fan separatrix (Figure 14(b)) observationally inferred from
erupting loops would contribute in alleviating the immediate constraint on the
core field. This would facilitate the subsequent eruption of underlying flux
rope (cf. Figures 7(a), 8(a) and 10). The removal of overlying flux as a cause
of the eruption of the underlying flux rope at different magnetic
configurations has also been investigated in earlier studies (e.g., Joshi et
al., 2013a; Cheng et al., 2013; Sterling et al., 2014). The decay index
analysis suggests that the torus instability may also play an important role
in triggering the eruption of the underlying flux rope. The instability zone
(i.e., region of decay index n$\gtrsim$1.5) lies at a height of $\approx$30 Mm
(see Figure 12). When the flux rope reached at this height within fan dome, it
attained eruptive motion (see similar results by Jiang et al., 2013, 2014). We
also note that, once the flux rope reached the region above the null point,
the value of corresponding decay index decreased below 1.5 which points toward
the stability zone within a height range in the higher coronal level. However,
the CME observations clearly reveal the successful eruption of the activated
flux rope without any further hindrance. We, therefore, see that the
triggering processes of the flux rope eruption with eruptive flare, initiated
below a null could be very complex with several factors being involved. Our
comprehensive multi-wavelength data analysis and coronal magnetic field
modeling suggest that, both the torus instability and breakout model can
contribute to the triggering mechanism for this eruptive flare. Hence, for
eruptive flares initiated below a null–point, more observational and
theoretical studies need to be done to determine the exact triggering
mechanism.

##  6 Conclusions

In this work, we present a multi–wavelength analysis of an interesting
multiple ribbon solar flare that occurred on 2014 December 17. The flare
occurred in a typical 3D null–point topology. The multi–wavelength
observations clearly reveal three distinct phases in the evolution of this
solar eruptive flare. The main results of this study are summarized below.

  1. 1.

Prior to the onset of eruption (i.e., pre–eruptive phase), we find evidence
for the formation and slow expansion of the flux rope which is corroborated by
the enhanced EUV emission from an expanding loops system and spatially
extended low energy X–ray sources $\rm(\lesssim 12~{}keV)$. The subtle yet
obvious manifestation of the circular ribbon along with the anemone shape of
the fan field lines during the pre–eruptive phase imply the onset and
persistence of null–point reconnection well before the later standard flare
reconnection. Simultaneous to the commencements of circular ribbon, we also
observed RB which overall agree with the close null–point configuration with
the outer spine as inferred from the extrapolations.

  2. 2.

In the impulsive phase, the flare underwent the dynamic restructuring of the
field lines below and above the fan via null–point reconnection along with the
eruptive expansion of the outer (overlying) hot coronal loops. The eruption of
the overlying fields would remove the constraining flux, thereby facilitating
the eruption of the underlying flux rope. The decay index analysis suggests
that the flux rope resided close to an unstable zone which starts at a height
of $\approx$30 Mm inside the fan dome. When the evolving flux rope would reach
this height, it would undergo eruptive expansion. Here we note that the decay
index decreases above the null point which may inhibit the further expansion
of flux rope. However, the combination of SDO/AIA and SOHO/LASCO observations
clearly reveal the successful eruption of the flux rope without any
interruption in the overlying coronal layers. In our case, we propose that the
combination of coronal breakout and torus instability within the fan-spine
dome facilitated the successful eruption of the flux rope resulting the large
M–class flare and a CME.

  3. 3.

In the subsequent stages, the characteristics of the eruptive flare match well
with the classical picture of the two–ribbon flare. Now, flare evolved with
the complete expulsion of the underlying flux rope, which subsequently gave
rise to a CME.

This event is a nice example of the destabilization and eruption of a flux
rope initially confined in a null–point topology. More such observational
studies and corresponding numerical simulations are needed to clearly
understand the eruption scenario in complex circular–cum–parallel ribbon
flares.

## Acknowledgements

We thank SDO, RHESSI, SOHO and GOES teams for their open data policy. SDO is
NASA’s missions under Living With a Star (LWS) and RHESSI was NASA’s missions
under SMall EXplorer (SMEX) programs. SOHO is a project of international
cooperative effort between ESA and NASA. We also thank Dr. Thomas Wiegelmann
for providing the NLFFF code used in the analysis. We thank Dr. Jaroslav
Dudík, the reviewer of our paper, for insightful comments that improved the
scientific content of the paper.

## Data Availability

Observational data from AIA and HMI on board SDO utilised in this article are
available at http://jsoc.stanford.edu/ajax/lookdata.html. X-ray observations
from RHESSI are available at http://hesperia.gsfc.nasa.gov/hessidata/. The
NLFFF code employed in this article for coronal magnetic field modelling is
provided by Dr. Thomas Wiegelmann. Different aspects of the code are explained
and discussed in https://doi.org/10.1023/B:SOLA.0000021799.39465.36,
https://doi.org/10.1007/s11207-006-2092-z,
https://doi.org/10.1051/0004-6361/201014391,
https://doi.org/10.1007/s11207-012-9966-z. The IDL-based code used for the
computation of $Q$ and $T_{w}$ is available at
http://staff.ustc.edu.cn/~rliu/qfactor.html.

## Supplementary Material

Videos are attached with Figures 3 (Movie-Figure3.mp4), 5 (Movie-
Figure5a.mpeg, Movie-Figure5b.mpeg), 7 (Movie-Figure7.mpeg), 8 (Movie-
Figure8.mpeg) and 9 (Movie-Figure9.mpeg) which are available in the online
article.

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