# A Full Study on the Sun-Earth Connection of an Earth-Directed CME Magnetic
Flux Rope

P. Vemareddy1 and W. Mishra2 1Indian Institute of Astrophysics, II Block,
Koramangala, Bangalore-560 034, India  2Department of Geophysics and Planetary
Sciences, University of Science and Technology of China, Hefei-230026, China
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We present an investigation of an eruption event of coronal mass ejection
(CME) magnetic flux rope (MFR) from source active region (AR) NOAA 11719 on 11
April 2013 utilizing observations from SDO, STEREO, SOHO, and WIND spacecraft.
The source AR consists of pre-existing sigmoidal structure stacked over a
filament channel which is regarded as MFR system. EUV observations of low
corona suggest a further development of this MFR system by added axial flux
through tether-cutting reconnection of loops at the middle of sigmoid under
the influence of continuous slow flux motions during past two days. Our study
implies that the MFR system in the AR is initiated to upward motion by kink-
instability and further driven by torus-instability. The CME morphology,
captured in simultaneous three-point coronagraph observations, is fitted with
Graduated Cylindrical Shell (GCS) model and discerns an MFR topology with
orientation aligning with magnetic neutral line in the source AR. This MFR
expands self-similarly and is found to have source AR twist signatures in the
associated near Earth magnetic cloud (MC). We further derived kinematics of
this CME propagation by employing a plethora of stereoscopic as well as single
spacecraft reconstruction techniques. While stereoscopic methods perform
relatively poorly compared to other methods, fitting methods worked best in
estimating the arrival time of the CME compared to in-situ measurements.
Supplied with values of constrained solar wind velocity, drag parameter and 3D
kinematics from GCS fit, we construct CME kinematics from the drag based model
consistent with in-situ MC arrival.

###### Subject headings:

Sun: heliosphere— Sun: flares — Sun: coronal mass ejection — Sun: magnetic
fields— Sun: filament — Sun: solar-terrestrial relations

††journal: Accepted in The Astrophysical Journal††slugcomment: Received 2015
May 29; Accepted 2015 October 6

##  1\. Introduction

Coronal Mass Ejections (CMEs) are magnetically driven gigantic events whose
disturbance in the outer corona influences the space-weather to a wide range.
When propagating from the Sun, they appear to have three-part structure in
white light (Illing & Hundhausen, 1985; Burlaga, 1988; Forsyth et al., 2006)
with leading edge, core and cavity. Although not quite clear in the
observations, the cavity is supposed to have its connections in the source
regions on the Sun and is approximated by a coherent, large scale magnetic
magnetic flux rope (MFR), manifested by twisted magnetic field lines. A recent
statistical study suggests that at least 40% of CMEs observed by space borne
instruments have a clear MFR structure (Vourlidas et al., 2013). Many studies
from space and ground based observations suggested that this MFR structure in
the outer corona is an evolved form of filaments seen in H$\alpha$ or sigmodal
structure in soft X-rays in the so called magnetic active regions (e.g.,
Lepping et al. 1990; McKenzie & Canfield 2008; Vemareddy et al. 2012; Zhang et
al. 2012; Howard & DeForest 2012; Cheng et al. 2012) on the Sun. Central to
the space-weather phenomena and the Sun-Earth connections of the CMEs having
signatures of this predicted MFR topology, a majority of past and current
scientific research dwells on basic questions like how such MFR like
structures formed or comes into existence (e.g., Pneuman 1983; van
Ballegooijen & Martens 1989; Fan 2001; Fan & Gibson 2004; Gibson et al. 2004,
2006; Leka et al. 1996), what are the initiating conditions in the source
active region (e.g., Moore et al. 2001; Priest & Forbes 2002; Lin et al. 2003;
Forbes et al. 2006; Fan & Gibson 2007; Kliem & Török 2006; Martin et al. 1985;
Antiochos et al. 1999; Chen 2011; Cheng et al. 2012; Vemareddy et al. 2012;
Vemareddy & Zhang 2014) and what kind of MFR evolution drive its outward
propagation (e.g., Temmer et al. 2012, 2011; Gopalswamy et al. 2000, 2001;
Vršnak & Gopalswamy 2002; Manoharan 2006; Vršnak et al. 2013; Davies et al.
2009; Webb et al. 2009; Forsyth et al. 2006; Harrison et al. 2012) in the
extended corona and interplanetary medium.

Two strong ideas that the past and current observations on the Sun implied
were emergence of the MFR from beneath the inner photosphere and formation of
the MFR from sheared arcade. In the process of active region formation while
it emerges, the MFR structure would emerge as a bipolar region and
equilibrates with the overlying, pre-existing structure (Fan, 2009). Numerical
simulations of the bodily emergence of the MFR (Fan, 2001; Fan & Gibson, 2003;
Magara, 2001; Gibson et al., 2004; Okamoto et al., 2009; Lites et al., 2010)
showed the formation of sheared arcade in the corona after the MFR axis
reached the photosphere. In the case of fully emerged active region, the
equilibrated MFR structure in the form of sheared arcade evolves to full
fledged MFR. Based on these ideas, different theoretical and observational
models have been proposed and constructed (Antiochos, 1998; Antiochos et al.,
1999; Lin et al., 2003; Forbes et al., 2006; Kliem & Török, 2006; Fan &
Gibson, 2007; Chen, 2011). In all of them, twisted MFR or sheared arcade which
is a source of magnetic helicity, is the basic ingredient of pre-eruptive
magnetic configuration. Pneuman (1983) showed how helical MFRs can be formed
by reconnection in a sheared coronal arcade. During the progressive
reconnection phase, the magnetic flux gets canceled, transforming the magnetic
field lines in the sheared arcade along the magnetic inversion line to
winding, helical field lines about a common axis of nearly formed MFR (Green &
Kliem, 2009; Green et al., 2011). Later, van Ballegooijen & Martens (1989)
proposed a mechanism for the formation of helical field lines from the
reconnection of less sheared arcade along the polarity inversion line and also
to build up the MFR. Submerging motion of fluxes about the PIL also plays
vital role in bringing less sheared to highly sheared arcade. Usually the
reconnection location is associated with the photospheric flux cancellation
(Yurchyshyn & Wang, 2001; Bellot Rubio & Beck, 2005) and is evidently reported
to be involved with the MFR formation and its eruption (Green et al., 2011).

In the low corona, triggering and driving of MFR eruption is another important
step in the eruption process. Filament, prominence or sigmoid eruptions
modeled by the numerical and theoretical constructions of MFRs have been
successful in many respects of observed eruption features. The physics of
these models essentially based on loss of equilibrium of MFR after reaching a
critical height (Forbes & Isenberg, 1991; Priest & Forbes, 2002), kink
instability due to exceeding MFR’s twist (Török et al., 2004; Török & Kliem,
2005), torus instability (Kliem & Török, 2006; Aulanier et al., 2010) of the
MFR when there is a rapid decline of the background field in the direction of
the expansion of the MFR.

In the case of source active regions located near the disc center, the CME MFR
eruption is very likely directed toward the Earth causing direct space weather
impacts. In order to estimate the arrival times of CMEs to Earth, a vital step
is to understand the kinematic evolution of CMEs while propagating through the
heliosphere. Based on Large Angle and Spectrometric Coronagraph (LASCO;
Brueckner et al. 1995) coronagraph observations on board the Solar and
Heliospheric Observatory (SOHO), many studies found that CME having fast speed
near the Sun, decelerates during its journey to the Earth while CME having
slow speed accelerates (Lindsay et al., 1999; Gopalswamy et al., 2000, 2001;
Yashiro et al., 2004; Manoharan, 2006). This finding clearly emphasizes the
interaction of CME with the ambient solar wind medium. LASCO observes only out
to $30R_{\odot}$ and can provide only projected kinematics of the CME while
CME speed changes significantly beyond the FOV of coronagraphs. Therefore two
point measurements of speed, one near the Sun and another near the Earth, are
not sufficient to fully capture the physics of CME evolution in the
heliosphere.

In the present era, the estimation of CME kinematics from its lift-off in the
low corona to the Earth or even beyond is possible with multiple views (A and
B) of the Sun-Earth space from the Solar Terrestrial RElations Observatory
(STEREO; Kaiser et al. 2008). Using coronagraphs (CORs) and heliospheric
imagers (HIs) of Sun-Earth Connection Coronal and Heliospheric Investigation
(SECCHI; Howard et al. 2008) onboard STEREO, several studies have been carried
out attempting to associate remote imaging observations with in situ
observations near the Earth (Davies et al., 2009; Möstl et al., 2010; Liu et
al., 2010; Harrison et al., 2012; Temmer et al., 2012; Lugaz et al., 2012;
Mishra & Srivastava, 2013; Liu et al., 2014a; Rollett et al., 2014; Möstl et
al., 2015). Single and/or multiple spacecraft reconstruction methods on HI
observations have shown major limitation in estimating kinematics and the
inherent difficulties involved in interpreting the HI observations of the
CMEs. However, most of these studies have been carried out mainly for Earth-
directed CMEs during STEREO separation was small. Therefore, the tracking of
the CME or its associated MFRs moving away form the observer seems to be
rarely undertaken for study (Liu et al., 2014b). Hence, the assessment of
relative performance of reconstruction methods with different geometry,
assumed for a CME receding from the observer, is an obvious next step for the
solar-terrestrial scientist.

In the present study, we focused on an eruption event of April 11, 2013 from
the NOAA AR 11719, uniquely involving its gradual build up and eventual
eruption to Earth directed CME. The initiation mechanism based on
morphological twist signatures of this MFR event was extensively studied in
Vemareddy & Zhang (2014, hereafter VZ14). Interestingly, the solar energetic
particle (SEP) event on 11 April, 2013 was found to originate from this
eruption event (Lario et al., 2014) which produced first large Fe-rich SEP
event of solar cycle 24 (Cohen et al., 2014). In view of further Sun-Earth
connection of this CME MFR event, in this manuscript, we extended the study of
VZ14 on the formation or development scenario of MFR in the source AR and its
propagation in the inner heliosphere after its eventual eruption from the
source AR. Utilizing detailed multi-wavelength EUV observations from
Atmospheric Imaging Assembly (AIA; Lemen et al. 2012), we study the evolution
history of the source AR prior to three days. In concurrent with the observed
morphological evolution, we analyzed vector magnetograms obtained from
Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) to support or revert
the scenario of MFR formation by canceling magnetic flux in the source active
region. Moreover, taking advantage of multi-view observations from
STEREO/SCCHI, SOHO/LASCO coronagraphs, we determined orientation of the
underlying MFR by a parametrized fitting model to the observed white light CME
morphology. We further tracked this CME, which is moving away from the STEREO
observer, and estimated its kinematics using stereoscopic and single
spacecraft reconstruction methods. The estimated arrival time of CME MFR at L1
is discussed in comparison with in situ plasma parameters to assess the
reliability of the employed tracking methods. CME Kinematics are also derived
and discussed using drag based model. Further, the AR twist signatures are
explored from in situ magnetic field observations of this CME associated
magnetic cloud. Such a study involving multi-scale observations examines the
complete Sun to Earth connection of an event and furthers the understanding in
space-weather phenomena.

The manuscript is structured as follows: in section 2, the requirement of
observations from various instruments is outlined, and in section 3-4, the
formidable conditions for the formation/development are explored using coronal
EUV and photospheric magnetic field observations. For completeness, the
details of onset and driving mechanisms of this MFR eruption (VZ14) are given
in section 5. The orientation of the MFR while expanding from the source
active region is determined in section 6. Its propagation kinematics toward
Earth and interplanetary twist signatures are presented in section 7. We
concluded with a summarized discussion of this investigation in section 8.

Figure 1.— Top left: Composite image of the solar disk prepared from AIA 304
and 94A observations. The source region of CME on the Sun is marked with
rectangular inset. The pre-eruptive AR 11719 consisted of sigmoidal structure
that deviates from the filament channel. Top right: Difference image
(07:12-07:03UT) of AIA 193Å indicates EUV disturbance and outlines the rapidly
expanding MFR from AR11719. Bottom Left: Propagating CME and bright leading
edge in C2 field of view on board SoHO. Image of the Sun from AIA 193Å
observation is also placed at the occulter disk position. Bottom Right: time
profile of GOES x-ray flux in low and high frequency bands. The peak flux
corresponds to M6.5 flare that commenced at 06:55UT (vertical green line)
subsequent to the onset of the MFR at 06:15UT (dashed grey vertical line). The
red vertical line indicates the time of the captured C2 image shown in the
left panel.

##  2\. Outline of Observations

The overall eruption event of our interest is outlined in Figure 1. The
observations of the source active region NOAA 11719, both at photospheric and
low corona heights, are well covered by the Solar Dynamic Observatory and its
component instruments AIA and HMI. Using AIA channels, especially 304 and 94Å
observations (0.6 arcsec/pixel), the pre-eruptive AR [at 06:50UT] magnetic
flux system is noticed to present an inverse-S sigmoidal structure (top left
panel) that is stacked over filament channels. During the initial upward rise
motion at 06:15UT (just before the main eruption around 06:55UT), the plasma
emission (in 131 and 94Å observations) along this sigmoidal structure supports
the interpretation that the sigmoid is manifested by a coherent core twisted
flux system surrounded by twisted overlying flux bundle (VZ14). We regard this
coherent core flux along the sigmoid as main body of the MFR, which is wound
by the overlying flux bundle. The time difference image of 193Å (top right
panel) shows an EUV disturbance in the low corona during this main phase of
eruption. This EUV disturbance also outlines the expanding MFR having legs
rooted from the pre-determined (”+”) sigmoid legs. The eruption of the sigmoid
MFR from the low corona is preceded by a GOES M6.5 flare (bottom right panel).
Importantly, its CME-driven shock propagates at high altitudes above the solar
surface and was likely the source of the solar energetic particles observed
near Earth (Lario et al., 2014; Cohen et al., 2014).

This propagating CME in the outer corona was well observed by the Large Angle
and Spectrometric Coronagraph (LASCO; Brueckner et al. 1995) on board the
Solar and Heliospheric Observatory (SoHO) and the SECCHI on board the STEREO
(A and B). The CME structure emerged out of the occulter to become a halo like
structure at around 08:30UT. Figure 1(bottom left) of LASCO/C2 image discerns
a bright annular structure on East limb of the disc resembling the leading
edge followed by invisible cavity of the MFR. While expanding, the transit of
the MFR through multiple heights, in the field-of-views (FOVs) of COR1
(1.1-4$R_{\odot}$), COR2 (2-15$R_{\odot}$), LASCO/C2 (1.5-6$R_{\odot}$),
LASCO/C3(3.5-30$R_{\odot}$) situated at perspective viewing angles, uniquely
show a direct connection between the heliospheric MFRs and the sigmoidal
structures in the source active region (more details in Section 6). The
majority of observed CMEs in the past solar cycle had clear MFR structures and
no presently known physical mechanism can produce a large-scale fast eruption
beyond 10$R_{\odot}$ without ejecting a MFR (Vourlidas et al., 2013). Having
these supporting observational signatures of MFR topology both in the source
region sigmoid and CME morphology, we use the term MFR while describing and
interpreting the observations in its favor. The CME propagation in the
heliosphere was tracked by HI-I (15-90$R_{\odot}$) and HI-II
(70-330$R_{\odot}$) instruments of SECCHI. In situ plasma and magnetic field
observations are obtained from WIND space mission. Taking advantage of these
detailed observations, we focus on the objectives mentioned in the last
section.

Figure 2.— The observational scenario of inverse-S sigmoidal MFR in AR 11719.
Top row: The observations of the corona in AIA 304, 94, 171Å passbands on 9
April 2013. Note the distant loops (OL) overly the cold filament, Bottom row:
composite images of 304, 171, and 94Å referring to presence of loops overlying
the filament and the developing sigmoidal MFR. Low lying loops L1 and L2 about
the sigmoid and their evolution over the long time infers a scenario of
tether-cutting reconnection after which they align the MFR axis. All image
panels are in heliographic coordinates in arcsec units. Figure 3.—
Observational scenario of sigmoid development in the source active region over
a period of three days. All panels depict composite images prepared from AIA
94 [red], 335 [green], 193Å[blue] passband observations. The eastward sigmoid
lobe above dark filament is well visible by 10 May, 2013 15:00UT. The last
panel shows the sigmoid morphology while rising upward. The entire sigmoid is
heated due to reconnection in current sheet underneath it.

##  3\. Development of MFR Structure: AIA Observations

The active region 11719 contains a well observed filament from its appearance
on the eastern limb of the solar disc. The filament consists of two sections
which together give an inverse S-shape to it. These coronal features are
identified to be associated with magnetic regions (labels in Figure 4(a)) at
the photosphere. The lower section originates from main sunspot (S1) and has a
cusp shape at the joining to upper section. Long coronal loops having
footpoints from flux region S2 are well captured in AIA passbands,
predominantly in 171Å and are observed to overly the filament, with conjugate
footpoints lying in N1. In hotter passbands (2-10MK) of AIA especially in 94,
131Å, the entire active region structure becomes complicated as further
features of loops filled with hot plasma are observed. However, the
surrounding structures from other parts of the flux regions have similar
thermal conditions. The field line system around the main filament is not
quite enough to reveal the underlying topological configuration in detail.
Because this entire configuration evolves under quasi-static conditions, we
observe no significant large scale structural change for hours.

The AIA filter passbands have a wide range of visibility of thermal plasma
from chromosphere ($LogT=10^{4}K$) to hot, diffused corona ($\approx 10$MK).
In order to disclose details of connection between low lying filament and the
overlying loops, we make use of composite images of different combinations
prepared from AIA passbands. For a simultaneous view of corona from
chromosphere, we showed in Figure 1(top left), the 304Å passband image at
06:50UT on April 11, 2013 blended with the image of 94Å passband at the same
time. From this, it is obvious that the low lying filament channel in 304Å
deviates in projection with the overlying hot sigmoid. The filament, the
sigmoid above it and the overlying flux bundle demonstrate a complex flux
systems stacked over each other.

A similar observational view persists well before on 9 April in the 304, 131
and 171Å channels (Figure 2). The cool filament channel is overlaid by long
plasma loops (OL) having their photospheric connections on either side of it.
This is analyzed in successive composite frames prepared from 304, 171, and
94Å (as shown in 2nd row panels of Figure 2). The central part of the filament
is increasingly surrounded by hot plasma illuminated in 131Å, which indicates
the augmenting scenario of the main body of the MFR by wrapped field lines.
This would be likely due to reconnection in the current sheets formed in the
interface of MFR and surrounding field, by which the thermal energy heats the
plasma to observable temperatures (Gibson et al., 2006).

The observations are of three-dimensional structures projected onto the plane
of the sky. Moreover, although plasma and field are frozen together in highly
conducting corona so that coronal plasma structures essentially trace the
magnetic field, plasma emission is the only possible distinct observable under
certain density and temperature conditions dictated by an observing
instrument. In this case, we made use of composite images prepared from
different combinations of AIA channels (for quiet and flaring corona with
combinations 94, 335, 193Å; flaring corona, chromospheres, transition region
in combinations of 131, 94, 304Å) for our interpretations. They provide
substantial evidence for the developing scenario of the sigmoidal structure
during three days of evolution (Images not shown here).

The augmentation scenario of the MFR appears to occur in two stages (Figure
2). In the first stage, the long overlying loops, (OL) in the form of arcade,
significantly turn to sheared arcade and then transform toward the east and
west lobes of the sigmoid structure. In the second phase, these increasingly
inclined loops turn towards two inverse J-sections having footprints lying
side by (L1 and L2) the filament. Evidently, the loops L1 and L2 reflect a
probable involvement in traditional tether-cutting reconnection (Moore et al.,
2001). Once reconnection of these L1 and L2 loops occurs, formation of
continuous sigmoid is inevitable, by added axial fluxtubes. These two phases
possibly occur in a slow dynamical evolution, where infinitesimal
displacements of the flux regions having these loops, induce continuous
reconnection, which adds twisted flux threads wounding some common axis of the
existing MFR. This mechanism therefore is identical to the sheared arcade to
rope transformation proposed by van Ballegooijen & Martens (1989). Indeed, the
observed magnetic flux distribution well supports this augmentation scenario
which shows the canceling and approaching opposite flux patches side by the
filament (Figure 4). Our interpretations are further supported by another set
of observations (Figure 3) below.

Earlier on 9 April (Figure 3), the existence of the sigmoidal structure is not
clear in hot channels except faintly observed filament channel. However,
emission from the lower lobe section (like inverse J) is conspicuously present
most of the time. After a day of evolution i.e., by April 10, a developing
sigmodal structure becomes apparent with a well visible East lobe.
Specifically, the hot overlying flux bundle at the middle of the sigmoid and
its geometric evolution is of interest (VZ14). While undergoing dynamical
evolution, this whole structure brightens intermittently, probably
corresponding to small scale reconnections of the loop systems. One such major
bright emission corresponds to a partial/failed eruption (around 18:00UT on
April 10) in which the MFR lifted and appears to split so that the upper part
expels and lower section settled back to its stable position (Gilbert et al.,
2001, 2007). Data gaps around this period constrain to reveal more details on
this partial eruption. After this, the two J-shaped sections merged to form a
continuous sigmoidal MFR which is very apparent (panels at 15:00/10, 01:00/11
April), by this time the magnetic flux distribution shows fragmented and
disappearing positive flux corresponding to the northern lobe structure of the
MFR.

Figure 4.— Line-of-sight magnetic field observations from HMI corresponding to
AIA coronal observations in Figure 3. Contours of $\pm 120$G are overdrawn in
each panel for highlighting magnetic regions from surrounding small scale
values. Positive flux in the enclosed region of yellow (dashed) contour
corresponds to East lobe leg of sigmoid and possibly involved in the course of
development of sigmoidal MFR. Note that flux distribution smears away
throughout three day evolution within this contour. Approaching and canceling
flux features in panel (d) discern a possible scenario of reconnection of
inclined loops inferred in Figure 2.

Further, during the evolution of three days, it is difficult to interpret the
magnetic topology of this flux system of filament/sigmoid from the projected
imaging information. Bald patch seperatrix surface (BPSS) and hyperbolic flux
tube (HFT) are two kinds of topological configurations associated with
theoretically predicted MFR models (Titov et al., 2002). As suggested by van
Ballagooijen, sigmoids formed from sheared arcades by photospheric flux
cancellation driven by converging motions, which is the case here, are more
likely associated with BPSS rather than HFT. When the sigmoid structure is
regarded as MFR lying low in height, its middle section dips into dense
photosphere and appears as two J-sections in the coronal observations like
x-ray or EUV. However, the associated BPSS topology may turn to HFT while slow
upward rise motion commences (Gibson et al., 2006) and continuous structure of
MFR will be envisioned. Because fast reconnection occurs in a thinning current
sheet with HFT, the MFR lifts off the filament completely with full eruption
and is very unlikely for the eruption to be suppressed at that stage.

Table 1Net Magnetic Flux from the contour region in Figure 4 Date [UT] | axial flux | total abs flux | ratio [%]
---|---|---|---
| [$10^{21}$ Mx] | [$10^{21}$ Mx] |
April 9, 02:00 | 4.1 | 28.9 | 14.1
April 9, 15:00 | 3.1 | 22.5 | 13.7
April 10, 02:00 | 2.9 | 22.7 | 13.0
April 10, 15:00 | 2.3 | 17.4 | 13.3
April 11, 01:00 | 2.4 | 17.3 | 13.6
April 11, 15:00 | 1.5 | 16.5 | 9.1

##  4\. Cancellation of Magnetic Flux and Build-up of Twist: HMI Observations

The corresponding details of the evolution of magnetic fields at the
photospheric surface are studied (See Figure 4) by vector magnetic field
observations. As explained earlier, the magnetic flux regions show little
evolution during three days with respect to their motion. The time evolution
of area integrated flux shows details about the change in the flux content.
Indeed, the time profile of absolute flux in the active region (Figure 5, top
panel) indicates a continuous decrease of magnetic flux from April 9 till the
eruption onset on April 11. During this period, the north polarity flux (south
polarity) decreased by 56% (48%) from its initial value at the early hours on
9 April. This decay or decrease includes polarity regions having flux rope
legs and the overlying loops. Note that these profiles have 12 hour periodic
variations probably related to orbital effects of the HMI instrument which
introduce variations in the field measurements both spatially and temporally
(Hoeksema et al., 2014).

As the time duration is about two days over which this significant decrease of
the fluxes observed, it is likely related to general evolution of the active
region in addition to slow reconnection and implies the usual scenario in
decaying active regions. Further, to identify the size distribution of these
fluxes, we overlaid contours of $\pm 120$G. From snapshots of three successive
days, all identified magnetic regions evolve with decreasing spatial
distribution of flux. Since one of the legs of the MFR is associated with
positive flux region N1 and N2, we isolate them (yellow contour) and measured
the flux content at different snapshots (Figure 2). Consistent with the
smearing flux distribution within this contour region, the measured net
positive flux (See Table 1) decreases from $4.27\times 10^{21}$ Mx on April 9
to a significant value of $1.98\times 10^{21}$Mx on April 11, 2013. A similar
measure of the main sunspot flux from which the MFR originated implies the
same conclusion.

Figure 5.— top panel: The evolution of flux content in the entire AR 11719.
The estimated net line-of-sight flux from north and south magnetic polarities
with respect to time is plotted, respectively. The monotonic decrease of the
flux in the both polarities infers to possible flux cancellation. Note the
steep decrease of the net flux till 15:00 UT on 10 April 2013 by which time
the magnetic system of sigmoidal MFR formed (see Figure 2 and 4). bottom
panel: Average alpha ($\alpha_{\rm av}$) evaluated over the entire active
region with respect to time for three days. Vertical green and red lines
indicate onset times of fluxrope rise and M6.5 flare, respectively.

These evolving conditions of fluxes support the sustainability and further
development of the MFR. Because the MFR channel is already formed well before
the observation on 9 April, under the slow motions of the flux regions that
are mostly driven by granular motions, reconnection of the field lines will
reinforce the MFR by added axial flux. Field lines connecting sunspot S1 to
N1, possibly reconnect in a traditional tether cutting fashion (Moore et al.,
2001) at the polarity inversion line with those connecting S2 and N2. However,
those branches of field lines overlying the MFR from S2 to diffused patch of
N2 provides downward tension force to balance the upward force of the MFR due
to enhanced currents developed by the continuously added axial flux. For the
occurrence of the successful eruption, the force balance should lost either by
the weakening the overlying flux or by strengthening the axial flux in the
MFR. Based on the observations, we argue that both of them could be conducive
factors. As described earlier, the overlying flux bundle exhibits kink rise
motion, which might allow for the initiation. The kink rise motion of the flux
bundle signifies the increasing twist, which means enhanced currents and more
axial flux in the MFR, supporting the second argument for force imbalance. In
the absence of accurate twist measurements at the fluxrope leg, the first
argument is the most reasonable to consider under the action play. Looking at
this point, parametric and numerical studies (Aulanier et al., 2010; Amari et
al., 2010) suggest a limiting value of the axial flux of the rope (6-10%) in
the active region flux, beyond which force balance be lost. In decaying active
regions, this value is in the range of 10-14% (Bobra et al., 2008; Su et al.,
2009; Savcheva & van Ballegooijen, 2009). In our case, although it is
difficult to separate these fluxes, for a quantitative approximation, the
axial flux in the contour region (Table 1) is calculated in a consistent range
(9-14%) of the total active region flux manifesting overlying polaidal flux.
So, these results delineate the marginal stability conditions for the MFR.

In order to further support the scenario of the formation or development of
flux rope, we compute the parameter

${{\alpha}_{av}}=\frac{\sum{{{J}_{z}}(x,y)sign[{{B}_{z}}(x,y)]}}{\sum{|{{B}_{z}}|}}$
(1)

as a proxy for twist of ARs. It is derived from the assumption of force-free
magnetic fields and signifies the extent of twist of field lines due to field
aligned currents. The error in $\alpha_{\rm av}$ is deduced from the least
squared regression in the plot of vertical field $B_{z}$ and vertical current
$J_{z}$ and is given by

$\delta\alpha_{av}^{2}=\frac{{{\sum{\left[{{J}_{z}}(x,y)-{{\alpha}_{av}}{{B}_{z}}(x,y)\right]}}^{2}}/|{{B}_{z}}(x,y)|}{(N-1)\sum{|{{B}_{z}}(x,y)}|}$
(2)

Where N is the number of pixels with $|Bt|>120$G (lower cut-off for the
transverse field). Its time evolution is plotted in Figure 3. The time of rise
motion of the flux rope and its eruption are indicate by vertical (green, red)
lines. The error limit is much smaller than the mean value. Note the negative
sign of $\alpha_{av}$ implies left handed helicity consistent with that of the
inverse S-sigmoid. The twist parameter has no corresponding evolution with the
decreasing flux till 11 April. It increased on 9 April following a gradual
decrease on 10 April. Then it commences increasing from 11 April till 15:00UT
to a value of -$2.3\times 10^{-8}m^{-1}$. Together with decreasing flux
content in the AR, the increasing average twist prominently from 11 April,
characterize the conditions to augment the existing sigmoidal structure as
inferred from EVU observations.

Figure 6.— The solar system upto 1 AU in the ecliptic plane. On April 11,
2013, the STEREO-A and B are separated by $276^{o}$ and located $133^{o}$ West
and $141^{o}$ East, respectively with respect to Sun-Earth line. Arrowed line
shows a possible direction ($13^{o}$ away from Sun-Earth line) of CME
propagation towards the Earth. The coordinates are heliocentric Earth ecliptic
Cartesian coordinates in units of 1AU.

##  5\. The Eruption Mechanism

At the time of eruption, the source AR contains a filament as seen in cool
temperatures of AIA/304Å, and over which a main inverse S-shaped sigmoid, and
multiple twisted flux bundles visible in AIA hot pass bands mainly 131,
94Å[last panel in Figure 2 and 3]. Interpreting this sigmoid system in terms
of MFR models, the initiation mechanism together with morphological, thermal,
kinetic and magnetic properties of this eruption event was studied in great
detail by VZ14. This sigmoidal MFR starts with a slow rise from 06:15UT
followed by fast rise from 06:40UT and eventual eruption. Consistent with our
observational signatures of development of the MFR over days, the results of
their study suggests that the cancelling fluxes are prime factors to the
monotonous twisting of the FR system reaching to a critical state to trigger
kink instability. The support for this instability comes from the observed
kink-like evolution of the overlying flux bundle (Figure 3 and Figure 2 in
VZ14) and the co-spatial localized distribution of increased twist parameter
in the main sunspot from where the MFR originated. This instability likely
initiates the rise motion until a critical height for a possible onset of
torus instability, from which the MFR likely undergoes self similar expansion
and outward propagation, subsequently resulting in the eventual eruption of
Earth-directed CME. Note the analysis based on MFR insertion model (Table 1),
the net positive flux (as a proxy for axial flux) over time indicates marginal
stability to this MFR system. The preceding flare of GOES M6.5/3B class (from
06:55UT, see Figure 1d) is a consequence of progressive reconnection in
thinning current sheet underneath the rising FR.

##  6\. Orientation of the CME MFR in Extended Corona

During the launch of 2013 April 11 CME from the Sun, the solar system in the
ecliptic plane upto 1 AU and the positions of STEREO-A and B spacecrafts are
depicted in the plot of Figure 6. The eruption is seen on the solar disc from
the Earth (SDO, LASCO) perspective and the CME was observed by SOHO/LASCO-C2
at 07:24 UT onwards as a full halo CME with a speed of the
CME111http://cdaw.gsfc.nasa.gov/CME_list/UNIVERSAL/2013_04/ in LASCO FOV was
861 km/s and was found to be decelerating. STEREO-A was located $133^{o}$ West
and STEREO-B was $141^{o}$ East of the Earth, and so they could not observe
the CME MFR during initial times within the low corona. However, the
separation angle between them ($276^{o}$) makes it possible to observe the MFR
as a bulk structure of the CME that emerged out of the occulter after 07:10 UT
in the East limb of STEREO-A and after 07:30UT in the West limb of STEREO-B on
April 11 (Figure 7 and 8, top panels). The MFR structure (as seen in classical
three part structured CME) could be identified as a dark cavity in the CME
morphology in COR1-B. Since this CME is halo event from COR-A and LASCO views,
its three part structure could not be identified there. The new definitions
suggest that the CMEs which travel beyond $10R_{\odot}$ are being supported by
MFR topology and ruling out other possibilities of loops and jets (Vourlidas
et al., 2013). Therefore, our description of MFR topology to the observed
morphology of source region sigmoid (sections 3-5) and the CME fits well with
the observed properties in both the low and upper corona as well.

Figure 7.—  Top panels: CME morphology observed from COR1-A, C2, and COR1-B
respectively at 07:30UT on April 11 2013. Bottom panels: Overplot of the best
fitted wireframe of MFR in GCS model. Note that in C2 the CME is halo directed
toward Earth, whereas it directs away from COR-A on farside. Note the GCS
parameters $\gamma=-45^{o}$, $\alpha=50^{o}$, $\kappa=0.45$ and $h=4R_{\odot}$
reproduce this CME morphology.

In order to reveal the underlying large scale structure and orientation of MFR
by exploiting the plane of sky projected images of plasma structures, we need
to determine its three-dimensional reconstruction using simultaneous imaging
observations from multiple view points. For this purpose, we employed
simultaneous three-point i.e., the SECCHI/COR-B, LASCO-C2/C3 and SECCHI/COR-A
white light observations of the CME, with a model called Graduated Cylindrical
Shell (GCS; Thernisien et al. 2009. In this model, the large scale structure
of MFR is approximated by two shapes; the conical legs and the curved
(tubular) fronts, which is known as the ”hollow croissant”. The involved
inherent assumption in this model is that the magnetic orientation of an
erupting CME MFR is constrained by the pre-eruptive magnetic configuration in
the source AR, invoked after a study of many CMEs and their source region
magnetic configurations (Cremades & Bothmer, 2004). Before applying this
model, a suitable background image was subtracted from a sequence of processed
total brightness images.

Figure 8.—  Top panels: CME morphology observed from COR2-A, C3, and COR2-B respectively at 10:54UT on April 11, 2013. Bottom panels: Overplot of the best fitted wireframe of MFR in GCS model. Note that in C3 the CME is halo directed toward Earth, whereas it directs away from COR-A on farside. Note the GCS parameters $\gamma=-45^{o}$, $\alpha=50^{o}$, $\kappa=0.45$ and $h=17.5R_{\odot}$ reproduce this CME morphology.  Table 2GCS fitting parameters at different times Time [UT], April 11 | $\kappa$ |  $\alpha$ [deg] | height [$R_{\odot}$]
---|---|---|---
07:30 | 0.45 | 50 | 4.0
08:24 | 0.45 | 50 | 8.5
09:54 | 0.45 | 50 | 13.5
10:54 | 0.45 | 50 | 17.5

Figure 7 and 8 (bottom panels) show the difference images of the CME at
07:30-07:24UT [COR1-A, C2 and COR1-B] and 10:54-10:24 UT [COR2-A, C3 and
COR2-B] on 11 April, respectively. These panels are overlaid with a wireframe
(green) of the MFR retrieved from an approximated fit of GCS model. While
fitting the GCS model, we input the source location position (latitude of
$9^{o}$ North, longitude of $13^{o}$ East), tilt-angle ($\gamma=-45^{o}$) of
magnetic polarity inversion line (see Figure 2) and vary the height, aspect-
ratio ($\kappa$, major and minor radius of the MFR), half-angle ($\alpha$)
until achieving the best visual fit to the observed Thomson scattered bright
emission of the CME. Table 2 summarizes these fitted parameters at four
different epochs of CME propagation in the inner corona. At all four time
instants, an half angle of $50^{o}$ and aspect ratio of 0.45 gives a best
resemblance to the projected MFR on to the plane of the sky. We point that the
constant value of $\kappa$ during the outward motion of MFR indicates its
self-similar nature of expansion as observed for many CME events (Subramanian
et al., 2014) in the inner corona. Given radial positions at successive time
instances, intermediate velocities and their average value can be estimated.
Thus calculated instantaneous velocities 967km/s [07:30-08:24UT], 644km/s
[08:24-09:54UT], 773km/s [09:54-10:54UT] arrive to an average value of
795km/s. Note the published average velocity in C2 fov from plane of sky
observations is 860km/s. From this analysis of Earthward-directed CME MFR, it
is clear that the determination of the parameters defining the MFR orientation
from three-point observations is somewhat a near approximation and useful to
reproduce oblique cases when MFR is not an edge-on (limb) event. As MFRs
rotate on their outward propagation (Lynch et al., 2009) due to their inherent
twist, it is quite possible that this MFR tilt be $-55^{o}$ within COR2 FOV as
this value too fits the observed morphology very well.

##  7\. Propagation of the CME MFR in the Heliosphere

###  7.1. Kinematics from Stereoscopic and Single Spacecraft Reconstruction
Methods

It has been shown that different parts (structures) of the CME propagate and
reach the Earth in the same order as observed in remote observations (Liu et
al., 2010; Byrne et al., 2010; Howard & DeForest, 2012). We acknowledge the
difficulty in tracking the MFR of a CME using running difference images from
HI. However, tracking of density enhanced feature as leading edge of the CME,
which is solar wind or coronal plasma pile-up ahead of the MFR and identified
as shock-sheath region in in situ data, is conveniently possible (Davies et
al., 2009; Möstl et al., 2010; Mishra & Srivastava, 2013). Assuming that the
3D kinematics of CME leading edge will mimic that of the associated MFR too,
we have estimated the 3D kinematics of the leading edge using COR2, HI1 and
HI2 observations from STEREO (Figure 9). From them, time-elongation maps
(J-map; Davies et al. 2009) are constructed as shown in Figure 10. Positive
inclination bright curves in the J-maps indicate the motion of the CME
features away from the Sun. Using these J-maps, we tracked the bright leading
front manually and derived their elongation-time profiles (dashed red line).

Figure 9.— top row: Left, middle, and right panels show the evolution of 2013
April 11 CME in the running difference image of HI2-A, HI1-A, and COR2-A
respectively. bottom row: Running difference images from COR2-B, HI1-B, HI2-B
in Left, middle and right panels, respectively. The contours of the elongation
angle (green) and the position angle (blue) are also deployed on each image.
In all panels, horizontal red line is along the ecliptic and indicates the
position angle of the Earth and vertical red line (left panel) refers $0^{o}$
position angle.

The three most widely used stereoscopic reconstruction methods to estimate the
kinematics of CMEs using SECCHI/HI observations are the Geometric
Triangulation (GT; Liu et al. 2010), Tangent to a Sphere (TAS; Lugaz et al.
2010) method and stereoscopic self-similar expansion (SSSE; Davies et al.
2013) method. These methods differ by assuming a different geometry for the
CME. (Davies et al., 2013) showed that GT and TAS methods are the special
cases of SSSE method corresponding to cross-sectional angular half-width
($\lambda$) of the CME as $0^{o}$ and $90^{o}$, respectively. We therefore,
implemented the SSSE method to estimate the kinematics for the present case.

Figure 10.— Time-elongation maps (J-map) in the ecliptic plane for spacecrafts
A(top) and B (bottom) on STEREO using running difference images of COR2, HI1
and HI2. The tracks of the 2013 April 11 CME is indicated with a red curve.

Using the elongation measurements (Figure 10) and position of STEREO
spacecraft, the estimated kinematics from SSSE method for different values of
$\lambda$ is shown in Figure 11. The plots for $\lambda=0,30,60^{o}$ are shown
till the CME reaches L1 location, i.e. approx. $214R_{\odot}$ from the Sun.
This is done to examine the role of cross-sectional angular extent of the CME
in estimating the kinematics. The estimated kinematics with $\lambda$ equal to
$90^{o}$ is shown for relatively larger distances. It is evident that the
estimated kinematics differs for different $\lambda$. It is to be noted that
although distances and speeds derived from these methods vary significantly,
the estimates of direction and its trend from these methods are within
$10^{o}$. Estimates of direction from all the methods suggest that the CME is
propagating towards the East of the Sun-Earth line in the ecliptic plane. This
is consistent with the solar source location of the CME and the estimated
direction in COR FOV from the GCS model.

Figure 11.— From top to bottom, the panels show the distance, propagation
direction, and speed, respectively, of the 2013 April 11 CME MFR. The
kinematics shown with red, blue, green and black are derived from SSSE method
with $\lambda$ equal to 0, 30, 60 and $90^{o}$, respectively. The estimated
speed has systematic fluctuations due to numerical differentiation and do not
represent the real effect on the CME. It highlights the propagation of error
into the kinematics because of even a little uncertain tracking of the CME.
Such a procedure for estimating the speed has potential to reveal crucial
short time variations in speed. However, the smoothed speed obtained by
fitting the estimated distance-time curve into a polynomial may hide the short
time variations in the CME speed.

We admit that there are several sources of errors (geometry, Thomson
scattering, optically thin nature of CMEs, breakdown of assumptions considered
in the methods itself) in implementing these methods and quantification of
such errors is extremely difficult. However, to examine the effect of
uncertainties in the estimated kinematics, we considered an error of 5 pixels
in the measurements of elongation angle. Such an error corresponds to
uncertainties of 0.02 degree, 0.1 degree and 0.35 degree in the derived
elongation angles in COR2, HI1 and HI2 FOV, respectively. Corresponding to
these elongation uncertainties, the calculated error for SSSE (with
$\lambda=0$) method maximally reaches up to $0.5R_{\odot}$ in distance, less
than few degree in direction and few tens of km/s for speed. These errors
certainly seem to be small but of course, they do not reflect the total error
in derived kinematics. Further study is required to quantify the actual errors
because of several invalid idealistic assumptions in the methods.

Also, at higher elongation (greater than approx. $40R_{\odot}$), larger
variations in the estimated kinematics from SSSE method for different
$\lambda$ are noted. From Figure 11, it is clear that the estimated distance
from GT method increased around 18:00 UT on April 11 at $90R_{\odot}$ from the
Sun. Such an unphysically fast increase in distance and speed is meaningless
due to the absence of forces capable of accounting for this acceleration at
distances farther from the Sun (Cargill, 2004; Vršnak et al., 2010). This is
more likely because of improper use of SSSE with $\lambda$ equal to $0^{o}$
(i.e. GT) method, especially for this CME which is propagating away from the
observer. This late acceleration is significantly reduced (still unphysical)
if a higher value of $\lambda$ is considered. SSSE with $\lambda$ equal to
$90^{o}$ (i.e. TAS) method gives the lowest limit of the estimated distance
and speed values. The kinematics from the TAS method is calculated up to
$365R_{\odot}$ from the Sun.

The aforementioned facts highlight that the assumptions made in the GT method
are not valid for a CME propagating away from the observer. Also, the
spherical front approximation in SSSE method with $\lambda$ equal to nonzero
value, becomes worse due to flattening of the CME front on its interaction
with solar wind. These limitations start to play a crucial role much nearer to
the Sun for a far-sided CME than for front sided CME (Liu et al., 2013).
However, the distance beyond which these effects are crucial depends on the
direction of propagation of the CME and its size. We note that for a CME
propagating at larger angle from the Sun-observer line, its kinematics depend
more on the chosen value of $\lambda$. This is because the flanks (not nose)
for such CMEs are always observed from the observer and even a little change
in its radius of curvature leads to huge difference in the estimated
kinematics from the SSSE method. It is noted that if direction of propagation
of a CME from sun-observer line becomes more than $90^{o}$, an unphysical
acceleration will be estimated from the SSSE methods irrespective of chosen
$\lambda$ value. However, such an acceleration is reduced with higher value of
$\lambda$ and gives more accurate kinematics.

To assess the relative performance, we also applied single spacecraft
reconstruction methods on STEREO-A and B observations. We employed the Fixed-
Phi (FP: Kahler & Webb 2007), Harmonic Mean (HM: Lugaz et al. 2009), Self-
Similar Expansion (SSE: Davies et al. 2012) methods on the derived time-
elongation variations of the CME (Figure 10). These methods essentially
convert the elongation into distance from the Sun assuming a fixed direction
(longitude, here $13^{o}$ East) of CME propagation as an input.

On applying the above methods on the STEREO-A and B observations, we noticed
that estimated kinematics also largely overestimates the speed (approx.
900-1200 km/s even beyond $100R_{\odot}$) of the CME and the method becomes
completely unreliable once the CME reaches higher elongations. The direction
of propagation of CMEs is $146^{o}$ and $128^{o}$ away from the line
connecting the Sun with STEREO-A and B spacecraft, respectively. As the CME
propagating in Eastward is little closer to $90^{o}$ from the STEREO-B
spacecraft, the derived kinematics and arrival time from this spacecraft are
more accurate than using STEREO-A observations. Among all the three single
spacecraft methods, the most inaccurate results are obtained from the FP
method and less inaccurate are from the HM method. This probably confirms the
assumption that the larger structure of CME is somewhat suitable for
estimating the time varying profile of the CME kinematics. However, the
failure of these single spacecraft methods at higher elongation could be due
to real deflection or artificial deflection because of expansion or/and due to
changes in the approximated idealized structure (Wood et al., 2010; Howard,
2011; Mishra & Srivastava, 2014).

We further applied the fitting version of the three single spacecraft
reconstruction methods, namely Fixed-Phi Fitting (FPF: Sheeley et al. 2008),
Harmonic Mean Fitting (HMF: Möstl et al. 2011), and Self-Similar Expansion
Fitting (SSEF: Davies et al. 2012). Noting the expressions for the elongation
as a function of speed and direction from the earlier FP, HM and SSE methods,
these methods fit the observed elongation-time profile of the CME to an
analytical function. From the FPF method on STEREO-A, we found that CME speed
as 654 km/s, propagation direction as $99^{o}$ from STEREO-A spacecraft and
its launch time at 11 April 05:05. Similarly, we also applied the HMF and SSEF
methods (with $\lambda=50^{o}$) and obtained the speed, propagation direction
and launch time of the CME. The results obtained for STEREO-A and B are shown
in Figure 13 and 14, respectively and summarized in Table 3. In these figures,
the results for SSEF, which fall between the FPF and HMF methods, are not
plotted to avoid cluttering.

Moreover, we have also analyzed the in-situ observations of this CME obtained
from WIND spacecraft (Figure 12). The actual arrival time of the CME is marked
by the arrival of a shock at 22:50 UT on April 13, which is followed by a
prolonged (18 hr) sheath region. This sheath region is followed by a MC from
17:35UT on April 14, whose signatures are indicated by rotation of the
magnetic field, an increase in the magnetic field strength to 14n and decrease
in the temperature (order of $10^{4}$ K). Duration of this MC traversal is
approximately 25 hours at a speed of approximately 450 km/s, suggesting its
width as approximately 0.27 AU, which is the average size of MCs as found by
previous studies (Liu et al., 2005, 2006, 2010). The arrival of the shock
(jump in density, temperature and speed) structure ahead of the CME is
expected to match the estimated arrival of the tracked density enhanced
feature in the heliosphere using the J-maps as shown in Figure 10. Therefore,
for a quantitative analysis, we compared the estimated arrival time by various
reconstruction methods to that of in-situ shock arrival and listed the errors
in Table 3.

The errors in the estimated arrival time from the SSSE method with $\lambda$
equal to 0, 30, 60, and $90^{o}$ are earlier than the actual time by 46, 31,
26 and 21.5 hr, respectively. This shows that the estimates of arrival time
from HI observations have large errors due to overestimated speed values. In
light of these findings, it appears that in such a case, SSSE methods with
higher value of $\lambda$ (larger elongation from the Sun) provide better
kinematics for the CME.

Figure 12.— From top to bottom, panels show the magnitude of magnetic field,
latitude, longitude of magnetic field vector, density, temperature, speed, and
plasma $\beta$ with respect to time. From the left, the first, second and
third vertical lines mark the arrival of CME driven shock (at 22:50UT on
13th), leading (at 17:35UT on 14th) and trailing edge (19:20UT on 15th) of
magnetic cloud, respectively. Figure 13.— Best fit FPF and HMF results, for
the tracked CME feature from STEREO-A location, are shown with red and blue
colors. top: time-elongation variation theoretically derived from FPF and HMF
approaches are overplotted on the observed elongation-time variation of the
tracked feature. bottom: Residuals between the derived elongation from fitting
functions and the observations. In the top panel, the labels Phi, speed and T
are the approximated constant speed, direction of propagation from the
STEREO-A, and launch time of the CME on the Sun, respectively. Figure 14.—
Best fit FPF and HMF results, for the tracked CME feature from STEREO-B
location, are shown with red and blue colors. top: time-elongation variation
theoretically derived from FPF and HMF approaches are overplotted on the
observed elongation-time variation of the tracked feature. bottom: Residuals
(i.e. the difference) between the derived elongation from fitting functions
and the observations. Residuals are estimated in a similar procedure to Möstl
et al. (2011). In the top panel, the labels Phi, speed and T are the
approximated constant speed, direction of propagation from the STEREO-B, and
launch time of CME on the Sun, respectively

Based on the kinematics determined from the FP, HM and SSE methods, the
arrival time of this CME is still estimated as 15-40hr before the actual
arrival. The error in the kinematics may be because of inaccurate fixing of
the propagation angle and therefore by changing the propagation angle of $\pm
10^{o}$, we again repeated the analysis and still found the huge error in the
arrival time of the CME. On applying these methods, we inferred less erroneous
kinematics obtained using the STEREO-B observations when the CME is fixed to
propagate eastward from the Sun-Earth line and vice-versa for STEREO-A
observations.

Table 3Summary of the propagation kinematics from Stereoscopic and Single
Spacecraft reconstruction methods

Method | Speeda | Directionb | Launch Timec | Arrival Time | Error in Arrival Timed
---|---|---|---|---|---
| [km/s] | [deg] | [UT] | [UT] | [h]
SSSE ($\lambda=0^{o}$) | 2900 | -7 | 11 April 07:40 | 12 April 01:00 | -46
SSSE ($\lambda=30^{o}$) | 1100 | -9 | 11 April 07:40 | 12 April 16:05 | -31
SSSE ($\lambda=60^{o}$) | 1140 | -12 | 11 April 07:40 | 12 April 21:00 | -26
SSSE ($\lambda=90^{o}$) | 1060 | -13 | 11 April 07:40 | 13 April 01:30 | -21.5
FPF(ST-A) | 654 | 34 | 11 April, 05:05 | 13 April, 19:55 | -3
FPF(ST-B) | 717 | -53 | 11 April, 04:56 | 13 April, 14:20 | -8.5
SSEF(ST-A) | 867 | 0 | 11 April, 05:50 | 13 April, 05:15 | -17.5
SSEF(ST-B) | 919 | -20 | 11 April, 06:01 | 13 April, 10:40 | -12.2
HMF(ST-A) | 979 | -13 | 11 April, 06:00 | 13 April, 01:10 | -21.6
HMF(ST-B) | 1016 | -10 | 11 April, 06:15 | 13 April, 23:15 | -23.5

  * a

for SSSE methods, the quoted speed is transit value

  * b

direction with negative (positive) sign refers to CME propagation in eastward
(westward) to the Sun-Earth line.

  * c

First COR2 appearance of leading edge is taken as launch time for SSSE methods

  * d

negative (positive) value of error in arrival time refers earlier (late)
arrival of the CME

We noted that the HMF and SSEF methods estimate the propagation speed of the
CME apex, which is not exactly towards the Earth, therefore we have applied
geometrical correction (Möstl & Davies, 2013) to estimate its speed in an off-
apex direction. This geometrically corrected speed, which is less than its
speed derived in the apex direction, is used to obtain the estimated arrival
time of the CME at L1 point.

From Table 3 it is obvious that, among all the single spacecraft
reconstruction methods, the most accurate estimation of CME arrival time
(within an error of 3-8 hr) is obtained by the FPF method and less accurate by
the HMF method. However, if we believe the direction of propagation of CME
estimated from GCS model as accurate, then estimation of the direction from
FPF methods is erroneous in agreement with (Lugaz, 2010). We find that even
the fitting methods overestimate the speed of the CME. In principle, these
fitting methods always overestimate the speed of fast CME as they estimate a
constant speed for CME and therefore they are unable to incorporate the real
deceleration due to acting drag forces on the CME. This limitation of these
methods is most obvious for CME propagating largely away from the Sun-
Spacecraft line. If we bear the uncertainties with the direction of
propagation of the CMEs, then FPF method does a good job for predicting
arrival time of CME at L1. We infer that in the FPF method, the two sources of
errors arising from not taking the geometry of the CME and physical
deceleration into account actually cancels each other. However, any such
physical deceleration is significantly counted in terms of geometrical (i.e.
apparent) deceleration, if SSEF and HMF methods are used. The analysis of this
event could help us to realize the potential differences in the results
because of different fitting methods.

Figure 15.— top: Analysis of the difference between the observed and
calculated travel times (o-c). Travel times are computed at different $w$
(indicated for each curve) as a function of $\gamma$. CME take off position
$r_{0}=17.5R_{Sun}$ and speed $v_{0}=650km/s$ are considered from GCS
kinematics. Intersecting point of the each curve on the horizontal (dotted)
line gives $\gamma$ value for the CME arrival at L1. bottom: CME trajectories
($r(t)$) as a function of time for ambient solar wind velocity w=350, 375 ,
400 km/s. Velocity ($v(t)$) is also plotted with y-axis scale on the right.
Dotted lines points the in-situ MC arrival time (April 14, 2013 at 17:35UT) on
the trajectories. Note that the arrival times are differed by 5h for the range
$350<w<400$.

###  7.2. CME trajectory reconstructed with Drag-Based-Model

Despite using the SSSE method with $\lambda$ equal to $90^{o}$, a rise in the
CME speed around 14:00 UT on 2013 April 12 at a distance of $160R_{\odot}$ is
noticed. This late increase is unphysical, for the reasons mentioned earlier
and also due to the limitations of the SSSE method described in Mishra &
Srivastava (2014). Moreover, the average in situ measured speed of the CME is
around 450 km/s whereas each method (even single spacecraft based) applied in
our study overestimates the speed of the tracked feature of the CME and is why
these methods estimate the arrival well before the in-situ arrival. Therefore,
beyond a certain radial distance from the Sun over which the CME is expected
to maintain its deceleration, we have applied the drag based model (DBM;
Vršnak et al. 2013) to estimate the arrival time and speed of the CME at L1.
The model is based on the hypothesis that beyond a certain distance the CME
dynamics becomes governed solely by the interaction of the CME and the ambient
solar wind via aerodynamic drag (Cargill, 2004; Vršnak et al., 2010). This
assumption relies on the fact that in the interplanetary space fast CMEs
decelerate, and slow ones accelerate, showing a tendency to have their
velocity trend towards that of the ambient solar wind. CMEs fulfill this
assumption generally at heliocentric distances around or beyond $20R_{\odot}$
(Vršnak et al., 2004). In the DBM model, the solution (position $r(t)$ and
velocity $v(t)$) to the equation of motion describing the dynamics of the CMEs
under the assumption of constant solar wind speed ($w$) and drag parameter
($\gamma$) is given by (Cargill, 2004; Vršnak et al., 2013).

$\displaystyle
r(t)=\frac{1}{\gamma}\ln[1+\gamma\left({{v}_{0}}-w\right)t]+wt+{{r}_{0}}$ (3)
$\displaystyle v(t)=\frac{{{v}_{0}}-w}{1+\gamma\left({{v}_{0}}-w\right)t}+w$
(4)

where $r_{0}$, $v_{0}$ are initial heliocentric distance, speed of the CME.

Based on earlier works (Lepping et al., 1990; Howard & DeForest, 2012), we
assume that the MFR corresponds to the magnetic cloud in in situ observations
and therefore, it is logical to compare the actual arrival of the magnetic
cloud (here April 14, 17:35UT) with that deduced from the propagation of the
MFR in COR images. As $w$ and $\gamma$ are unknown under which conditions the
CME is propagating (see Equation 3), using the GCS kinematics as input to DBM,
we performed a parametric analysis to obtain their approximate constrained
values.

From the GCS fitting shown in Table 2, we constructed radial distance profile
by including more points. We fit that profile to a second order polynomial and
then derived the velocity profile by invoking a smooth cubic spline
interpolation procedure. This results in an expected deceleration of the CME
in its outward propagation from $4R_{\odot}$ onward. From the heliocentric
distance of $17.5R_{\odot}$ at the time instance 10:54UT, we find that the CME
is moving at a speed of $650km/s$. We assume from this distance onwards that
the further CME propagation has no influence of Lorentz force and has not
deflected because of interaction with another CME.

Supplying $r_{0}=r(t=10:54UT\,on\,11)=17.5R_{\odot}$,
$v_{0}=v(t=10:54UT\,on\,11)=650km/s$ (obtained from GCS fit) to Equation 3, we
calculated the time difference between calculated (c) and observed (o: in-
situ) arrival time of CME at $r(T=17:35UT\,on\,14)=214R_{\odot}$, by varying
$\gamma$ at a range of w values. This time difference (o-c) as a function of
$\gamma$ is plotted in Figure 15(top). Note that the curves for fast
($w>400km/s$) and slow ($w<350km/s$) solar wind speed intersect the zero time
difference line at $\gamma$ values which are unsuitable for this medium mass
CME (Vršnak et al., 2013) and therefore the values for $\gamma$ should lie for
the curves $350<w<400km/s$. Statistical studies have shown that while
implementing DBM, the choice of $\gamma$ has lesser effect than ambient solar
wind speed in determining the arrival time and transit speed of CMEs at 1AU
(Vršnak et al., 2007, 2013). So, assuming a constant value for $\gamma$
($=0.54\times 10^{-7}km^{-1}$ which is the intercept for the curve at
$w=375km/s$) within this range of solar wind, we plotted in Figure 15(bottom)
the CME trajectory (Equations 3 and 4) for its initial take off position and
speed obtained from GCS fit. As can be noted from this plot, the arrival times
are differed only by 5hrs about the mean value curve of $w=375km/s$. Also, the
transit velocities vary from mean value 428km/s by only 24km/s. This
parametric analysis constructs the CME kinematics reasonably well, once we
admit significant uncertainties in the CME takeoff position and speed.

Figure 16.— One-minute averages of the in situ magnetic field of this CME
associated MC near Lagrange point L1. Field measurements are in GSE coordinate
system. Note that $B_{y}$ component of the MC changes sign while passing the
spacecraft. Vertical lines, from left to right, mark the arrival of the CME
shock, leading and trailing edge of the MC, respectively. Figure 17.—
Schematic of the MFR orientation in par with in-situ magnetic field
observations. Rotation of observed $B_{y}$ component is demonstrated by
azimuthal field and its handedness in the MC, which is shown by cross-section
of MFR in XY-plane of the GSE coordinate system. Note that axial field
contributes to positive $B_{z}$ component (northward directed) consistent with
in-situ observations.

###  7.3. Orientation of the magnetic field in MC of MFR

The source AR twist signatures are also explored in in-situ observations of
MC. When a CME reaches Earth, the magnetic field strength associated with the
MC is stronger than the ambient field. Depending on the orientation of the
MFR, the components of MC magnetic field vary in time. We plotted, in Figure
16, the observations of magnetic field components by WIND instrument situated
near Lagrange point of Earth. These are one-minute averages and are in
Geocentric Solar Ecliptic (GSE) coordinate system, where the X-axis points
from Earth toward the Sun, Y is in the ecliptic plane but negative in the
direction of planetary motion, and Z is parallel to the ecliptic North pole.
Before the MC arrival, the field components exhibit rapid fluctuations due to
shock and sheath regions. When MC passes, the magnetic field components show
systematic variation indicating strong magnetic field associated to MFR.
$B_{x}$, $B_{z}$ components remain positive, while $B_{y}$ component changes
sign from positive to negative around the mid time (around 07:00UT on April
15) of the MC passage. Based on this information and the nature of the twist
in the source AR, we interpreted the possible orientation of the MFR upto L1
(Burlaga, 1988; Yurchyshyn et al., 2001).

In Figure 17, we schematically sketched the Sun-Earth connections by MFR in XZ
plane of the GSE system. In this figure, axis of the MFR is approximately in
meridian plane whereas the MFR is having around $-45^{o}$ tilt angle in the
source AR. We point that there is now substantial observational evidence for
the rotation of MFRs during their dynamic evolution and propagation (Green et
al., 2007). Our schematic, however, is motivated by the observations of MFR
rotation by about $45^{o}$ depending on its magnetic chirality (Lynch et al.,
2009). In our case, although the tilt can be upto $-55^{o}$ in COR FOV, it can
even smoothly vary upto $-90^{o}$ tending toward the meridian plane. In a
majority of cases ( 64%), CMEs in COR FOV do have their orientation angles
differed within $\pm 45^{o}$ with their interplanetary counterparts
(Yurchyshyn et al., 2007).

The axial field is northward directed (Ecliptic North) contributing to the
$B_{z}$ component, which is positive. In this predicted orientation, the MFR
cuts the XY plane in a circle having azimuthal field information and magnetic
helicity (handedness) signatures of the MC. When MC passes, different regions
of this cross-section encounter the spacecraft at different time phases (say
t1, t2, t3 sequentially, here t2 is 07:00UT on April 15). The projection of
the azimuthal field on y-axis at those time instances explains the sign and
magnitude of the observed $B_{y}$ component. We can suitably fix the
spacecraft position on the y-axis depending on the observed sign of $B_{x}$
component, which is positive here. Obviously, the handedness of this azimuthal
field should be negative (left) in order to match the observed
$B_{y}$-component variation from positive to negative, which is consistent
with the source AR signatures of inverse S-sigmoidal structure and the
negative value of $\alpha_{av}$. This event is similar to the one observed on
2000, February 21 (Yurchyshyn et al., 2001) with right hand twist, where the
$B_{y}$ component of MC changes sign from negative to positive value. It is
possible to explore the twist quantitatively by reconstructing the magnetic
field components in the MC cross section (Hu et al., 2014), however those
details are beyond the focus of this paper and requires a separate study.

##  8\. Summary

CME eruptions from source active regions having soft x-ray sigmoids or
H$\alpha$ filaments are modelled as manifestations of MFRs to describe many
observational features. In the context of Sun-Earth connections of an eruption
event on April 11, 2013, we investigate the formation/develoment scenario of a
sigmoid/MFR, initiation of rise motion and its propagation toward Earth. From
EUV observations of AIA, the pre-eruptive source AR consisted of a filament
channel stacked over by a faintly visible inverse-S sigmoidal structure since
past three days. In view of the description of this flux system as an MFR of
field lines wound about some common axis, the morphological study of its
evolution during 48 hour period implies a scenario of augmenting MFR. This
augmentation evidently found to occur by reconnection of inclined loops lying
side by the filament. Under the slow flux motions, both the transformation of
distance overlying loops toward sheared arcade (stage 1), and their
reconnection (stage 2) at the middle of the sigmoid are the suggested
scenarios involved in the development of this sigmoidal MFR.

The HMI magnetic fields measurements in the source AR support the EUV
observations, showing monotonic decreasing net flux for the last two days. The
net flux from the rope leg and the entire AR, according to MFR insertion
models (Bobra et al., 2008; Savcheva & van Ballegooijen, 2009), implies a
marginal stability of the system of axial flux confined by the overlying
polaidal flux. The average twist of the flux system in the AR also suggests a
rapid build up of the MFR structure past 7 hours to the onset of the eruption.
It also suggests the availability of critical twist (VZ14) in order to
initiate rise motion of the MFR. Therefore, this study of EUV and magnetic
fields suggests that the developed MFR system is initiated to upward motion by
kink-instability to reach to a height (31Mm) from where steep gradients of
horizontal field (torus-instability criteria, (Török & Kliem, 2005) drives its
further outward motion in the outer corona.

While expanding in the extended corona (after 07:10UT, 2-30$R_{\odot}$), the
CME morphology captured from COR1, COR2, and LASCO views, visually fits with a
parametrized MFR orientation, which aligns with the orientation of magnetic
neutral line in the source active region. Tilt angle is a crucial parameter in
determining orientation of MFR. MFRs by virtue of inherent twist, are shown to
rotate upto $50^{o}$ while propagating (2-4$R_{\odot}$) in the low corona
(Lynch et al., 2009). This backsided halo CME did not allow us to detect the
exact extent of possible MFR rotation. However, a tilt angle of $-45^{o}$
projects the MFR on to the plane of sky to sufficiently map the white light
features of this halo CME event. An unchanged value of aspect ratio (ratio of
minor to major radius of MFR=0.45) at successive stages of this CME MFR
indicates its self-similar nature of expansion. Tracking methods found that
the CME is propagating about $10^{o}$ to the East of the Sun-Earth line. This
is consistent with the solar source location of the CME and the estimated
direction in COR FOV from the GCS model.

Although source AR magnetic configuration defines the MFR orientation, due to
bulk in size combined with projection effects, the exact orientation of MFR in
the interplanetary space is difficult to predict within $45^{o}$ (Yurchyshyn
et al., 2007). The predicted MFR orientation (MFR axis is in a vertical plane
to ecliptic, see Figure 17) identifies the source AR twist signatures, which
is left handed, in the in situ magnetic field observations of MC. This
predicted orientation based on in situ observations, if correct, alternatively
suggests a possible rotation (clockwise as seen in line-of-sight direction, to
align with meridian plane) of MFR apex upto $45^{o}$ while traveling from Sun
to the near-Earth environment. It is worth pointing that the $B_{z}$ component
of this MC is northward, consequently no geomagnetic activity was associated
with this CME.

Our analysis underlines the overestimation of the speed from all the
stereoscopic methods applied on 2013 April 11 CME. Therefore, for the selected
CME, when the STEREO is behind the Sun, tracking of CME shock, leading edge,
and flux ropes and predicting their arrival time at 1 AU is challenging.
Further, for the position of STEREO between February 2011 and 2019 June, any
Earth-directed CME will be moving away from the STEREO space craft and hence,
the estimation of kinematics and arrival time of CME during this time is
expected to result in large errors.

Stereoscopic reconstruction methods lead to worse results than single
spacecraft reconstruction methods. We note that fixed-phi fitting method seems
to perform best among all the reconstruction methods used in our study. As the
physical deceleration of the CME is translated as geometrical deceleration in
fitting methods, the SSEF and the HMF method seems to work poorer than the FPF
method, for this quickly decelerating CME. Based on our analysis limited to a
single event, we suggest that the use of FPF method should be done for
practical purpose of arrival time prediction of such a CME. However, in the
absence of fitting methods, we must use the reconstruction methods (i.e. TAS
and HM) which approximates the CME as a very wide structure (i.e. higher value
of $\lambda$) for estimating the kinematics and arrival time of CME moving at
higher angle from Sun-spacecraft line.

As almost all applied reconstruction methods failed to estimate accurate
arrival time, alternatively, our study suggests that the estimated kinematics
by the implementation of GCS model on COR2 observations can preferably be used
as inputs in the DBM (Vršnak et al., 2010) to reconstruct the CME trajectory
and thereby estimate the arrival time. By a combination of parametric study
and the observations, the unknown parameters like solar wind speed and drag
parameter can be constrained suitably to match the in-situ arrival.

We are grateful to the referee for a detailed list of constructive comments
and suggestions. SDO is a mission of NASA’s Living With a Star Program, STEREO
is a third mission in NASA’s Solar Terrestrial Probes program, and SOHO is a
mission of international cooperation between ESA and NASA. The authors
sincerely thank Prof. A. Vourlidas, Prof. J. Zhang, Prof. N. Srivastava for
their comments and suggestions on an earlier version of this manuscript which
undoubtedly brought to its present stage. P.V. is supported by an INSPIRE
grant of AORC scheme under the Department of Science and Technology. W.M is
funded by Chinese Academy of Sciences President’s International Fellowship
Initiative (PIFI) Grant No. 2015PE015, NSFC Grants No. 41131065 and 41574165.

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