# Deciphering The Slow-rise Precursor of a Major Coronal Mass Ejection

X. Cheng School of Astronomy and Space Science, Nanjing University, Nanjing
210093, China<EMAIL_ADDRESS>
Max Planck Institute for Solar System Research, G$\ddot{o}$ttingen 37077,
Germany
C. Xing  School of Astronomy and Space Science, Nanjing University, Nanjing
210093, China<EMAIL_ADDRESS>
Sorbonne Université, Observatoire de Paris - PSL, École Polytechnique,
Institut Polytechnique de Paris, CNRS, Laboratoire de physique des plasmas
(LPP), 4 place Jussieu, F-75005 Paris, France
G. Aulanier  Sorbonne Université, Observatoire de Paris - PSL, École
Polytechnique, Institut Polytechnique de Paris, CNRS, Laboratoire de physique
des plasmas (LPP), 4 place Jussieu, F-75005 Paris, France
Rosseland Centre for Solar Physics, Institute for Theoretical Astrophysics,
Universitetet i Oslo, P.O. Box 1029, Blindern, 0315 Oslo, Norway
S. K. Solanki  Max Planck Institute for Solar System Research,
G$\ddot{o}$ttingen 37077, Germany
H. Peter  Max Planck Institute for Solar System Research, G$\ddot{o}$ttingen
37077, Germany
M. D. Ding  School of Astronomy and Space Science, Nanjing University, Nanjing
210093, China<EMAIL_ADDRESS>

(Received August 8, 2023; Revised August 22, 2023; Accepted August 24, 2023)

###### Abstract

Coronal mass ejections (CMEs) are explosive plasma phenomena prevalently
occurring on the Sun and probably on other magnetically active stars. However,
how their pre-eruptive configuration evolves toward the main explosion remains
elusive. Here, based on comprehensive observations of a long-duration
precursor in an event on 2012 March 13, we determine that the heating and slow
rise of the pre-eruptive hot magnetic flux rope (MFR) are achieved through a
precursor reconnection located above cusp-shaped high-temperature precursor
loops. It is observed that the hot MFR threads are built up continually with
their middle initially showing an “M” shape and then being separated from the
cusp of precursor loops, causing the slow rise of the entire MFR. The slow
rise in combination with thermal-dominated hard X-ray source concentrated at
the top of the precursor loops shows that the precursor reconnection is much
weaker than the flare reconnection of the main eruption. We also perform a
three-dimensional magnetohydrodynamics simulation that reproduces the early
evolution of the MFR transiting from the slow to fast rise. It is also
disclosed that it is the magnetic tension force pertinent to “M”-shaped
threads that drives the slow rise, which, however, evolves into a magnetic
pressure gradient dominated regime responsible for the rapid-acceleration
eruption.

Solar coronal mass ejections (310) — Solar flares (1496) —
Magnetohydrodynamics (1964) — Solar magnetic reconnection (1504)

##  1 Introduction

Stellar mass ejections and accompanying flaring result in energetic events
(Maehara et al., 2012; Argiroffi et al., 2019) that may prevent life from
thriving on orbiting exo-planets (Dong et al., 2018). At present, these issues
can best be studied in the solar system thanks to the direct visibility of
coronal mass ejections (CMEs) and solar flares that release a large quantity
of magnetized plasma ($\sim$1011–1013 kg), strong electromagnetic radiation
and sub-relativistic energetic particles into the heliosphere (Forbes et al.,
2006; Chen, 2011; Schmieder et al., 2015). When directed toward the Earth,
CMEs interact with the magnetosphere and ionosphere and can disrupt
communications, overload power grids, and present a hazard to astronauts
(Gosling, 1993; Webb et al., 2000; Solanki et al., 2004).

The energetic eruptions are essentially consequences of the destabilization
and reconfiguration of the coronal magnetic field. Prior to such eruptions, in
a long-lasting quasi-static phase, the magnetic field, in particular above the
polarity inversion line (PIL) of active regions (ARs), is gradually stressed
by various flows at the photosphere, resulting in accumulation of magnetic
free energy (Cheung & Isobe, 2014). The stressed magnetic fields are organised
in an orderly fashion as either sheared arcades or a magnetic flux rope (MFR,
a coherent structure with all field lines wrapping around its central axis).
Regardless of the difficulty in directly measuring the coronal magnetic field,
some observables serve as proxies of pre-eruptive magnetic configurations
including filaments/prominences (Kuperus & Raadu, 1974; Mackay et al., 2010;
Schmieder et al., 2013), sigmoids (Hudson et al., 1998; Rust & Kumar, 1996;
Green et al., 2007), cavities (Gibson et al., 2006; Wang & Stenborg, 2010) and
hot channels (coherent plasma structure with a temperature above 8 MK (Zhang
et al., 2012; Cheng et al., 2013)). Among them, the hot channels and analogues
seem to be a promising proxy of the MFR, which can even be used for
prediction, as they usually appear prior to the eruption (Zhang et al., 2012),
sometimes for hours (Patsourakos et al., 2013; Nindos et al., 2020), and then
continuously evolve toward the eruptions (Cheng et al., 2013; Gou et al.,
2019; Mitra & Joshi, 2019).

Nevertheless, how these pre-eruptive configurations evolve, in particular,
toward the very onset of the fast eruption is yet to be ascertained (Aulanier,
2014, 2021). In order to initiate the eruption, many physical mechanisms have
been proposed including tether-cutting and breakout reconnection (Moore et
al., 2001; Antiochos et al., 1999) and ideal MHD instabilities etc. (Forbes &
Isenberg, 1991; Török et al., 2004; Kliem & Török, 2006). Although evidence
has been presented for the action of individual process (Moore et al., 2001;
Williams et al., 2005; Chen et al., 2014; Cheng et al., 2020), it could be
extremely difficult for a sole mechanism to initiate a real eruption. Many
comprehensive observational studies suggest that the initiation process of
CMEs is much more complicated than expected, multiple physical processes are
often coupled to each other even though the dominated one may change from one
phase to the other (Cheng et al., 2020). Once the eruption has been initiated,
the dynamic energy release via runaway magnetic reconnection is switched on,
during which the different structural components of CMEs are quickly formed
and accelerated, giving rise to flare radiation at the same time (Priest &
Forbes, 2002; Lin et al., 2015; Veronig et al., 2018).

The other important but still puzzling characteristic during the early rise
phase is that the pre-eruptive MFR is found to be much, almost one order of
magnitude, hotter than the background quiet corona of 1-3 MK (Cheng et al.,
2012), which is true for over half of major eruptions based on a statistical
survey (Nindos et al., 2015). It is speculated that the heating is most likely
due to magnetic reconnection (Dudík et al., 2014). One piece of evidence is
that the pre-eruptive hot MFR shows an increase in toroidal flux and stays
stable for hours before it erupts successfully (Patsourakos et al., 2013). On
the other hand, a number of pre-flare activities are detected prior to the
eruption such as slow rise of pre-eruptive configurations (e.g., Zhang et al.,
2001; Sterling & Moore, 2005; Kliem et al., 2014; McCauley et al., 2015; Cheng
et al., 2020), H$\alpha$ line broadening of pre-eruptive filaments (e.g., Cho
et al., 2016), enhancement of soft X-ray emission (e.g., Zhang & Dere, 2006;
Priest, 2014), brightenings at the footpoints of chromospheric kernels (e.g.,
Wang et al., 2017; Chen et al., 2019), changes in magnetic topology (e.g.,
Chintzoglou et al., 2015; Liu et al., 2018a) and even appearance of non-
thermal particles (e.g., Syntelis et al., 2016; Awasthi et al., 2018;
Hernandez-Perez et al., 2019). All these pre-flare activities are also
suggested to be more or less caused by magnetic reconnection. However,
justifying a clear and integrated physical picture that links the formation,
heating and early rise of the MFR, as well as various observed pre-flare
characteristics, to magnetic reconnection remains rather difficult. The major
difficulty is that these pre-eruptive signatures are often of short-lived
($\sim$minutes), in particular for those from ARs (Cheng et al., 2020).
Moreover, it is also limited by observational capacity, e.g., the field-of-
view of instruments (such as Goode Solar Telescope) is too small to observe
the entire pre-eruptive structure that usually approximates to the size of
ARs, and/or only the signatures of pre-flare activities in the lower
atmosphere were detected (Wang et al., 2017). Furthermore, it is almost hardly
to disentangle critical characteristics in real observations as which are more
complex than models. Such a problem becomes even worse due to inevitable
projection effects (Zhang et al., 2017; Zhou et al., 2017; Gou et al., 2019;
Awasthi et al., 2018; Hernandez-Perez et al., 2019).

Here, through comprehensive analyses of a long-duration precursor phase of a
major CME/flare on 2012 March 13 which overcomes part of aforementioned
limitations, we dislcose the relations intertwined among the heating and early
rise of the pre-eruptive hot MFR, various pre-flare characteristics and
precursor reconnection. With a combination of observation-inspired three-
dimensional magnetohydrodynamics simulation, it is suggested that the magnetic
tension force within the MFR drives the slow rise; while the magnetic pressure
gradient one is responsible for the following acceleration eruption.

##  2 Instruments and Data

The Atmospheric Imaging Assembly (AIA; Lemen et al., 2012) on board Solar
Dynamics Observatory (SDO; Pesnell et al., 2012) images the solar atmosphere
almost simultaneously with ten passbands covering temperatures from 0.06 to 20
MK. The temporal cadence and spatial resolution of seven (two) EUV (UV)
passbands are 12 (24) s and 1.2 arcseconds, respectively. Among the seven EUV
passbands, the 131 Å and 94 Å, sensitive to the high-temperature plasma above
6 MK, are used for detecting the hot pre-eruptive MFR; the 171 Å, 193 Å, 211 Å
and 335 Å for observing the large-scale background corona; the 304 Å, 1600 Å
and 1700 Å for searching for signals of the eruption in the lower atmosphere
(O’Dwyer et al., 2010). The EUV imaging data from the Sun Earth Connection
Coronal and Heliospheric Investigation (SECCHI; Howard et al., 2008) on board
the Solar Terrestrial Relations Observatory (STEREO), which was separated from
SDO by an angle of $\sim$110∘ at the time the analysed observations were made,
provide the second perspective on the eruption even though with a lower
cadence (5 minutes) and resolution (3.2 arcseconds).

In order to locate the reconnection during the precursor phase and reveal its
physical properties, we utilize the Ramaty High Energy Solar Spectroscopic
Imager (RHESSI; Lin et al., 2002) that is capable of performing X-ray imaging
and spectroscopic diagnostics for hot plasma and accelerated electrons. The
hard X-ray images are reconstructed with the Clean algorithm based on the
detectors 3, 5, 6, 7, 8 and 9. The X-ray spectra from the detector 3 are
analysed in detail to derive the temperature of hot plasma and low energy cut-
off of accelerated electrons. The spectra from the other detectors are also
examined but not showed here because the results from all detectors were very
similar.

In addition, to inspect the CME generated by the MFR eruption, we also make
use of the data from the Large Angle and Spectrometric Coronagraph (LASCO;
Brueckner et al., 1995) on board the Solar and Heliospheric Observatory (SOHO)
and the SECCHI instrument suite on board STEREO-A. The CME velocity in the
higher corona is from the CDAW Data Center111https://cdaw.gsfc.nasa.gov/. The
Geostationary Operational Environmental Satellite (GOES) provides the soft
X-ray (SXR) fluxes of associated flares at two bands of 1-8 Å and 0.5-4 Å. The
Helioseismic and Magnetic Imager (HMI; Schou et al., 2012) also on board SDO
provides the photospheric vector magnetic field of the investigated AR with a
temporal cadence of 12 minutes and spatial resolution of 1.2 arcsecond.

##  3 Results

Figure 1: Pre-eruptive MFR and pre-flare emission. a. A composite of the AIA
131 Å (red) and 171 Å (green) images showing the pre-eruptive hot MFR and
induced precursor loops (left) for the eruption on 2012 March 13. The AIA 131
Å difference image (subtracting the image on 15:50 UT) displaying zoom-in of
the MFR (right). b. Temporal evolution of the GOES SXR 1–8 Å flux (red),
temperature (blue), X-ray energy loss rate (yellow), integrated AIA 131 Å
(cyan) and 304 Å (brown) intensity for NOAA AR 11429 with the FOV shown by the
white box in panel a. The three dash-dotted lines indicate the onset, peak and
end time of the main flare phase, respectively.

###  3.1 Overview of major CME eruption

On 2012 March 13, an M7.9 class flare, taking place in the NOAA AR 11429
(Figure 1a), started at $\sim$17:12 UT, peaked at $\sim$17:41 UT and ended at
$\sim$18:25 UT (Figure 1b). It also produced prominent 30 THz emissions
(Kaufmann et al., 2013; Trottet et al., 2015) and was accompanied by a very
energetic CME that included an erupting MFR as its main body. The projected
average speed of the CME was over 1900 km s-1, as measured in the field of
view of LASCO. Figure 1a shows that a loop-like pre-eruptive structure had
appeared prior to the main flare and was associated with a long-lasting cusp-
shaped precursor structure. Using the visibility of the cusp-shaped structure,
such a precursor is found to last for more than one hour, much longer than
that usually observed (several minutes) in previous events (Zhang et al.,
2012; Cheng et al., 2013; Hernandez-Perez et al., 2019), thus enabling us to
decipher the heating and early rise of the pre-eruptive hot MFR.

###  3.2 Formation and heating of pre-eruptive MFR

Figure 2: Build up of pre-eruptive MFR. The AIA 131 Å difference image
(subtracting the image taken at 15:50 UT) showing the build up of the pre-
eruptive MFR and its relation to the cusp-shaped precursor loops. The two flux
bundles of the pre-eruptive MFR are delineated by two curves in yellow and
blue (d–f). The oblique arrow in panel b shows the orientation of the main
PIL. The animation 1 that starts at 2012 March 13 16:00 UT and ends at 17:59
UT is available online to show the detailed evolution of the slowly rising MFR
and precursor loops with the duration of 10 s.

The long precursor of interest caused evident coronal emissions at different
AIA bands as shown in Figure 1b. The GOES SXR 1–8 Å flux started to increase
at $\sim$16:00 UT and reached a plateau for 20 min. After that, it was further
enhanced. At $\sim$16:50 UT, the SXR flux reached a peak and then decreased
slightly followed by the onset of the main phase. This evolution at the X-ray
band is very similar to that of the integrated intensity of the AIA high-
temperature 131 Å passband. In contrast, for the AIA low-temperature 304 Å
passband (peaking at roughly 80 kK), only a slow increase in the integrated
intensity is observed except for some small fluctuations. The distinction
indicates that the energy release process primarily occurred in the corona.
Figure 1b also displays the evolution of the SXR radiation rate and
temperature, which are estimated based on fluxes at the two X-ray bands of
GOES. One can see that the temperature is mostly above 8 MK during the
precursor phase, consistent with the similarity between the evolutions of the
SXR 1–8 Å flux and integrated 131 Å intensity. The peak temperature of the
precursor appeared at $\sim$16:40 UT, preceding that of the GOES SXR 1–8 Å
flux and radiation rate by about 5 min, implying that the plasma is first
heated and then induces an enhanced radiation as what happens during the main
flare phase (Sun et al., 2014).

Thanks to the capability of the AIA 131 Å and 94 Å passbands to image hot
plasma, it is disclosed that the formation of the pre-eruptive MFR involved
that of two sets of hot flux bundles. The cusp-shaped hot structure, also
named as precursor loops hereafter, is found to be the main source of the
precursor emission (Figure 2 and animations 1 and 2). Its activation could be
related to a small flare occurred at the nearby neighboring AR 11430 (Figure
2a). At $\sim$16:00 UT, the first set of relatively diffuse hot threads
gradually showed up with their middle being concave and connecting to the top
of the cusp-shaped structure. They were almost aligned with the direction of
the main PIL and much longer than the precursor loops, presenting an “M” shape
in morphology at $\sim$16:30 UT (Figure 2c). During the formation, the middle
of the hot threads also rose up slowly, being separated from the top of
precursor loops, and then became flat (Figure 3a). At $\sim$16:30 UT, the
second flux bundle started to appear with the left footpoints almost being
mixed with that of the first one but with the right footpoints far away from
the AR 11429. The visibility of the remote dimming at the AR 11430 indicates
that the second flux bundle connects the ARs 11429 and 11430 (Figure 8c1–c2).
The two sets of flux bundles constitute the pre-eruptive channel-like MFR with
a bifurcated right leg (also see Zhong et al., 2019). Afterwards, the two sets
of threads rose up as a whole continuously. This is different from a rise
following by a descent of the erupting flux detected in confined eruptions
(Patsourakos et al., 2013; Liu et al., 2018b). The continuous rise of the pre-
eruptive MFR also caused a slight amplification of the reconnection as
indicated by the brighter precursor loops (Figure 2) and the increases of the
SXR flux, temperature and integrated 131 Å intensity (Figure 1b). However,
comparing with the flare main phase, the SXR flux was still one order of
magnitude smaller, indicating that the reconnection still proceeded in a
gentle way. Nevertheless, although being moderate, it was critical for the
pre-eruptive MFR to be formed and heated (Figure 3a).

Figure 3: Cusp-shaped precursor loops and its relation to pre-eruptive MFR. a.
The AIA 131 Å difference image (subtracting the image taken at 16:16 UT)
showing the cusp-shaped precursor loops and pre-eruptive MFR (left). The rise
and change in morphology of the MFR threads are indicated by the curves in
zoom-in images (right). The oblique dashed line indicates the main eruption
direction. The oblique arrow shows the orientation of the main PIL. b. DEM-
weighted average temperature (left) and total EM (right) maps. The temperature
contours (black) of 7 MK (corresponding to a logT of 6.85) with an “X” shape
configuration are also overplotted in the EM map. The dashed boxes in black
outline the field-of-view of the right of panel a. The animation 2 that starts
at 2012 March 13 16:00 UT and ends at 17:00 UT is available online to show the
evolution of the MFR threads as shown in the right portion of panel a with the
duration of 12 s.

The temperature map shows that the average temperatures of the pre-eruptive
MFR and precursor loops are about 8 MK and 10 MK, respectively (Figure 3b).
They are in agreement with the average temperature of the full flaring region
estimated from the ratio of two GOES SXR broadband (0.5-4 Å and 1-8 Å) fluxes
(see Thomas et al., 1985). Moreover, we find an interesting X-shaped high-
temperature plasma structure prior to the eruption, highly resembling to the
structure of magnetic reconnection during the eruption (Cheng et al., 2018;
Chen et al., 2020). It consists of the upper part of the cusp-shaped loops and
the middle of the M-shaped MFR as shown by the contour of 7 MK (right panel of
Figure 3b). Its projected height is $\sim$20 Mm. The two features suggest that
magnetic reconnection takes place during the precursor phase and in a high
altitude to build up and heat the pre-eruptive structures.

Figure 4: X-ray emission and spectra. a. RHESSI X-ray source in the energy
ranges of 3–6 keV (blue), 6–12 keV (red) and 12–25 keV (yellow) overlaid on
the AIA 131 Å difference images (subtracting the image taken at 15:50 UT)
showing the energy release locations by precursor reconnection. The two
contours for each energy band denote 50% and 80% of their maximum emissions.
The image on the left and right is scaled linearly and logarithmically,
respectively. b. Spectra of X-ray emission and their temporal evolution. The
curves in blue display the best fitting to background-subtracted spectra
(curves in grey) with the ones in red and yellow indicating the thermal and
non-thermal thin-target model, respectively. The resulting fitting residuals
are shown in the bottom panels.

###  3.3 Locating X-ray emissions

The RHESSI hard X-ray (HXR) data show that, during the time period of
16:00-16:20 UT, the HXR emissions only appeared in the energy bands below 12
keV and were from the source concentrated at the top of precursor loops, as
shown in Figure 4a. The left two panels of Figure 4b display that the
corresponding X-ray spectra at $\sim$16:01 and 16:15 UT can be well fitted by
a thermal model. It gives a thermal temperature of $\sim$10 MK, very similar
to the DEM-average temperature of the region at the top of precursor loops as
derived from the DEM analysis, indicating pertinent reconnection process being
of thermal-dominated. As the pre-eruptive MFR formed, the HXR emissions at the
top of the precursor loops were gradually enhanced. At $\sim$16:47 UT, the
emissions in the energy range of 3–6 keV and 6–12 keV increased by almost one
order of magnitude relative to the value observed half an hour earlier (Figure
4b). At the same location, the emission in the higher energy range (e.g.,
12–25 keV) also appeared (the right two panels of Figure 4a), suggestive of a
non-thermal property. The combination of a thermal model and a thin-target
model best fits the X-ray spectra at two following times (middle and right
panels of Figure 4b). The fitting gives a thermal temperature of 11-12 MK and
a cut-off energy of 12.8 keV for the non-thermal electrons. This indicates
that magnetic reconnection in the later stage of the precursor phase was also
capable of accelerating electrons. However, the accelerated electrons still
have a relatively low energy, mostly $<$20 keV, showing that the reconnection
process was not energetic, probably similar to that during micro-flares as
recently observed by the Spectrometer/Telescope for Imaging X-rays (STIX)
onboard Solar Orbiter (Battaglia et al., 2021).

###  3.4 Initiation of MFR-induced CME

The temporal variations of the height and velocity of the pre-eruptive MFR
provide valuable information to disentangle initiation models. Figure 5a shows
the long-duration slow rise of the pre-eruptive MFR consisting of two rising
flux bundles. After $\sim$17:00 UT, the MFR gradually became vague because of
its expansion. During the entire precursor phase, as a response to the rise of
the hot MFR, the overlying field also gradually expanded, as indicated by
diamonds in Figure 5b, and then evolved toward the CME leading front during
the main phase.

Figure 5: Early kinematics and initiation of pre-eruptive MFR. a. Slice-time
plot of the AIA 131 Å difference images showing the evolution of two flux
bundles of the pre-eruptive MFR. Diamonds and filled circles indicate their
height-time measurements. b. Same as panel a but for the AIA 171 Å passband
representing the expanding overlying field. c. Temporal evolution of the
heights of the MFR (red) and expanding overlying field (yellow). d. Temporal
evolution of the velocities overplotted by the GOES SXR 1–8 Å flux (gray) and
its time derivation (black). The uncertainty in velocity is mainly from that
in height, which is estimated to be 2 Mm. The vertical slits in panel c and d
indicate the onset of the CME impulsive acceleration and flare main phase with
their width denoting the uncertainty (one minute). e. The radial component of
HMI Cylindrical Equal-Area (CEA) vector magnetogram. The white (black)
indicates the magnetic field upward (downward). f. The decay index
distribution with height above the PIL, which is an average of all height-
profiles of the decay index at the yellow dots as shown in panel e. The bars
in grey denote its uncertainty as derived by the standard deviation of height-
profiles. The dots in blue and yellow represent the initial and onset height
(35 and 100 Mm) of the MFR axis, respectively. Their reference point is the
midpoint of the line segment connecting the two footpoints of the cusp-shaped
precursor loops. The dot in red points out the the critical decay index of 1.5
for a ring current.

Figure 5c–d display that the MFR velocity increased very slowly in the
precursor phase, varying from $\sim$5 km s-1 at $\sim$16:15 UT to $\sim$25 km
s-1 at $\sim$16:40 UT. The average acceleration was only $\sim$13 m s-2.
Afterwards, the MFR even started to slow down, the velocity decreased from
$\sim$25 km s-1 at $\sim$16:40 UT to $\sim$20 km s-1 at $\sim$16:55 UT, with a
deceleration of about –6 m s-2. At $\sim$17:00 UT, because of the second flux
bundle, the MFR velocity increased again. The temporal evolution of the
velocity of the pre-eruptive MFR during the whole precursor phase roughly kept
in step with the variation of the GOES 1–8 Å SXR flux. For the CME leading
front, its velocity kept a small value ($\sim$14 km s-1) before eruption at
$\sim$17:12 UT. However, as the main phase began, the velocity of the CME
leading front increased to $\sim$110 km s-1 in 6 minutes. The MFR was
accelerated more impulsively, the velocity increased from $\sim$50 km s-1 at
$\sim$17:12 UT to $\sim$450 km s-1 at $\sim$17:20 UT with an acceleration of
$\sim$830 m s-2, almost two orders of magnitude larger than that during the
precursor phase. Meanwhile, the SXR flux also increased impulsively (see its
time derivative), in synchronisation with the variation of the MFR velocity.

The MFR fast acceleration may be triggered by the torus instability, which
occurs when the decay of the background magnetic field with height exceeds a
threshold (Kliem & Török, 2006; Fan & Gibson, 2007; Aulanier et al., 2010).
From the distribution of the decay index as shown in Figure 5f, one can see
that the decay index first quickly and then gradually increases with height.
At the onset time of the impulsive acceleration (17:13 UT), the upper and
lower edges of the MFR reached heights of $\sim$110 and $\sim$90 Mm,
respectively. The average ($\sim$100 Mm) of them is regarded as the height of
the MFR axis, where the decay index is found to be $\sim$2.0, obviously
exceeding all critical values of torus instability derived theoretically
(Kliem & Török, 2006; Démoulin & Aulanier, 2010). This shows that the torus
instability has occurred, probably earlier than 17:13 UT, because it takes
time to accumulate speed in an exponentially-accelerating instability starting
from a weak perturbation to overtake the slow-rise velocity caused by the
independent precursor reconnection.

We also inspect the decay index during the slow rise phase. For the
acceleration stage of the precursor phase (16:15–16:40 UT), the height of the
MFR axis was below 60 Mm, the corresponding decay index was mostly smaller
than $\sim$1.5, the critical value for a toroidal current ring (Kliem & Török,
2006), and the statistical average of critical decay indices for AR eruptions
(Cheng et al., 2020). Furthermore, the deceleration of the MFR during the
following 15 minutes conflicts with an expected exponential acceleration
during the early development stage of torus instability (Török & Kliem, 2005;
Schrijver et al., 2008). Thus, although the decay index keeps increasing as
the MFR is elevated continuously, the torus instability seems to not take
effect in the most of precursor phase. In contrast, once entering the main
phase, the temporal variation of the MFR height is found to exactly follow an
exponential form (Figure 9). These results support that the torus instability
plays a critical role in initiating the MFR impulsive acceleration and fast
flare energy release, or in other words, it is the key to turn the moderate
reconnection in the precursor phase to the runaway reconnection in the main
phase.

###  3.5 Driver of MFR Slow-rise

To understand the dominant driving mechanisms underneath the long-term slow
rise of the MFR and the transition toward the eruption, as well as the
relations of various involved features to the inferred moderate precursor
reconnection, we run a zero-$\beta$ three-dimensional (3D) magnetohydrodynamic
(MHD) simulation. To broadly compare with observations, in our numerical
model, the initial magnetic configuration consists of an asymmetric bipolar
field. It is driven by means of line-tied shearing motions at the bottom
boundary, which are often observed near the PIL. The flux cancellation is also
introduced by magnetic diffusion at the bottom boundary. The parameter setups
are the same as Aulanier et al. (2012) only with a higher spatial resolution
(375$\times$375$\times$336).

Figure 6: 3D magnetic field lines at five different times displaying the slow
rise and early eruption of the MFR. The blue and orange tubes show the MFR
field lines, the red tube in panel b shows one precursor loop. The bottom
images show the vertical magnetic field components at the bottom boundaries of
the MHD simulation domain. The vertical planes (y=-0.06) perpendicular to the
MFR axis show the distribution of current density $j$ with the contours in
green indicating $\log Q=3$. The onset time of the MFR eruption is in period
of 120-125$t_{A}$. The animation 3 is available online to show the evolution
of 3D M-shaped field lines during the early rise phase with the duration of 46
s.

The 3D MHD simulation shows that, as the bald-patches (BPs) bifurcates into a
quasi-separatrix layer (QSL) containing a coronal hyperbolic flux tube (HFT;
Titov et al., 2002) lying below the MFR, the MFR is slowly evolving before it
reaches an eruptive stage. The HFT reconnection is believed to inject newly
formed flux into the MFR, making it ascend further (Aulanier et al., 2010).
Although the MFR in the simulation only includes one set of helical threads,
many characteristics are still similar to observations, including (1) that the
newly reconnected flux first presents an “M” shape and then becomes flat
(orange field lines in Figure 6a-6d); (2) that the precursor reconnection
forming the “M”-shaped MFR field lines and precursor loops is not energetic
prior to the main eruption; (3) that the MFR eruption does not start until its
axis reaches an altitude where the decay index of the background field is
large enough to allow the occurrence of ideal torus instability (Section F);
and (4) that the height of the erupting MFR during the early acceleration
phase increases exponentially (see Figure 10).

Figure 7: Lorentz force during the slow rise and early eruption of the MFR. a.
Distributions of the vertical component of the Lorentz force density $F_{z}$
at the plane y=-0.06, as shown in Figure 6, at four different times. The
boundaries of the MFR are delineated by the dashed lines; the contours of
$\log Q=3$ are shown by the curves in green. b–d. Temporal evolution of the
MFR accelerations ($a_{F_{z}}$, $a_{(F_{t})_{z}}$, $a_{(F_{p})_{z}}$)
contributed by the vertical components of the Lorentz force $F_{z}$, magnetic
tension $(F_{t})_{z}$ and magnetic pressure gradient $(F_{p})_{z}$,
respectively. Their errors indicated by vertical bars are mainly from the
uncertainty in determining the MFR outer boundary, which is achieved through
changing $\log Q$ value from 2.4 to 3.6. The horizontal dotted lines indicate
zero acceleration.

The MHD simulation enables disclosing the driving forces acting in the slow
rise of the pre-eruptive MFR and the following acceleration phase,
respectively. The distribution of the vertical component of the Lorentz force
in the plane perpendicular to the MFR axis and crossing the HFT show that the
Lorentz force near the HFT and the outer part of the MFR is pointing upward
but that in the central part of the MFR is mostly directed downward (Figure
7a). Nevertheless, the downward force within the MFR is negligible, so that
the net force of the MFR is obviously dominated by the upward one which drives
the MFR to rise up slowly with a small acceleration (Figure 7b). On the other
hand, the Lorentz force below the HFT is mainly pointing downward, which
causes shrinkage of precursor loops. The Lorentz force is further decomposed
into two components (magnetic tension and pressure gradient). One can find
that, during the slow rise phase of the MFR, the upward directed Lorentz force
producing a positive acceleration is primarily contributed by the upward
directed magnetic tension (Figure 7c), in agreement with the observation that
the middle part of the “M”-shaped flux tends to rise up obviously and
gradually becomes flat. As the fast eruption starts, the acceleration induced
by the upward Lorentz force quickly increases, explaining the fast
acceleration of the MFR eruption as observed. However, the driving force for
the large acceleration is no longer the magnetic tension but the magnetic
pressure gradient. The latter gradually changes from negative to positive and
significantly counteracts the negative magnetic tension as the eruption enters
into the main phase (Figure 7d).

##  4 Summary and discussions

In this paper, we present comprehensive observations of a long-lasting
precursor phase before a major solar eruption. With further combination of
suitable viewing angle and multi-wavelength data, it is disclosed that the
heating and slow rise of the pre-eruptive hot MFR are achieved through the
precursor reconnection as often speculated previously (Wang et al., 2017; Zhou
et al., 2017; Awasthi et al., 2018; Chen et al., 2019; Hernandez-Perez et al.,
2019; Gou et al., 2019). The precursor reconnection is found to take place at
the X-shaped high-temperature plasma sheet. The continual formation of the
“M”-shaped hot threads via the precursor reconnection results in the heating
and early rise of the entire MFR, as well as the formation of precursor loops.
It is surprising that the main features generally observed in the impulsive
phase have counterparts in the precursor phase that are physically linked to
the precursor reconnection. However, both the slow rise of the pre-eruptive
hot MFR ($<$30 km s-1) and the relatively low energy of accelerated electrons
($<$20 keV) suggest that the precursor reconnection is far less efficient than
that in the main eruption phase (e.g., Cheng et al., 2018).

In spite of being moderate, the precursor reconnection is critical for lifting
the MFR along an equilibrium sequence in a mutual feedback process. On the one
hand, the precursor reconnection forms the M-shaped flux that accumulates and
rises up as illustrated in Figure 11. On the other hand, the rising MFR
slightly enhances the reconnection that can further inject flux to the MFR.
Such a feedback is strongly indicated by the simultaneity between the
increases in the height of the pre-eruptive MFR and the enhancement of
associated SXR emissions. The transition from moderate reconnection to fast
reconnection is switched on by the fast acceleration of the MFR. This is most
likely caused by the ideal torus instability as the transition from the slow
rise to the fast acceleration of the MFR occurs at the height where the decay
index of the background field exceeds the thresholds of torus instability and
that the temporal evolution of the MFR acceleration highly resembles an
exponential profile. Once entering the main eruption phase, the moderate
reconnection immediately transitions to runaway reconnection responsible for
the flare impulsive phase. The fast reconnection rapidly accelerates the CME
eruption, which vice versa drives the opposite-directed magnetic fields to
continuously participate in the reconnection. With the feedback more
efficiently operating in this period, the eruption is finally accelerated to a
high speed in about one hour. Moreover, as shown in the MHD simulation, the
precursor reconnection occurs between highly sheared arcades (also see
Aulanier et al., 2012), the guide field of the reconnection is thus large,
which could be the reason why the precursor reconnection is not that energetic
(e.g., Leake et al., 2020; Dahlin et al., 2022).

The synergism of the moderate-reconnection-formed MFR and ideal torus
instability causing the transition from the precursor phase to the main
eruption phase as revealed and further testified by our 3D MHD simulation can
be used to clarify the applicability of the initiation models proposed in the
past decades. The tether-cutting-like topology of the precursor reconnection
seems to support the tether-cutting initiation model (Moore et al., 2001),
which, however, is insufficient if working alone without the presence of the
torus instability. The tether-cutting reconnection is found to be only
efficient once initiated by tearing mode instability as proved by recent
numerical simulations (Jiang et al., 2021). This is at variance with the
results of observation-constrained simulation (Inoue et al., 2018) and
observational characteristics for the 2012 March 13 event, where the
reconnection is found to be moderate before the onset of the fast eruption.
Moreover, in the event under study, no prominent signatures for the MFR
writhing motion are observed during the slow rise phase. Thus, we tend to
exclude the possibility of the kink instability (Török & Kliem, 2003) causing
both the precursor phase and the main eruption phase. It is worthy of noticing
that the first bundle of the pre-eruptive MFR seems to present an untwisting
motion in the early phase of the eruption (Figure 2f). However, after a
careful inspection, it is more likely to be the apparent manifestation of the
MFR morphology varying from the “M” to semicircle shape as previously detected
(Zhang et al., 2012; Cheng et al., 2013). In addition, it was suggested that
the onset of the eruption may correspond the transition of magnetic field
topology that embeds the pre-eruptive MFR, so to say, from BPS to HFT
(Savcheva et al., 2012). However, in our observations, only an HFT-like
configuration appears in the precursor phase. Therefore, as proved in our
numerical model, such a topological transition may occur much earlier than the
initiation of the eruption, if it exists at all.

The long-duration precursor is equivalent to a confined flare preceding the
following eruptive one, during which both magnetic helicity and twist are
thought to be quickly injected to the pre-eruptive MFR (Priest & Longcope,
2017). However, it presents two characteristics obviously different from those
during confined eruptions. First of all, a continuously rising pre-eruptive
MFR toward the eruption differs from the MFR during confined flares that
initially rises but finally stops at the high corona (Liu et al., 2018a; Kliem
et al., 2021). Secondly, the high-temperature of the pre-eruptive MFR in
combination with its morphology evolution and the appearance of thermal X-ray
source above the precursor loops provide solid evidence for slow reconnection
heating during the slow rise prior to the main eruption; while such a process
may be unnecessary, even absent (Patsourakos et al., 2013; Chintzoglou et al.,
2015), in the interval between the preceding confined flares and the following
successful eruptions.

Lastly, as only one particular event is investigated here, more similar
observations and in-depth MHD modelling are suggested in the future to justify
the universality of the mechanisms we have determined for the heating and slow
rise precursor of pre-eruptive configurations of solar eruptions.

We appreciate all referees who reviewed the manuscript and provided their
comments and constructive suggestions. We also thank Chun Xia, Bernard Kliem,
Jie Zhang, Jun Chen and Lakshmi Pradeep Chitta for their helpful discussions.
AIA data are courtesy of NASA/SDO, a mission of NASA’s Living With a Star
Program. STEREO/SECCHI data are provided by a consortium of NRL (US), LMSAL
(US), NASA/GSFC (US), RAL (UK), UBHAM (UK), MPS (Germany), CSL (Belgium), IOTA
(France), and IAS (France). X.C., C.X. and M.D.D. are supported by National
Key R&D Program of China under grants 2021YFA1600504 and by NSFC under grant
12127901. X.C. is also supported by Alexander von Humboldt foundation. G.A.
and C.X. acknowledge financial support from the French national space agency
(CNES), as well as from the Programme National Soleil Terre (PNST) of the
CNRS/INSU also co-funded by CNES and CEA.

##  Appendix A DEM inversion

The differential emission measure (DEM) is reconstructed by the
“xrt¯dem¯iterative2.pro” routine in the Solar Software (SSW) using six co-
aligned AIA EUV images. The observed intensity $I_{i}$ for the passband ${i}$
can be written as:

${I_{i}}=\int DEM(T)\times R_{i}(T)\mathrm{d}T+\delta I_{i},$ (A1)

where $DEM(T)$ denotes the plasma DEM, $R_{i}(T)$ is the temperature response
function and $\delta I_{i}$ is the uncertainty in intensity $I_{i}$. The
temperature range of inversion is set as 5.5$\leq$ log${T}\leq$ 7.5.

We calculate the average temperature and total EM by means of the following
two formulae:

$\bar{T}=\frac{\int DEM(T)\times TdT}{\int DEM(T)dT}\\\ $ (A2)

$EM=\int DEM(T)dT.\\\ $ (A3)

We also ran 100 Monte Carlo (MC) simulations by adding a random noise
corresponding to the uncertainties of the observed intensities, derived by
“aia¯bp¯estimate¯error.pro” in SSW, to the intensity $I_{i}$ and then
resolving the DEM. It is found that in the temperature range of 5.7$\leq$
log${T}\leq$ 7.4, which is selected to integrate Equation (A2) and (A3), the
100 MC solutions are well constrained.

##  Appendix B Dimmings

Figure 8 shows the evolution of the three dimming regions and flare ribbons
from the two perspectives of SDO and STEREO-A before and during the eruption.
It is found that the east dimming has appeared prior to the main eruption, as
seen in the SDO-AIA difference images (Figure 8a1). Not surprisingly, the left
footpoints of the pre-eruptive MFR were cospatial with the east dimming (ED in
Figure 8c1). Considering that the pre-eruptive MFR consists of two sets of
threads that have a different connectivity on the right, their footpoints are
expected to correspond to two dimmings, which is confirmed by the EUVI-A 195 Å
running-difference images. It is revealed that the one is on the right of the
main flare loops and the other is near the AR 11430. As the MFR took off, the
two dimming regions expanded outward and further darkened, implying a plasma
rarefaction caused by the eruption (Figure 8a2-8a4). The erupted fluxes should
be mostly from NOAA 11429 as where the main dimmings were observed (ED and DR1
in Figure 8c1).

Figure 8: a1–a3. Time-sequence of composite of the AIA 131 Å (red) and 211 Å
(cyan) difference images showing the early rise and eruption of the pre-
eruptive MFR and induced flare. b1–b3. The AIA 1600 Å images displaying the
flare ribbons, the field-of-view is indicated by the box in panel a1. c1–c3.
The EUVI 195 Å difference images (subtracting the image at 14:00 UT)
representing the dimming regions, which include the footpoints of the erupting
MFR. The left footpoint (L) is indicated in panel a1, the left dimming (ED)
and right two dimmings (DR1 and DR2) are pointed out by the arrows in panel
c1.

##  Appendix C Kinematical analyses

To measure the MFR height, we take a slice along the MFR eruption direction
(Figure 3a) and make slice-time plots of the AIA 131 Å and 171 Å base-
difference images (Figure 5a–5b). Based on the slice-time plots, we measure
projected heights of the MFR upper edge and CME leading front as shown in
Figure 5a–5c. The projected heights are simply corrected assumes that the
eruption is along the radial direction during the early phase (as indicated by
the oblique dashed line in Figure 3a). With the first order numerical
derivative, we then calculated the velocities of the MFR and CME leading
front.

By comparing multiple fit functions, it was found that, for the majority of
events, the height-time profiles of solar eruptions in the lower corona can be
best fitted by the function:

$h(t)=a\exp(bt)+ct+d,\\\ $ (C1)

which is a superposition of a linear and exponential component, mimicking the
slow-rise phase and the early impulsive acceleration phase, respectively
(Cheng et al., 2020). Here, we take advantage of the superposed function to
fit the height-time profile of the second MFR bundle that continuously evolved
from the precursor to the main phase. Figure 9 shows that the measured height-
time data are perfectly fitted by Equation C1. Furthermore, all velocities,
even accelerations, that are directly calculated by numerical derivative of
height-time data are also found to follow the derivative curve of the fit
function with a very small discrepancy except for the last point.

In terms of the best fitted function, we further estimate the onset of the
impulsive acceleration phase, i.e., the break-point time where the velocity of
the exponential term starts to dominate (equal) that of the linear term. This
gives an onset time of $\sim$17:13 UT. Moreover, we also estimate directly
from the acceleration-time profile the onset time, i.e., when the acceleration
begins to obviously increase at $\sim$17:12 UT. The onset times we derived by
two different methods are synchronized with that of the main flare phase
(17:12 UT). For more details on determination of the eruption onset and its
uncertainty, the reader can refer to Cheng et al. (2020).

Figure 9: Model fitting for temporal evolution of the height (left), velocity
(middle) and acceleration (right) of the second MFR bundle. The dots in red
show measured data points with the vertical bars indicating the uncertainties.
The curves in grey show the fitted results. The vertical dotted lines in the
left and middle panels represent the onset time of the main acceleration phase
derived by the model. The solid line in the right panel shows the onset
directly from the acceleration-time profile.

##  Appendix D 3D coronal magnetic extrapolation

Based on a potential field model, we extrapolate the 3D coronal magnetic field
by the Green function method using the radial component of the HMI vector
field as shown in Figure 5e as the bottom boundary. The constrained background
field over the erupting MFR is approximated by the horizontal component of
extrapolated potential field. The decay index of the background field is
calculated as follows

$\centering n(h)=-\frac{d(\ln B_{\mathrm{t}})}{d(\ln h)},\@add@centering$ (D1)

where $B_{\mathrm{t}}$ and $h$ denote the horizontal component of the
background field and the height above the photosphere, respectively.

The accuracy of the extrapolated 3D coronal potential field largely depends on
that of the bottom boundary, which is selected as the radial component of the
HMI vector magnetogram at 15:00 UT on 2012 March 13. The 180∘ ambiguity in the
horizontal component is removed using a minimum energy method. In addition,
the data are reprojected from helio-projective Cartesian to heliographic
Cylindrical Equal-Area (CEA) coordinates. Finally, it is worth mentioning that
the measured vector field close to the solar limb is still less accurate than
that near the disk center. This may influence the accuracy of the calculated
background field and thus the decay index. However, as discussed previously
(Cheng et al., 2020), the decay property of the background field is primarily
determined by the large-scale structure of ARs, which generally evolve slowly
after their emergence. The influence is thus not expected to be fatal.

##  Appendix E The MFR Geometry

The thresholds of an MFR taking place torus instability are closely related to
its geometry. For a straight and toroidal thin current ring, two particular
limited cases, the critical decay index of the background field was deduced to
be 1 and 1.5, respectively (Kliem & Török, 2006; Démoulin & Aulanier, 2010).
For the current 2012 March 13 event, the pre-eruptive MFR presents a curved
loop-like structure, deviating from a full torus. Moreover, the pre-eruptive
MFR is composed of two flux bundles with the right footpoints being located at
the different regions. This is essentially a result of the nonuniform
distribution of the MFR current. The two factors may influence the critical
value of torus instability, however, based on Kliem & Török (2006), which is
not expected to be significant.

##  Appendix F The MHD model

We run a zero-$\beta$ MHD simulation performed by the Observationally driven
High-order Magnetohydrodynamics code (OHM; Aulanier et al., 2005, 2010). The
simulation starts from an asymmetric bipolar potential field. To drive the
potential field evolving toward a highly sheared state, we impose the driving
motion at the bottom boundary, which is mainly manifested as two shearing
flows on two sides of the main PIL, reaching its maximum close to the PIL and
has little effect in the center of each polarity. In addition, since the
driving motion follows the contours of $B_{z}$, the vertical component of the
magnetic field at the bottom boundary is hardly changed by this motion.

The simulation is composed of the shearing phase with shearing motions imposed
and the relaxation phase without driving motions at the bottom boundary.
During the shearing phase, the flux cancellation is achieved by adding a
photospheric resistivity $\eta^{phot}=1.44\times 10^{-3}$ on the bottom; an
uniform coronal resistivity, $\eta=4.8\times 10^{-4}$, is set in the whole
domain except the bottom boundary. During the relaxation phase, the
photospheric resistivity is set to be zero, and the coronal resistivity is
multiplied by 4 during the eruption for numerical stability.

We determine the onset time of the MFR eruption with a series of tests, in
which we stop the driving motion at different times and then relax the system.
We find that the MFR fails to erupt in a control simulation where the driving
motion is switched off at $t=120t_{A}$ (with an interval of $2\Delta
t=6t_{A}$) but erupts successfully in the simulation where the driving motion
is stopped at $125t_{A}$ as analysed here. Thus, the onset time of the
eruption should be in the time period of $120-125t_{A}$. The decay index at
the height of the MFR axis at $t=125t_{A}$ is found to be close to the
theoretical threshold of the torus instability ($\sim$1.5; Kliem & Török,
2006). Afterwards, both the height and velocity of the MFR increase
exponentially (Figure 10).

Figure 10: Temporal evolution of the height and velocity of the MFR in the
simulation. The height of the MFR is estimated by tracking an overlying field
line that is located at the top of the MFR in the direction of the eruption.
The vertical dashed lines mark the time interval in which the driving motion
at the bottom boundary gradually decreases to zero by following a ramp
function.

##  Appendix G Determining the MFR boundary

We investigate the mechanism that drives the slow rise of the MFR by analyzing
the integrated z-components of the Lorentz force and its two components
(magnetic tension and pressure gradient) at the section of the MFR
perpendicular to its axis. Note that, the magnetic tension force (pressure
gradient) analyzed here refers to the component of magnetic tension force
(pressure gradient) in the normal direction of magnetic field as the
tangential component has no contribution to the acceleration.

To identify the MFR boundary, we calculate the squashing degree Q, which
measures the mapping of the field lines. The squashing degree Q is defined by
Titov et al. (2002) as:

$\centering Q=\frac{(\frac{\partial X}{\partial x})^{2}+(\frac{\partial
X}{\partial y})^{2}+(\frac{\partial Y}{\partial x})^{2}+(\frac{\partial
Y}{\partial y})^{2}}{|\frac{\partial X}{\partial x}\frac{\partial Y}{\partial
y}-\frac{\partial X}{\partial y}\frac{\partial Y}{\partial
x}|},\@add@centering$ (G1)

where $(x,y)$ and $(X,Y)$ are coordinates of two footpoints of a field line.

It is believed that the MFR boundary corresponds to the QSL, where the
squashing degree $Q$ is very large. In practice, we identify the top and side
boundaries of the MFR mainly by following the outer contours of $\log Q=3$. To
enclose the bottom boundary of the MFR, the inner contours of $\log Q=5$,
which clearly present the HFT configuration (Figure 11), are used for a
reference. The integrated vertical components of the Lorentz force, magnetic
tension force, magnetic pressure gradient and mass density are calculated by
summing up the corresponding quantities within the boundary of the MFR at the
plane. The acceleration caused by the Lorentz force and that by its two
components are obtained by dividing the integrated forces by the integrated
mass density. In order to estimate the uncertainty in determining the top and
side boundaries of the MFR, we also use the contours of $\log Q=2.4$ and $\log
Q=3.6$ instead of $\log Q=3.0$ to repeat the same procedure. The integrated
quantities shown in Figure 12 and the accelerations in Figure 7 are the
averages of three measurements and their errors are corresponding standard
deviations.

Figure 11: Left. 3D rendering of one MFR field line (orange) and two sheared
arcades (green) at $t=100t_{A}$ that are separated by the MFR boundary as
delineated by the black curve in the right panel. Right. Distribution of $\log
Q$ overlaid with the contours of $\log Q=2.7,3.0,5.0$ in purple, blue and
magenta, respectively, at the plane y=-0.06 perpendicular to the MFR axis. The
positions of the MFR field line and sheared arcades passing the plane are
represented by the dots in orange and green, respectively.

Figure 12: Temporal evolutions of the integrated vertical components of the
Lorentz force, magnetic tension, magnetic pressure gradient and the mass
density within the MFR cross section as shown in Figure 7a. The errors
(vertical bars) are from the uncertainty in determining the MFR boundary.

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