How Does Magnetic Reconnection Drive the 
Early-stage Evolution of Coronal Mass 
Ejections?
Authors: Chunming Zhu, Jiong Qiu, Paulett Liewer, 
Angelos Vourlidas, Michael Spiegel, and Qiang Hu
This is a preprint of an article that originally appeared in The Astrophysical Journal on April 2020. 
The final version can be found at 10.3847/1538-4357/ab838a.
Zhu, Chunming, Jiong Qiu, Paulett Liewer, Angelos Vourlidas, Michael Spiegel, and Qiang Hu. 
“How Does Magnetic Reconnection Drive the Early-Stage Evolution of Coronal Mass Ejections?” 
The Astrophysical Journal 893, no. 2 (April 24, 2020): 141. doi:10.3847/1538-4357/ab838a.
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
Draft version March 26, 2020
Typeset using LATEX modern style in AASTeX61
HOW DOES MAGNETIC RECONNECTION DRIVE THE EARLY STAGE
EVOLUTION OF CORONAL MASS EJECTIONS?
Chunming Zhu,1 Jiong Qiu,1 Paulett Liewer,2 Angelos Vourlidas,3, 4
Michael Spiegel,5 and Qiang Hu6
1Physics Department, Montana State University, Bozeman, MT 59717, USA
2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
3Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
4IAASARS, National Observatory of Athens, GR-15236, Penteli, Greece
5Physics Department, University of California, Davis, CA 95616, USA
6Department of Space Science/CSPAR, University of Alabama in Huntsville, Huntsville, AL 35805,
USA
ABSTRACT
Theoretically, CME kinematics are related to magnetic reconnection processes in
the solar corona. However, the current quantitative understanding of this relation-
ship is based on the analysis of only a handful of events. Here we report a statistical
study of 60 CME-flare events from August 2010 to December 2013. We investigate
kinematic properties of CMEs and magnetic reconnection in the low corona during
the early phase of the eruptions, by combining limb observations from STEREO with
simultaneous on-disk views from SDO. For a subset of 42 events with reconnection
rate evaluated by the magnetic fluxes swept by the flare ribbons on the solar disk
observed from SDO, we find a strong correlation between the peak CME acceleration
and the peak reconnection rate. Also, the maximum velocities of relatively fast CMEs
(& 600 km s−1) are positively correlated with the reconnection flux, but no such cor-
relation is found for slow CMEs. A time-lagged correlation analysis suggests that
the distribution of the time lag of CME acceleration relative to reconnection rate ex-
hibits three peaks, approximately 10 minutes apart, and on average, acceleration-lead
events have smaller reconnection rates. We further compare the CME total mechan-
ical energy with the estimated energy in the current sheet. The comparison suggests
that, for small-flare events, reconnection in the current sheet alone is insufficient to
fuel CMEs. Results from this study suggest that flare reconnection may dominate
Corresponding author: Chunming Zhu
chunming.zhu@montana.edu
arXiv:2003.11134v1  [astro-ph.SR]  24 Mar 2020
2 Zhu et al.
the acceleration of fast CMEs, but for events of slow CMEs and weak reconnection,
other mechanisms may be more important.
CME Kinematics and Magnetic Reconnection 3
1. INTRODUCTION
Coronal Mass Ejections (CMEs), originally observed in white light by the coron-
agraph as discrete and bright features moving outward from the Sun (Tousey 1973;
Gosling et al. 1974), have also been detected in extreme ultra-violet (EUV), soft X-
rays, and radio (reviews by Alexander et al. 2006; Hudson et al. 2006). Typically, the
CMEs carry masses ranging from 1013 to 1016 g, with velocities between several tens to
a few thousand km s−1, and energies of 1022−25 J (Vourlidas et al. 2002; Yashiro et al.
2004; Vourlidas et al. 2010). A comparison of the coronal energy sources and the re-
quired energy of typical CMEs suggests they are generally driven by the release of
magnetic energy (Forbes 2000).
MHD models have been developed to study the evolution of the coronal mag-
netic field leading to the CME eruption (see recent reviews by Chen 2017;
Green et al. 2018). In these models, the coronal magnetic structure rises slowly
due to gradually changing boundary conditions in the photosphere, such as a
shear motion, converging motion, or flux emergence. Free magnetic energy in
the corona is stored during this quasi-equilibrium evolution. At a certain point
in this evolution, an abrupt eruption can be triggered either by an ideal MHD
instability or loss of equilibrium (e.g., Lin & Forbes 2000; Fan & Gibson 2007;
Török et al. 2004; Kliem & Török 2006; Aulanier et al. 2010), or magnetic recon-
nection (Mikic & Linker 1994; Antiochos et al. 1999). The onset of magnetic re-
connection may also restructure the previously stable magnetic configuration by
adding magnetic twist to a pre-existing flux rope, or by forming a twisted flux
rope from a sheared arcade (Van Ballegooijen & Martens 1989; Mikic & Linker 1994;
Longcope & Beveridge 2007; Priest & Longcope 2017), which then erupts. During
the eruption, a CME can reach speeds of several hundred km s−1 within a few min-
utes (e.g., Patsourakos et al. 2010).
Although magnetic reconnection in the corona is a crucial process, it is not currently
directly observable. However, magnetic reconnection forms closed loops and energizes
plasmas and particles therein, resulting in impulsively enhanced flare radiation. The
observed coincidence between the evolution of the CME kinematics and that of the
flare X-ray fluxes indicates that the CME eruption is related with the reconnection
which produces solar flares (Zhang et al. 2001, 2004; Temmer et al. 2008; Bein et al.
2012; Patsourakos et al. 2013), as predicted by CME initiation models (e.g., Chen
2011). Apart from flare light curves, morphological evolution of flare emission in
the lower atmosphere has also been used to infer the reconnection process in the
corona and indirectly measure the rate of magnetic reconnection (Forbes & Priest
1984; Poletto & Kopp 1986). With such measurements, Qiu et al. (2004) analyzed
two well-observed CME-flare events and demonstrated that the acceleration of the
studied CMEs was temporally correlated with the magnetic reconnection rate esti-
mated from the magnetic flux swept through by flare ribbons (Qiu et al. 2002). This
correlation is also shown in a few recent case studies of Hu et al. (2014) and Song et al.
4 Zhu et al.
(2018) using observations with higher tempo-spatial resolutions than earlier studies.
Because of the difficulty in observing CME evolution and measuring CME acceler-
ation in the low corona, many studies instead compare the CME velocity measured
at a few solar radii after the peak acceleration phase, and the total magnetic flux re-
connected during the flare. These studies found that, in fast CME events, these two
quantities are positively correlated (Qiu & Yurchyshyn 2005; Deng & Welsch 2017;
Toriumi et al. 2017; Tschernitz et al. 2018; Pal et al. 2018). Note that most of these
studies have focused on fast CMEs and strong flares, and it is unclear whether this
relationship applies to a broader range of CMEs, in particular, slow CMEs.
Magnetic reconnection almost always occurs during a CME eruption, yet it is
not clear whether reconnection initiates the eruption or it is a consequence of the
eruption. Investigating the relative timing between CME acceleration and flare re-
connection over a large number/types of events should shed light on this question
(e.g., Karpen et al. 2012). For such a study, it is essential to simultaneously measure
CME acceleration and flare reconnection signatures in the low corona during the early
phase of the eruption. Between 2010 and 2013, the separation between the STEREO
and SDO spacecraft (80 – 140 degrees) provides a unique opportunity to observe
CMEs from the limb and associated flare signatures and magnetic field evolution in
the source regions on the solar disk. These missions have obtained observations with
unprecedented temporal cadence and spatial resolution, crucial for quantifying the
dynamics in the early phase of the eruption. Here, we carry such a statistical study
of a large sample of CME-flare events, using observations from multiple viewpoints:
we track the CME evolution in the low corona via limb observation by STEREO,
and measure the magnetic reconnection rate by analyzing flare signatures and mag-
netograms in simultaneous on-disk observations by SDO.
In Section 2, we provide the related information about SDO and STEREO, and the
methods used here for the measurements of the CME kinematics and reconnection
properties during the early stage evolution of the CME-flare events. The statistical re-
sults are presented in Section 3 on the CME kinematics and the reconnection process,
and in Section 4 on the time evolution of the CME kinematics, flare reconnection,
and flare X-ray emission. We then evaluate energetics for these events in Section 5.
Conclusions and discussion are given in Section 6.
2. DATA AND METHOD
2.1. Data
The data set under investigation start from the launch of SDO (Pesnell et al. 2012)
in 2010, continuing until late 2013. During this period, the separation angle be-
tween STEREO (Kaiser et al. 2008) and the Earth (or SDO) increased from ∼80 to
∼140 degrees. STEREO is composed of twin spacecraft: STEREO-A (Ahead) and
STEREO-B (Behind). Three instruments from the Sun Earth Connection Coronal
and Heliospheric Investigation (SECCHI; Howard et al. 2008) on board each space-
CME Kinematics and Magnetic Reconnection 5
craft have been used to track the early evolution of the Earth-side CMEs which are
located near the solar limb when viewed from STEREO. These three instruments in-
clude the Extreme Ultraviolet Imager (EUVI; <1.7 R⊙; Wülser et al. 2004), the inner
coronagraph COR1 (1.3 – 4 R⊙; Thompson et al. 2003) and the outer coronagraph
COR2 (2.5 – 15 R⊙). For EUVI, we prefer to use high-cadence (75 s) images in 171 Å
when there are such data available; otherwise we use 195 Å observations at ∼5 min
cadence. For each event observed by STEREO, a single viewpoint is chosen (Table 1)
based on a closer proximity of the source region to the Earth-side limb and a higher
data cadence if it exists.
The on-disk observations are provided by SDO spacecraft. The Atmospheric Imag-
ing Assembly (AIA; Lemen et al. 2011) on board SDO takes full-disk images of the
Sun in 10 EUV/UV channels (log T ∼ 3.7 – 7.3), with ∼12 – 24 s cadence. Full-disk
magnetograms are from the Helioseismic and Magnetic Imager (HMI; Schou et al.
2012), with 1′′ spatial resolution and 45 s cadence. When choosing the CME-flare
events, we require that a flare is associated with each CME by checking if flare rib-
bons can be clearly detected in UV (using 1600 Å on transition region and upper
photosphere) and/or EUV (here using 304 Å on transition region and chromosphere).
Then we determine the CME source regions based on the timing and location of the
flares.
Examining joint STEREO and SDO observations between 2010 and 2013, we have
selected 60 CME-flare events, listed in Table 1. For these events, STEREO observa-
tions have very well covered the initial stage of the CME. 54 out of the 60 CME-flare
events are located within ±30 degrees from the limb in the STEREO field of view.
The source regions of the 60 CMEs are identified from SDO observations, and we find
that 27 events originate from active regions (ARs), and the other 33 from quiet regions
or decaying plage regions with weak magnetic fields. Using GOES light curves, we
have further identified magnitudes of flares associated with 41 of the CMEs, including
1 X, 11 M, 16 C, and 13 B class flares. For the remaining 19 events the GOES X-ray
curves are either affected by the background emission or other flaring regions on the
solar disk, or have no flare information available. We track the time evolution of the
CME height and flare ribbons in the source region, and measure and compare CME
kinematics and flare reconnection properties in these events.
2.2. Measurement of CME Kinematics
An example of a CME-flare observed on 2012/07/12 (SOL2012-07-12T16:53) is dis-
played in Fig. 1, which demonstrates the methods we used to track a CME and
measure the reconnection flux. To help identify the structures or features in solar
images, we use the wavelet processed images for EUVI1 (Stenborg et al. 2008), while
the COR1 and COR2 data are first processed with secchi prep and then converted
to base differences by subtracting a pre-eruption image, see Fig. 1(b). Then the im-
1 http://sd-www.jhuapl.edu/secchi/wavelets/
6 Zhu et al.
ages are projected to a rectangular Plate Carrée (PC) system (Thompson 2006) with
axes of radial distance from solar disk center and position angle measured counter-
clockwise around the Sun from solar north (Fig. 1(c)). A virtual slit with a width
of 2 degrees and along the center of the erupting CME in the PC-projected images
is chosen to generate time-height stackplots for each of the three instruments. The
stackplots are then co-aligned, to form a map displaying the CME trajectory, i.e. a
“J-map” (Sheeley et al. 1999), as shown in Fig. 1(d). We note that apparent radial
CME eruptions have been preferred during our data selection. The CME front is
tracked in COR1 and COR2. The CME front is sometimes difficult to identify in
EUVI images due to the temperature and density response of the EUV bandpasses
and/or the reduced compression at the front in the early evolution of the eruption.
Therefore, we manually select the foremost detectable feature in the EUV, recognizing
that it may not always correspond to the white light front. As shown in Fig. 1(d), the
identified heights of the feature(s) are superimposed on the J-map. We estimate the
errors of the heights in EUVI, COR1, and COR2 to be 4, 2, and 2 pixels, respectively
(e.g., Song et al. 2018).
With the CME height-time measured, it is straightforward to compute the pro-
jected CME velocity and acceleration by using the time derivatives (Fig. 2(a)).
For SOL2012-07-12T16:53, its acceleration increased abruptly from nearly zero at
16:05 UT to a peaking value of ∼500 m s−2 at 16:23 UT, then gradually de-
creased to ∼10 m s−2 in 1.3 hours. This acceleration profile is similar to that of
the CME reported by Gallagher et al. (2003), both suggesting an exponential rise
followed by another exponential decay. Here we follow Gallagher et al. (2003) and
model the CME acceleration with the two-phase exponential function in the form of
a(t) = [1/[ar exp(t/τr)] + 1/[a exp(−t/τ )]]
−1
d d , where ar and ad are the magnitudes
of acceleration in the two phases, and τr and τd are the corresponding e-folding times,
respectively. These four parameters characterize CME kinematics in the early phase.
To derive the four parameters in the acceleration function, we fit the observed
CME velocity profile, obtained as the time derivative of the CME height measured
from EUVI, COR1, an∫d COR2 observations, to the time integral of the acceleration
function v(t) = v0 + a(t)dt, where v0 is the fifth parameter from the fitting. We
choose to fit the velocity profile because it exhibits a relatively smooth-varying be-
havior. On the other hand, there can be a gap in the CME heights measured between
EUVI and COR1, and between COR1 and COR2, most likely due to different sen-
sitivities to various parts of a CME by different instruments observing in different
spectral ranges. The uncertainty in tracking the weak signatures of the CME leading
edge, together with the varying time cadence, also results in spurious features in the
CME acceleration profile derived as the second time derivative of the measured CME
height. Therefore, fitting to the velocity profile is an optimal choice for modeling
CME acceleration.
CME Kinematics and Magnetic Reconnection 7
Fig. 2(a) shows the model CME velocity profile v(t) from the fitting (the blue/middle
curve) superimposed with the measured CME velocity (blue symbols, smoothed with
a boxcar of three measurements) for the event SOL2012-07-12T16:53 (Fig. 1). The
acceleration profile a(t), which is calculated as the time derivative of v(t), is presented
as the pink/top curve; it agrees w∫ell with observational measurements. Finally, the
time integral of v(t), h(t) = h0 + v(t)dt, is fitted to the heights of the CME front
measured in COR1 and COR2 observations (EUVI observations are not included here
because of possible inconsistency of the tracked features) to yield the last parame-
ter, the CME initial height h0. Here h0 corresponds to an upper limit if considering
possible pileup at the CME front (e.g., Howard & Vourlidas 2018). For the SOL2012-
07-12T16:53 event, we find v0=11.4 km s
−1, and h0 = 0.47 R⊙. Note that h(t), v(t),
and a(t) refer to the CME height, velocity, and acceleration projected on the plane
of the sky (POS), respectively. To compensate for the projection effect, a factor of
1/cos θ is multiplied to each projected height, where θ is the longitudinal separa-
tion angle between the source region viewed from SDO and the limb of the observer
(STEREO A or B) by simply assuming that the eruptions are radial. Table 1 lists
the parameters characterizing CME kinematics for all the 60 CME events.
2.3. Measurement of Reconnection Properties
We also analyze flare signatures in CME source regions to infer the rate of mag-
netic reconnection using SDO observations. Magnetic reconnection occurring in
the corona forms flare loops, and releases energy in these loops; accelerated parti-
cles or thermal conduction travel along newly reconnected field lines (flare loops)
and deposit energy at their footpoints in the chromosphere, causing the bright-
enings there thus forming the flare ribbons in optical and ultraviolet wavelengths
(Forbes & Priest 1984; Poletto & Kopp 1986; Longcope & Klimchuk 2015). There-
fore, magnetic reconnection, which occurs in the corona yet can be hardly mea-
sured there, is mapped in the lower atmosphere by flare radiation, and the recon-
nection rate is measured by summing up photospheric magnetic fluxes covered by
spreading flare ribbons. This method has been widely used to measure the mag-
netic reconnection rate (e.g., Qiu et al. 2002, 2004; Isobe et al. 2002; Asai et al. 2004;
Krucker et al. 2005; Miklenic et al. 2007; Veronig & Polanec 2015; Kazachenko et al.
2017; Zhu et al. 2018). In this study, the brightening pixels are collected from AIA
imaging observations in 1600 Å or 304 Å passband to measure the reconnection rate
in flares ranging from X-class to B-class.
Flare emission in the 1600 Å passband is primarily produced by enhanced C iv
line emission due to heating at the chromosphere/transition region foot-points of
reconnection formed flare loops. The flaring pixels are chosen automatically with the
criteria that the intensity (in the unit of data number) is greater than ∼4 times the
median intensity of the region of interest before the flare, and that the brightening
should persist for at least 3 minutes. Such threshold is chosen to be above the mean
8 Zhu et al.
intensity of the active region plage (Qiu et al. 2010), and the persistence requirement
effectively removes spurious brightening features such as short-lasting brightening due
to projection of erupting filaments. Instantaneous reconnection flux is measured by
summing up HMI-measured longitudinal magnetic flux swept by newly brightened
flare ribbon pixels. The events selected for this study were observed near the disk
center from the SDO point of view. In this study, we do not correct the projection
effect, and do not extrapolate the photosphere magnetic field to the chromosphere
where flare ribbons form, considering that the two effects partially cancel each other.
Uncertainties in the measured reconnection flux are derived by varying the intensity
threshold between 3 and 5 times the pre-flare median intensity, and also by the
difference in the measured magnetic flux in the positive and negative polarities.
For weak flares, usually below C class, emission in the 1600 Å passband is not
significantly enhanced against the background; alternatively, we use observations in
the 304 Å passband to select flare pixels with an intensity threshold of 8 times the
pre-flare median intensity. The 304 Å channel is dominated by He ii line. It is
more sensitive to weak heating signatures and can help capture flare ribbons in minor
flares below C-class. The difference in the measured reconnection flux using these
two passbands for the same flares of C to low M-class is about 20%, which is usually
within the uncertainty of the Φr measurement. In large flares, significantly enhanced
chromosphere emission tends to saturate the 304 Å passband, and this passband also
captures emission in post-flare loops during the late phase of the flare; therefore, we
do not use 304 Å observations to measure reconnection flux in large flares.
The example of the SOL2012-07-12T16:53 showing the flaring ribbons (Fig. 1(e))
sweeping through the magnetic fields is given in Fig. 1(f), where the colors indi-
cate the flux reconnected in different time intervals (see colorbar). Among the 60
CME-flare events in our database, we analyze flare ribbon evolution and measure the
reconnection fluxes using 1600 (304) Å passband in 26 (16) events, respectively, while
in the remainder 18 events of weak flares, reconnection flux is not measured, because
contamination of emissions by erupting filaments or post-flare loops is difficult to be
separated from flare ribbon emissions. For the 42 flares, the measured total reconnec-
tion flux Φr is in the range 1.5 × 10
20 – 5.5 × 1021 Mx, with an average uncertainty
of 35%. The rate of flare reconnection is the time derivative of the reconnection flux,
in units of Mx s−1. The total reconnection flux and peak reconnection rate for the 42
flares are listed in Table 1.
With the flare ribbon pixels identified in the 42 events, we also evaluate two impor-
tant properties, i.e. the length of the ribbons along the interface of the positive and
negative magnetic polarities (polarity inversion line; PIL) LR, and the average dis-
tance of the flare ribbons to the PIL D. Same example of SOL2012-07-12T16:53
is displayed in Fig. 3. The ribbon pixels in the positive and negative polarities
are perpendicularly projected to the PIL respectively, thus giving the correspond-
ing lengths along the PIL, L+ and L−. The ribbon length is the average of L+ and
CME Kinematics and Magnetic Reconnection 9
L−, i.e. LR = (L++L−)/2. The average perpendicular distances of the ribbon pixels
to the PIL is the ribbon distance D. For this flare, LR and D have values of 103
Mm and 23 Mm, respectively. Measurements of these geometric properties are used
to estimate energetics in the reconnecting current sheet in the corona (Section 5).
3. STATISTICS OF CME KINEMATICS AND FLARE RECONNECTION
PROPERTIES
3.1. CME kinematics
The selected 60 CME-flare events were observed from August 2010 to December
2013, during the rise of solar cycle 24. Following the methods introduced in Section 2,
we track the CME eruptions from the solar limb to 15 R⊙, covered by EUVI, COR1
and COR2 on board STEREO. Fig. 4 shows the fitted profiles (heights, velocities, and
accelerations projected on the POS) of the 60 CMEs. For comparison, we aligned
the time profiles for each event, so that the zero time is at the peak acceleration
of that event. These plots reveal a clear trend that fast CMEs are accelerated for
shorter durations yet with greater acceleration rates in the low corona, as shown by
Zhang & Dere (2006). All the kinematic profiles (along with the error bars) of the 60
CME-flare events can be found online at MSU website2.
With these plots, we study the initial height of the CMEs, and for how far CMEs
are accelerated. Histograms of the de-projected heights of the CME fronts are given
in Fig. 5(a–c). The initial heights of the CME fronts (h00 ≡ h0/ cos θ) primarily range
from 0.4 – 1.0 R⊙ above the solar surface, with a median value of 0.6 R⊙ (Fig. 5(a)).
Both the value of h0 (an upper limit of the initial height) and the projection correction
could have led to slightly larger values than those in Bein et al. (2011). For most of
the CMEs the acceleration peaks at heights (hmax acc) between 0.5 and 1.9 R⊙, with
a median value of 1.0 R⊙ (Fig. 5(b)). The distance between the two heights of h00
and hmax acc ranges from 0.15 to 1.2 R⊙, with a median value of 0.4 R⊙ (Fig. 5(c)).
The red curves in Fig. 5 are events originating from active regions (AR, see Table 1),
which exhibit very similar height (distance) distributions.
The distributions of the acceleration properties from the fitted curves (Fig. 4(c)) are
shown in Fig. 5(d–f). The acceleration duration here is measured using the full width
at half maximum of the acceleration profiles. The peak magnitude and duration of
the CME accelerations tend to follow log-normal distributions (Fig. 5(d&e)), similar
to Bein et al. (2011). The peak acceleration apk and duration of the acceleration
τa are anti-correlated with a Pearson correlation coefficient R = -0.91, and their
relationship can be described by a power-law a 4.3 −1.2pk = 10 τa (Fig. 5(f)). These
results are consistent with previous studies ( Zhang & Dere 2006; Vršnak et al. 2007;
Bein et al. 2011).
2 http://solar.physics.montana.edu/czhu/outgoing/CF60/
10 Zhu et al.
We note that Zhang & Dere (2006) analyzed 50 CMEs observed by LASCO from
1996 June to 1998 June, at the start of solar cycle 23, and Bein et al. (2011) analyzed
90 CMEs observed by STEREO between 2007 January and 2010 May during the
transition between solar cycle 23 and 24. The 60 CMEs in this study were observed
by STEREO from 2010 August to 2013 December, from the rise to maximum of the
solar cycle 24, and the kinematic properties of CMEs in this study are derived using a
method different from Zhang & Dere (2006) and Bein et al. (2011). The consistency
of the results in these different studies, therefore, suggests that the statistical proper-
ties of CME kinematics, illustrated in Fig. 5, do not depend on the phase of the solar
cycle.
3.2. Comparison between CME kinematics and reconnection properties
Out of the 60 CMEs, 42 have reconnection properties unambiguously measured
using flare ribbon signatures. Fig. 6(a&b) display the histograms of the mean per-
pendicular distance D from the ribbon to the PIL and the mean flare ribbon length
LR along the PIL. D ranges from 8 to 40 Mm, with a median value of 20 Mm in
AR, slightly smaller than 23 Mm in the quiet Sun (QS) regions. The distributions of
LR are similar between AR and QS, both centering at around 80 Mm. Interestingly,
when comparing D with the CME initial heights h00 (Fig. 6(c)), though D is small
compared to h00 (∼5–20%), there is a trend (R = 0.43) that larger ribbon separations
are associated with larger h00. Flare ribbons are produced by energy release due to
reconnection in the corona, and in general, reconnection occurring at a higher alti-
tude forms larger flare loops with a greater ribbon separation. Therefore, the h00 –
D plot in the figure suggests a scaling relationship between the initial height of the
CME front and the height of flare reconnection, and these two parameters provide
the characteristic scale of the flux system involved in the eruption.
Using flare radiation signatures and magnetograms, we have measured reconnection
flux and reconnection rate. The peak reconnection rate (Φ̇pk) spans over two orders
of magnitude, from 6×1016 to 6×1018 Mx s−1. In Fig. 7(a), we compare Φ̇pk with the
peak CME acceleration (apk). The figure shows that CMEs with larger accelerations
are associated with flares with greater reconnection rates, which is expected in a
theoretical work by Vršnak (2016). For the 42 events, the correlation coefficient R
between Φ̇pk and apk is 0.75, and the Φ̇pk – apk relation can be well fitted to a power
law a = 102.78Φ̇0.56pk pk , with Φ̇pk in uint of 10
18 Mx s−1. It is also noted that, the median
(mean) peak acceleration of these 42 CMEs is 3.8 (3.5) times that of the other 18
CMEs associated with weak flares in which reconnection rate is not measured. These
results provide a strong argument that flare reconnection is key to CME acceleration.
Previous studies have shown that the maximum velocities vmax of fast CMEs are
positively correlated with the total reconnection flux Φr (Qiu & Yurchyshyn 2005;
Vršnak 2016; Deng & Welsch 2017; Toriumi et al. 2017; Pal et al. 2018). Here we
investigate such a relationship with the 42 events, as displayed in Fig. 7(b). We
CME Kinematics and Magnetic Reconnection 11
notice that, for the relatively fast CMEs with vmax & 600 km s
−1 (Howard et al.
1985; Gopalswamy et al. 2000), their maximum velocity vmax is positively correlated
with the total reconnection flux Φr, similar to previous findings. Here vmax can be
linearly scaled with the reconnection flux (R = 0.75) with vmax = 0.86Φr+0.73, where
vmax has a unit of 10
3 km s−1, and Φr has a unit of 10
22 Mx. However, this trend
breaks down for slow CMEs with maximum velocities below ∼600 km s−1. Finally,
16 out of the 18 CMEs without reconnection flux measurements are slow CMEs and
are associated with weak flares.
Our results, based on a much broader and larger event sample than previous studies,
demonstrate that the CME peak acceleration is strongly related to the peak recon-
nection rate. Our study also confirms the positive correlation between the CME peak
velocity and the total reconnection flux for fast CMEs. For slow CMEs, a signif-
icant positive correlation is still present between peak reconnection rate and peak
CME acceleration, but the CME peak velocity and the flare reconnection flux are not
correlated. The implication of these results will be discussed in Section 6.
4. TEMPORAL ANALYSIS
In this study, we track CMEs from the solar surface to several solar radii without
data gap, with cadences as high as 75 seconds in the EUVI images and 2.5 minutes in
COR1 images, and we measure the flare reconnection rate with a 24-second cadence.
This is a unique dataset to perform a time series analysis of the CME evolution with
respect to the progress of flare reconnection. We note that, with very few exceptions,
prior studies often use the GOES soft X-ray (SXR) light curves as a proxy for flare
progress to compare with CME evolution. To relate our study with previous studies,
we also examine the time evolution of CME acceleration and flare reconnection with
respect to the GOES SXR light curve.
4.1. Time profiles of CME acceleration and flare reconnection
Fig. 2 suggests that, on the timescale of a few minutes dictated by the observing ca-
dence of CMEs, the CME acceleration a(t), and flare reconnection rate Φ̇r(t), exhibit
very similar temporal profiles, rising and decaying on nearly the same timescales. To
examine the timing of the CME acceleration and flare reconnection, we conduct a
time-lag analysis of a(t) and Φ̇r(t). The analysis yields the time lag of CME acceler-
ation with respect to flare reconnection ∆τ ≡ ta − tr, and the maximum correlation
coefficient Rmax a r between a(t) and Φ̇r(t) at ∆τ . Fig. 8 presents these results for
the 42 events with reconnection flux measurements. Rmax a r lies within 0.68 – 0.99,
and peaks at ∼0.9, revealing a strong correlation between a(t) and Φ̇r(t).
Meanwhile, the measured time lag ∆τ in Fig. 8(b) ranges between -20 and 20
minutes, and appears to form three groups roughly centered at −10, 0, 10 min. Since
5-min is the synoptic cadence of the EUVI and COR1 observations, we consider that
CME acceleration leads flare reconnection for 11 events with ∆τ < −5 min, flare
reconnection and CME acceleration are simultaneous for 19 events with −5 ≤ ∆τ ≤
12 Zhu et al.
5 min, and flare reconnection leads CME acceleration for the remaining 12 events
of ∆τ > 5 min, respectively. The median (and standard deviation) of ∆τ of these
three groups are −10 ± 2.9, 1.2 ± 2.6, 10 ± 2.8 min, respectively, consistent with the
histogram in Fig. 8(b). The corresponding widths of the three peaks at ∼5–6 min is
less than the 10-min separation between adjacent peaks, suggesting the robustness of
the finding.
Examples of the three groups in Fig. 8(b) are given in Fig. 9. (I) Among the first
group of 11 events, the C8.7 flare of SOL2011-06-21T03:27 (Fig. 9(a)) corresponds
to one of the strongest flares in this group. For this eruption, the CME appears to
accelerate ∼12 min ahead of the reconnection rate. A similar event can be found in
Song et al. (2018). (II) SOL2010-08-01T08:56 (Fig. 9(b)) is an example among the 19
events where the a(t) evolve simultaneously with Φ̇r(t). (III) SOL2011-12-26T20:31
(Fig. 9(c)) belongs to the third group. In this event, the acceleration profile falls
behind the reconnection rate by around 12 min.
As we compare the properties of magnetic reconnection and CME kinematics among
these three groups, we find that all acceleration-lead events have peak reconnection
rates below 0.5×1018 Mx s−1, with the median at 0.2×1018 Mx s−1, whereas the peak
reconnection rate of the other two populations is higher, with the median ∼0.4×1018
Mx s−1, more than twice that of the acceleration-lead events. We find no significant
differences among the three populations, in other properties, such as the CME initial
height.
4.2. Comparison with GOES X-ray light curves
The time derivative of GOES SXR profile has been often used as a proxy of the
energy release, based on the Neupert effect (Neupert 1968; Dennis & Zarro 1993).
To allow comparison of our results with past studies, we apply the time-lag analysis
between the GOES SXR time derivative, Ẋr(t), and the reconnection rate, Φ̇r(t), and
CME acceleration, a(t) (Fig. 10).
The relationship of Ẋr(t) and Φ̇r(t) is shown in Fig. 10(a&b). Only 22 of the 42
events exhibit correlation Rmax Xd r greater than 0.6 (Fig. 10(a)). Interestingly, all
22 events originate in ARs and tend to be associated with the larger flares, which,
in turn, are more consistent with the Neupert effect (Dennis & Zarro 1993). The
histogram of their time differences tXd − tr suggests delays of Ẋr(t) with respect to
Φ̇r(t) by 1–5 min with an average of 2.9 min (Fig. 10(b)).
Similarly, Fig. 10(c&d) give the relationship of a(t) to Ẋr(t). The same 22 events
exhibit a good correlation (Rmax a Xd > 0.6). But the distribution (Fig. 10(c)) ap-
pears to be flatter than the previous two (Fig. 8(a)&10(a)), and gives poorer corre-
lation. Again, among the 22 events, the distribution of their time difference ta − tXd
(Fig. 10(d)), still displays three peaks though shifted by about 3 minutes, due to the
delay of Ẋr(t) in Fig. 10(b).
CME Kinematics and Magnetic Reconnection 13
There are several reasons for the overall poor correlation using the time derivative
of the GOES SXR light curve Ẋr(t). After the peak SXR emission, Ẋr(t) becomes
negative; however, reconnection energy release, reflected by the formation of new flare
loops, still continues into the decay of the SXR emission, as illustrated in Fig. 2&9.
Furthermore, for weak flares, the SXR emission measured by GOES may include
a significant contribution from other regions. Therefore, the magnetic reconnection
rate measured in the host region is a better proxy for the energy release process in
the CME-flare study. The time profile analysis in this part shows that, using the
reconnection rate as the proxy, the timing of energy release is, on average, 3 minutes
earlier than the timing determined using the GOES light curve.
4.3. Start times of CME acceleration and flare reconnection
To complement the foregoing correlation analysis on the overall progress of the
CME acceleration and flare reconnection, here we investigate the timings when CME
acceleration or flare reconnection begins to rise (Kahler et al. 1988; Zhang et al. 2001;
Temmer et al. 2008; Liu et al. 2014; Wang et al. 2019). We choose the start time
of CME acceleration ta st or that of flare reconnection rate tr st to be the moment
when CME acceleration (or reconnection rate) has increased to 10% of the peak
(Berkebile-Stoiser et al. 2012; Bein et al. 2012). For this analysis, the time profile
of the reconnection rate is smoothed with a boxcar of 5 min, similar to the time
cadence of the CME observation. Fig. 11(a) displays a comparison of the start times
of the flare reconnection and CME acceleration for the subset of 42 CME-flare events.
The time differences ∆τst ≡ ta st − tr st are primarily within ±25 min, and have a
median value of -1.7 min. The number of events for ∆τst < −5 min, |∆τst| 6 5
min, and ∆τst > 5 min are 16, 14, and 12, respectively. Thus the distribution is
slightly asymmetric with a few more events where CME acceleration appears to rise
earlier than the rise of flare reconnection. This asymmetry is consistent with but
less remarkable than that using the CME acceleration and the hard X-ray emission
reported by Berkebile-Stoiser et al. (2012).
Fig. 11(b) displays a scatter plot of ∆τst with respect to the magnitude of GOES X-
ray in 1–8 Å for 35 out of the 42 events (the remainder 7 events are not included due
to the presence of simultaneous strong emission from other regions or unavailability
of GOES data). The scatter plot can be also divided into three groups. For 13 events
with |∆τst| 6 5 min, the magnitude of the flare SXR emission spans three orders of
magnitude, and the average peak reconnection rate of these events is 1.2± 1.6× 1018
Mx s−1. Similarly, the 9 events with earlier flare reconnection (∆τst > 5 min) exhibit a
range of flare SXR flux, and have an average peak reconnection rate of 1.2±1.7×1018
Mx s−1. For the remainder 13 events where CME acceleration begins earlier than flare
reconnection (∆τst < −5 min), the amount of time lag |∆τst| is roughly anti-correlated
with the flare SXR peak flux, i.e. shorter time differences for stronger flares. The
14 Zhu et al.
reconnection rate for this group is 0.4±0.4×1018 Mx s−1, evidently smaller than the
other two groups.
Overall, the distribution of the time lag between the time profiles of acceleration
and reconnection rate appears to be symmetric, displaying three peaks with ∼10 min
apart (Fig. 8(b)). The distribution of the difference in the start times is slightly
asymmetric (Fig. 11(a)), with a few more events in which CME acceleration rises
earlier than the flare reconnection. In both cases, we find that acceleration-lead
events are associated with lower reconnection rates.
5. CURRENT-SHEET PROPERTY AND ENERGETICS
Magnetic reconnection takes place in a current sheet (CS) that forms during CME
eruption. Reconnection in the CS re-configures the global magnetic field, forming
flare loops and changing the CME structure, and in this course, releases free magnetic
energy. The amount of released magnetic energy is equivalent to the work done by
electric fields on electric currents integrated in the entire space. The reconnection rate
in the CS can be described by the local reconnection electric field (e.g., Lin & Forbes
2000). Approximating the flare-CME configuration by a 2D model, we can estimate
the mean reconnection electric field and the electric current along the CS, using the
measured reconnection rate in terms of Φ̇r(t) and the length of flare ribbons LR. We
can then estimate the amount of work done by the reconnection electric field in the
CS, and compare it with the CME energy.
Properties of the CS can be estimated by applying the minimum-current corona
(MCC; Longcope 1996) to a single current sheet following a separator of total length
LR. If magnetic flux Φr reconnects across this separator it must initially carry a net
current with order of magnitude I0 ∼ Φr/µ0LR. The mean reconnection electric field
will be
〈E〉 = |Φ̇r(t)|/LR ,
and the total magnetic energy released will be
∫
W 2r = I dΦr ∼ (Φr) /2µ0LR .
where µ0 is the permeability of free space. The MCC model addresses the build-up
and release of magnetic energy in a three-dimensional corona. For the energy release
process, it assumes that reconnection at the current in the CS has decreased to zero.
Thus Wr here corresponds to an upper limit.
The distributions of the peak 〈E〉 and I0 are shown in Fig. 12(a&b). 〈E〉pk, deter-
mined using the peak reconnection rate, ranges 5 – 500 V/m. The values here are
typical when compared to the studies by Qiu et al. (2004), Jing et al. (2005), and
Song et al. (2013). The median value of 〈E〉pk in AR (95.5 V/m) is about 5 times as
large as that in QS (20.6 V/m). Meanwhile, the pre-reconnection current intensity
I0, ranging between 1.3−72×10
10 A, displays a stronger median value of 6.7×1010 A
CME Kinematics and Magnetic Reconnection 15
in ARs compared to 3.0×1010 A in QS. Finally, the estimated work done by the
reconnection electric field, Wr, is in the range 10
22−25 J.
Fig. 13 gives the relationship between Wr and the CME mechanical energy (Ecme ∼
Ek + Ep) for the studied CME-flare events, where Ek is the CME kinematic en-
ergy, and Ep is its gravitational potential energy. The CME masses, based on
the theory of Thomson scattering (Billings 1966; Hayes et al. 2001; Howard 2011;
Vourlidas & Howard 2006), are derived by following the procedures described in
Vourlidas et al. (2010) and making use of the COR2 data and scc calc cme mass.pro
in the SolarSoftware. We measure the CME mass at a time when the CME ar-
rives at ∼10 R⊙. The angle from the POS is determined because of the multi-
viewpoint observations here, to be the same as θ. This gives CME masses ranging
from 8.7×1014 to 1.9×1016 g. The error of the CME masses is estimated to be a factor
of 2 (Vourlidas et al. 2010). In this way, Ek is estimated by using E = mv
2
k max/2. We
were able to measure the CME mass for 40 events. Two could not be analyzed due
to a lack of good pre-event images.
Fig. 13 shows that the CME energy (Ek or Ecme) is roughly scaled with Wr. We
first discuss Ek – Wr relation (top panels in Fig. 13). The correlation coefficient
between these two quantities for the 40 events is 0.56, and Ek – Wr can be fitted
by a power-law function, with the power-law index of 0.36. If we only consider the
relatively fast CME events with vmax & 600 km s
−1, a stronger correlation (R =
0.76) is found, and E 15.64 0.37k = 10 Wr . There is no clear trend for slower CMEs with
vmax . 600 km s
−1. Similar relations hold for the total CME energy, Ecme, and Wr
(lower panels in Fig. 13).
The diagonal dashed line in the figure marks equality and separates the energies into
two regions: below this line, Ecme < Wr, so W may provide the necessary energy for
the eruption; For events above this line, Ecme > Wr, therefore Wr is inadequate and
the eruption requires additional energy sources. We discuss the Ecme –Wr relationship
further in Section 6.
6. CONCLUSIONS AND DISCUSSION
6.1. Summary
We conduct a statistical study of 60 CME-flare events by combining observations
from different viewpoints by SDO and STEREO. The on-disk observations from the
SDO provide measurements of the photospheric magnetic field and flare ribbon evo-
lution, enabling the estimation of the magnetic reconnection flux (and reconnection
rate) and the flare-ribbon geometry. The limb views from STEREO (EUVI, COR1
and COR2) yield measurements of the height of the Earth-side CMEs from 0 to 15
R⊙. Based on these measurements, we study the kinematics of these 60 CMEs, and
examine the magnitude and time evolution of the CME acceleration with respect to
the progress of magnetic reconnection in 42 events (in which reconnection rate can
be measured). We then compare the CME mechanical energy with the estimated
16 Zhu et al.
amount of work done by the reconnection electric field in the CS. Our major findings
are summarized as follows.
1. A strong correlation (Rmax a r & 0.7) exists between the CME acceleration
and the reconnection rate (Fig. 8(a)), regardless of whether CMEs are fast or
slow. The CME peak acceleration shows a power-law scaling with the peak
reconnection rate (Fig. 7(a)). A positive correlation is also found between the
maximum speed of CMEs and the total reconnection flux (Fig. 7(b)), but only
in relatively fast CMEs (vmax & 600 km s
−1), whereas no clear correlation is
found for the slower CMEs.
2. The CME acceleration and flare reconnection exhibit very similar time pro-
files from rise to decay, and the temporal correlation between the two is much
stronger than the correlation between either of them and the time deriva-
tive of the GOES SXR light curve. For the studied 42 events, the distribu-
tion of the time lag of the CME acceleration with respect to the reconnec-
tion rate (∆τ ≡ ta − tr) displays a symmetric distribution with three peaks
at -10.0±2.9 (11 events), 1.2±2.6 (19), and 10.0±2.8 min (12), respectively
(Fig. 8(b)). For a comparison, the distribution of the time lag of their start
times (∆τst ≡ ta st − tr st) is slightly asymmetric (Fig. 11(a)), with a few more
events where acceleration begins earlier than the flare reconnection. On aver-
age, the peak reconnection rate of the acceleration-lead population is smaller
than that of the other two populations.
3. The CME total mechanical energy Ecme displays a good correlation (R ∼ 0.6)
with the estimated work Wr done by the reconnection electric field in the CS.
Ecme – Wr can be fitted to a power-law function with the power-law index of
∼1/3 (Fig. 13).
Past studies have shown a scaling law between CME maximum velocity and total
reconnection flux, for relatively fast CMEs and strong flares (Qiu & Yurchyshyn 2005;
Deng & Welsch 2017; Toriumi et al. 2017; Tschernitz et al. 2018; Pal et al. 2018). In
this study, making use of observations from multiple views, we have analyzed a broad
range of CME-flare events, i.e. B to X-class flares, and both slow and fast CMEs.
Our results from this extended sample demonstrate a significant correlation between
CME acceleration and flare reconnection in various aspects. These results provide a
strong argument that flare reconnection is key to acceleration of both fast and slow
CMEs, and may dominate the acceleration of fast CMEs.
On the other hand, the finding that the maximum speed of slow CMEs is not
correlated with the total reconnection flux may indicate that other physical processes
play a more important role during the acceleration of these CMEs. Note that the
apk – τa scaling indicates that, statistically speaking, an event with smaller peak
acceleration (and also a smaller peak reconnection rate) tends to be accelerated for a
CME Kinematics and Magnetic Reconnection 17
longer period of time; it seems that, for slow CMEs, the effect of CME acceleration by
flare reconnection during this extended time period is relatively weak in comparison
with other mechanisms.
Our results suggest that the significance of flare reconnection in CME acceleration
is different in fast and slow CMEs. The results from the energetics and time-lag
analyses bear similar indications, which will be further discussed.
6.2. Energetics
Our analysis reveals a good correlation between the CME mechanical energy and
the estimated electrodynamic work Wr done by the reconnection electric field in the
CS, especially for the relatively fast CMEs (Fig. 13). For events with Wr & 2×10
24 J
(X and M flares; Fig. 13(e)), Wr is larger than or comparable to Ecme and should
be able to provide a significant amount of energy for the CME eruption. This result
supports the argument that flare reconnection dominates CME acceleration in fast
CMEs.
However, for events with smaller flares, i.e. B and C flares, Ecme is 1 – 2 orders of
magnitude larger than Wr. This large ratio of Ecme/Wr would suggest that, in these
events, the work done by the reconnection electric field in the CS itself might not be
enough to fuel the eruption. It is possible that reconnection also occurs elsewhere,
such as the breakout type of reconnection (Antiochos et al. 1999; Karpen et al. 2012).
In events with very weak or little flare radiation signature, reconnection may occur
at higher altitudes and produce less plasma heating, as suggested by Robbrecht et al.
(2009) and Vourlidas & Webb (2018). Signatures of these reconnection events are
either undetectable by current instrumentation or require different analysis method-
ologies (Robbrecht & Wang 2010).
Apart from reconnection, several other mechanisms can also impact the kinematics
of these events. If a flux rope is present – whether it is generated prior to or at the
time of the eruption – and carries a sizable amount of electric current, a significant
amount of work can be done on this flux rope current during its eruption. Mass
unloading may also help accelerate a CME (Low 1996; Klimchuk 2001). It is likely
that these other mechanisms are more important in events characteristics of slow
CMEs and weak reconnection.
The Ecme – Wr scaling (Fig. 13) may also shed light upon the increased association
rate between CMEs and flares production rates with the rising flare intensity reported
by Yashiro et al. (2005). For small flares, the requirement of additional 1–2 order
larger energy sources would make it very difficult to drive a CME. Thus the free
energy associated with the current sheet(s) can be either released through a series
of small flares without CMEs, or wait until additional energies become available
(e.g., formation of flux ropes). On the other hand, for large flares where Wr & Ecme,
they require little additional energy. Thus it would appear to be easier for the large
flares to produce simultaneous CMEs. A more comprehensive evaluation of various
18 Zhu et al.
energies, the CME energy, flare energy, and free magnetic energy including Wr, will
be conducted in future studies.
6.3. Timing
Our unique dataset with CMEs observed in the low corona and flares observed on
the disk provides the advantage to examine relative timings of the CME acceleration
and flare reconnection in the early phase of the eruption. In this study, a time-
lagged correlation analysis is performed to compare the temporal evolution of CME
kinematics with respect to the progress of flare reconnection. The resultant time lag is
determined by the slow-varying component of the time profiles, in particular, the times
of the global maximum of the analyzed time series (see Fig. 9). Our analysis reveals
the presence of all three populations, namely, the acceleration-lead, the simultaneous,
and the reconnection-lead events, and adjacent populations are separated by about
10 minutes.
These results may be discussed with respect to some eruption models. For exam-
ple, in the framework of a 2D loss-of-equilibrium (LOE) model (Lin & Forbes 2000),
Reeves (2006) has shown that reconnection energy release rate – the product of the
reconnection electric field and magnetic field – in the CS beneath the erupting flux
rope always lags the CME acceleration, and the amount of the lag grows when ei-
ther the reconnection rate (represented by the Alfvén Mach number in the CS) or
the background magnetic field decreases. The time lag analysis from this model is
qualitatively consistent with the observed acceleration-lead events; but this model,
and perhaps other models that drive eruption ideally, cannot explain other events
in which flare reconnection leads, or evolves simultaneously with, CME acceleration.
We recognize that a detailed model-observation comparison in terms of the time lag
requires consideration of many other properties, such as the geometric properties and
aerodynamic drag (e.g., Chen & Krall 2003; Vršnak 2016), and is beyond the scope of
the present study; nevertheless, this study has established an observational database
to help construct or constrain parameter studies with numerical models.
An acceleration-lead event is likely driven by an ideal instability, such as in the
LOE model, yet it is still possible that the eruption is triggered by reconnection
(Green et al. 2018). We note that the time-lagged correlation analysis (Fig. 8) is
not suited to answer the “trigger” question, namely, whether the start of the fast
CME motion occurs before or after the onset of flare reconnection (e.g., Karpen et al.
2012). We also attempted to estimate the start times of CME acceleration and flare
reconnection (Fig. 11), using the analytical function to describe CME acceleration and
much smoothed time profiles of flare reconnection. The resultant time lag distribution
is similar to that of the correlation analysis, which is also likely governed by the
slow-varying trend of the time profiles, and is subject to the uncertainties primarily
determined by the time cadence (5 min) of CME observations. To probe the “trigger”
of the eruption in the future study, it is crucial to explore new methods, identify
CME Kinematics and Magnetic Reconnection 19
fast-varying features in the early stage using unsmoothed time profiles, and examine
their associated signatures in the low corona prior to the eruption. This requires
analysis of flare and CME observations at high temporal and spatial resolutions with
the combination of all available capabilities including SDO and RHESSI (Lin et al.
2003).
The authors thank the referee for several constructive comments. We thank
Dr. Dana W. Longcope for helpful discussion. The authors gratefully acknowledge the
funding of NASA Heliophysics Guest Investigator (HGI) program (80NSSC18K0622).
C.Z. and J.Q. also thank the funding of NASA HGI 80NSSC19K0269. This work is
also supported by NSF REU program (1156011) at Montana State University.
Facilities: SDO, STEREO, GOES
20 Zhu et al.
Figure 1. STEREO and SDO observations of a CME on 2012/07/12 (SOL2012-07-
12T16:53), illustrating the procedures used in this study for deriving a CME’s early tra-
jectory and the associated magnetic reconnection rate. (a) Positions of STEREO/A&B,
and SDO around the Sun. The CME source region is indicated by the star sign. (b) Joint
observations from STEREO/A EUVI 171 Å, COR1, and COR2. (c) The Plate-Carrée pro-
jection of the joint observations. A slit (dashed line) along erupting features is chosen to
generate a time-space stackplot (J-map). The slit location in the original images is also
shown in (b). (d) The generated J-map, with trajectories of the tracking features indicated
by the plus signs. (e) A snapshot of the flaring ribbons, from SDO/AIA 1600 Å. (f) The
expanding flare ribbons in 1600 Å (colored) which swept the magnetic fields measured by
SDO/HMI (gray).
CME Kinematics and Magnetic Reconnection 21
Figure 2. CME kinematics and a related X1.4 flare of SOL2012-07-12T16:53. (a) Projected
heliocentric height (h), velocity (v), acceleration (a) of the CME. For h, the red, green,
and blue squares delineate the trajectories from STEREO/A EUVI, COR1 and COR2,
respectively. The blue curve of v corresponds to the fit. The other two curves (black and
pink) are from the integration and derivative of the fitting of v, respectively. (b) Magnetic
reconnection rate and the accumulated reconnection flux. (c) GOES X-ray flux of 1.0–8.0 Å
and its time derivative.
22 Zhu et al.
Figure 3. Measurement of the flare ribbon geometry for SOL2012-07-12T16:53 (Fig. 1&2).
The ribbon lengths L+ (L−) along the PIL (white thick curve) are measured by projecting
the flare ribbon located in the positive (negative) polarity to the PIL, respectively. Similarly,
the ribbon distances of D+ and D− in the opposite polarities are determined by averaging
the distances of the flaring pixels to the PIL. The color scale along the ribbons denotes the
PIL distance. The HMI LOS magnetogram is shown as gray background.
Figure 4. Overview of the kinematics of the selected 60 CMEs, including heights (a),
velocities (b), and accelerations (c). The curves are co-aligned relative to the time of peak
acceleration for each event. The colors of the curves are based on the peak acceleration
values, as seen in (c).
CME Kinematics and Magnetic Reconnection 23
Figure 5. Histograms of the CME heights, acceleration peaks and durations. (a) Initial
heights (h00) of the CME fronts above solar surface. (b) The heights of each CME at
maximum acceleration. (c) The distances between the h00 and the height of of CME front
at the maximum acceleration. (d) The peak values of CME accelerations. (e) The duration
of CME acceleration. (f) Relationship of the peak and duration of CME acceleration. The
histograms for all events are indicated with black curves, while those for AR CMEs are
indicated with red curves. The blue curves in (d) and (e) give the log-normal fittings,
with the parameters noted at top. A linear fitting in (f) is included, with the correlation
coefficient R, the correlation, and the uncertainties σab of the corresponding parameters
displayed at the top.
Figure 6. Distributions of the average distances of the flare ribbons to the PIL D for the
CME-flare events (a), the ribbon length along PIL (b), the correlation between D and h00
(c).
24 Zhu et al.
Figure 7. Relationship between the peaks of the acceleration and reconnection rate (a),
and between the CME maximum velocities and the total reconnection fluxes (b). The
dashed line in (b) marks 600 km s−1 which roughly separates two types of CMEs based on
their maximum velocities. The corresponding fits are also displayed in each panel.
Figure 8. Distributions of the maximum correlation coefficient Rmax between the shifted
profiles of acceleration and reconnection flux rate (a), and their time differences ta − tr
(b). A negative time difference here means that the acceleration profiles comes earlier, vice
versa. The distributions of events in ARs are indicated with red curves.
CME Kinematics and Magnetic Reconnection 25
Figure 9. Three examples of the relationships between the CME kinematics, the reconnec-
tion flux, and flare X-rays, corresponding to the three peaks in Fig. 8(b), using the format
of Fig. 2: the profile of the CME acceleration a(t) leads the reconnection rate (a, SOL2011-
06-21T03:27), simultaneously (b, SOL2010-08-01T08:56), and a(t) follows the reconnection
rate (c, SOL2011-12-26T20:31).
26 Zhu et al.
Figure 10. Distributions of Rmax (a) and the time differences (b) between the GOES time
derivative and reconnection flux rate. Distributions of the Rmax (c) and the time differences
(d) between the acceleration and GOES time derivative. Only the events with Rmax > 0.3
are shown in the left panels, and the events with Rmax > 0.6 are shown in the right panels.
The distributions of events in ARs are indicated with red curves.
Figure 11. Time difference between the start times of CME acceleration and flare recon-
nection rate, i.e. ∆τst ≡ ta st − tr st. Panel (a) displays a histogram of ∆τst. Panel (b)
shows a scatter plot of ∆τst vs. peaking GOES X-ray flux, with ±5 min indicated by the
dashed lines.
CME Kinematics and Magnetic Reconnection 27
Figure 12. Histograms of the average electric field strength in the current sheet at the
timing of peaking reconnection rates (a), and the integrated current intensity in the current
sheet before the CME eruption (b).
Figure 13. Comparisons of the CME kinetic energy Ek (top panels), CME total mechanical
energy (Ecme = Ek + Ep; lower panels) with the released energy Wr related to the current
sheet during the CME-flare events. Left panels (a&d): Total 40 events with available
measurements of both reconnection flux and CME mass. Middle panels (b&e): 26 events
with vmax & 600 km s
−1. Right panels (c&f): 14 events with vmax . 600 km s
−1. The
diagonal dashed line denotes equality.
28 Zhu et al.
Table 1. List of 60 CME-flare events observed by STEREO and SDO.
Event STE. SDO xy AR Sep. EUVI h00 apk τa vmax rec. wav. Φr Φ̇pk GOES mcme Ep
ta peak a,b arcsec num deg Å R m s
−2 min km s−1 Å 1021Mx 1018Mx s−1⊙ class 1015g 1023J
01 20100801 08:13 a [-480, 190] 11092 78 171 0.51 588 23.1 1008 1600 1.4±0.70 0.31± 0.04 C3.2 4.0 6.5
02 20100807 18:08 a [-530, 170] 11093 79 171 0.22 931 11.2 747 1600 1.6±0.39 1.28± 0.12 M1.0 6.7 11.3
03 20100911 01:33 a [-400, 450] 82 171 0.58 82 52.8 326 304 0.4±0.10 0.07± 0.01 B3.1 6.1 10.1
04 20101130 18:40 a [-600, 230] 85 195 0.53 131 48.2 490 304 0.2±0.04 0.07± 0.01 B1.7 2.4 3.9
05 20101214 15:17 a [ 700, 400] 11133 85 195 1.36 241 42.9 771 C2.3
06 20110216 02:17 b [-400, 500] 94 195 0.66 63 57.5 266 304 0.4±0.13 0.06± 0.01 2.4 3.9
07 20110621 02:30 a [ 100, 240] 11236 96 171 0.47 318 41.6 1001 1600 2.5±1.76 0.27± 0.14 C7.8 5.8 9.5
08 20110709 00:20 b [-350,-330] 11247 92 171 0.45 275 33.8 690 304 0.8±0.14 0.21± 0.03 B4.9 3.2 5.3
09 20110802 06:19 a [ 240, 160] 11261 100 171 0.49 521 20.6 791 1600 3.6±1.02 1.12± 0.08 M1.5 7.1 11.7
10 20110910 02:59 a [ 300, 450] 103 171 0.80 93 95.7 645 304 0.2±0.10 0.08± 0.02 B5.5 3.9 6.4
11 20110913 22:58 a [ 220, 220] 103 171 0.61 152 29.3 342 304 2.2±0.48 0.47± 0.05 4.3 7.0
12 20111001 09:48 a [ 90, 50] 11305 104 195 0.19 405 17.9 533 1600 1.9±0.41 0.78± 0.02 M1.3 9.0 13.6
13 20111022 01:40 a [ 500, 400] 105 195 1.27 66 136.2 634
14 20111107 23:45 a [ 450, 450] 106 195 0.61 148 49.6 542 304 0.3±0.11 0.08± 0.02 2.9 4.6
15 20111109 08:30 a [-250,-500] 106 195 0.79 67 74.4 380
16 20111109 13:08 b [-500, 320] 11342 103 195 0.90 568 15.9 658 1600 2.1±1.00 1.11± 0.32 M1.2 7.7 12.7
17 20111114 20:08 a [ 480,-450] 106 171 0.55 193 40.9 558
18 20111117 16:10 a [ 350,-450] 106 195 0.65 80 37.2 246
19 20111126 07:02 a [ 600, 250] 11353 106 195 0.77 474 23.5 804 304 0.9±0.11 0.35± 0.04 C1.2 8.9 14.1
20 20111225 00:20 a [ 200, 400] 107 195 0.31 338 21.6 521 304 0.6±0.08 0.30± 0.03 C1.1 3.4 5.2
21 20111226 11:28 b [ 20, 350] 11384 110 195 0.65 733 15.1 788 1600 1.2±0.58 0.38± 0.12 C5.8 5.4 8.9
22 20111226 20:28 a [ 600,-360] 11387 107 195 0.61 307 20.5 458 1600 1.6±0.30 2.31± 0.30 M2.4 0.7 1.1
23 20120119 10:45 a [ 600, 600] 108 195 1.11 31 154.4 309
24 20120119 14:47 b [-350, 600] 11402 113 195 1.09 316 47.2 1122 1600 2.8±0.80 0.65± 0.10 M3.2 13.0 21.8
25 20120123 03:42 b [ 300, 580] 11402 114 171 1.60 1000 10.5 763 1600 4.9±0.86 2.50± 0.01 M8.8 19.4 31.9
26 20120210 19:51 b [-200, 550] 116 195 1.24 128 59.0 534 304 0.4±0.19 0.10± 0.04 4.3 7.2
27 20120224 03:16 b [-450, 500] 117 195 0.18 168 38.1 480
28 20120309 03:46 b [ 50, 400] 11429 118 171 0.66 1171 13.5 1149 1600 5.8±0.88 4.96± 0.52 M6.4 6.6 10.5
Table 1 continued on next page
CME Kinematics and Magnetic Reconnection 29
Table 1 (continued)
Event STE. SDO xy AR Sep. EUVI h00 apk τa vmax rec. wav. Φr Φ̇pk GOES mcme Ep
ta peak a,b arcsec num deg Å R⊙ m s
−2 min km s−1 Å 1021Mx 1018Mx s−1 class 1015g 1023J
29 20120310 17:31 a [ 350, 400] 11429 110 171 0.11 1234 13.1 1158 1600 6.8±1.44 5.88± 0.47 M8.5 13.6 21.9
30 20120405 21:01 a [ 480, 370] 11450 111 171 0.63 445 20.5 648 1600 1.1±0.82 0.11± 0.04 C1.6 10.8 18.4
31 20120419 15:46 b [-620,-350] 119 171 0.13 75 126.5 677
32 20120429 08:41 b [-650, 400] 118 195 0.48 84 76.5 539 B5.6
33 20120507 00:58 a [ 500,-300] 11471 114 195 0.51 170 50.3 629 1600 0.9±0.64 0.19± 0.03 C2.0 6.1 9.6
34 20120508 09:33 a [ 50, 300] 114 195 0.40 345 16.4 412 1600 0.7±0.56 0.15± 0.06 2.6 3.9
35 20120603 11:58 b [-620,-300] 117 195 0.87 104 51.2 385 1600 0.5±0.37 0.10± 0.01 3.1 5.2
36 20120614 13:49 b [-100,-300] 11504 116 171 0.55 499 31.8 1140 1600 3.4±1.08 1.13± 0.20 M1.9 6.6 11.0
37 20120712 16:22 a [ 20,-300] 11520 120 171 0.67 552 27.7 1188 1600 6.9±1.70 2.88± 0.11 X1.4 18.5 30.7
38 20120814 02:46 a [ 300,-320] 11542 123 195 0.33 75 59.7 334 304 0.7±0.11 0.21± 0.01 C1.2 1.6 2.9
39 20120817 23:03 a [ 650, 380] 123 195 0.58 298 19.7 470
40 20120831 19:41 b [-600,-400] 11562 116 171 0.18 814 16.3 949 1600 1.4±0.58 0.38± 0.19 C8.5 20.2 32.7
41 20120927 23:40 a [ 490, 80] 11577 126 195 0.83 892 16.3 1052 1600 1.1±0.51 0.43± 0.13 C3.8 8.5 13.8
42 20120929 08:45 a [ 600, 40] 126 195 0.60 168 34.6 426
43 20121023 08:07 a [ 380, 180] 11593 127 195 0.77 173 29.4 372 1600 1.4±0.98 0.32± 0.11 C2.9 2.5 3.9
44 20121120 11:55 a [ 350, 200] 128 195 0.66 181 51.5 660 304 1.0±0.20 0.32± 0.05 5.2 8.5
45 20121122 08:57 b [-280,-380] 125 195 0.80 91 75.0 480 304 0.4±0.09 0.11± 0.02 B6.4 3.5 5.9
46 20121126 04:27 a [ 300,-480] 128 195 0.58 129 55.0 427 304 0.4±0.10 0.12± 0.04 B7.3 2.1 3.4
47 20130206 02:46 b [-500, 440] 137 195 0.63 137 60.6 618 1600 0.5±0.40 0.10± 0.07 C1.3 3.3 5.3
48 20130212 22:58 a [ 720,-460] 130 171 0.83 310 38.6 854 B5.9
49 20130301 18:48 a [ 620,-180] 131 195 0.46 68 57.7 364 B6.7
50 20130316 14:15 a [ 750, 450] 132 195 0.60 244 36.2 587 B7.5
51 20130404 21:22 a [ 600,-250] 133 195 0.50 131 42.7 400 304 0.1±0.03 0.08± 0.01 B5.6
52 20130421 20:11 a [ 750,-250] 11723 134 195 0.45 252 30.9 578 1600 0.4±0.17 0.24± 0.02 C2.8 2.6 4.5
53 20130511 23:42 a [ 500, 500] 136 195 0.45 96 70.6 493
54 20130806 01:44 b [-350, 320] 138 171 0.31 996 8.3 630 304 0.2±0.03 0.22± 0.03 B4.4 3.2 5.3
55 20130817 00:46 b [-350, 450] 138 195 0.71 48 81.9 316 B4.6
56 20130829 05:43 a [ 400,-550] 145 195 0.93 68 119.9 621
57 20130830 02:20 b [-650, 160] 11836 138 195 0.98 662 21.1 989 1600 1.4±0.59 0.49± 0.07 C8.4 7.9 13.4
58 20131011 12:16 b [-570,-470] 11865 140 195 0.15 471 16.3 592 1600 0.6±0.33 0.37± 0.06 C6.3
59 20131026 12:41 a [ 600,-600] 148 195 0.86 95 84.1 590
60 20131207 07:21 a [ 720,-250] 11909 150 195 0.16 1246 11.5 1016 1600 0.7±0.21 0.77± 0.13 M1.3 2.7 4.9
30 Zhu et al.
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