How Does Magnetic Reconnection Drive the Early-stage Evolution of Coronal Mass Ejections?

The data set under investigation started from the launch of SDO (Pesnell et al. 2012) in 2010, continuing until late 2013. During this period, the separation angle between STEREO (Kaiser et al. 2008) and the Earth (or SDO) increased from ∼80° to ∼140°. 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 spacecraft have been used to track the early evolution of the Earth-side CMEs that are located near the solar limb when viewed from STEREO. These three instruments include 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-minute 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.

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	${\dot{{\rm{\Phi }}}}_{{pk}}$	GOES	mcme	Ep
ta_peak	a, b	(arcsec)	num	(deg)	(Å)	(R⊙)	($m\,{s}^{-2}$)	(minutes)	(km s−1)	(Å)	(1021 Mx)	(1018 Mx s−1)	Class	(1015 g)	(1023 J)
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
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

Download table as:  ASCIITypeset images: 1 2

The on-disk observations are provided by the SDO spacecraft. The Atmospheric Imaging Assembly (AIA; Lemen et al. 2011) on board SDO takes full-disk images of the Sun in 10 EUV/UV channels (logT ∼ 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 whether flare ribbons 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 observations have very well covered the initial stage of the CME. A total of 54 out of the 60 CME-flare events are located within ±30° 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 either are 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 we measure and compare CME kinematics and flare reconnection properties in these events.

An example of a CME-flare observed on 2012 July 12 (SOL2012-07-12T16:53) is displayed in Figure 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 EUVI⁷ (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 Figure 1(b). Then, the images are projected to a rectangular Plate Carrée (PC) system (Thompson 2006) with axes of radial distance from solar disk center and position angle measured counterclockwise around the Sun from solar north (Figure 1(c)). A virtual slit with a width of 2° and along the center of the erupting CME in the PC-projected images is chosen to generate time–height stack plots for each of the three instruments. The stack plots are then co-aligned, to form a map displaying the CME trajectory, i.e., a "J-map" (Sheeley et al. 1999), as shown in Figure 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 owing 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 Figure 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).

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With the CME height–time profile measured, it is straightforward to compute the projected CME velocity and acceleration by using the time derivatives (Figure 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 and then gradually decreased to ∼10 m s⁻² in 1.3 hr. 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 $a(t)={[1/[{a}_{r}\exp (t/{\tau }_{r})]+1/[{a}_{d}\exp (-t/{\tau }_{d})]]}^{-1}$, where a_r and a_d are the magnitudes of acceleration in the two phases and τ_r and τ_d are the corresponding e-folding times. These four parameters characterize CME kinematics in the early phase.

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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, and COR2 observations, to the time integral of the acceleration function $v(t)={v}_{0}+\int a(t){dt}$, where v₀ is the fifth parameter from the fitting. We choose to fit the velocity profile because it exhibits a relatively smooth-varying behavior. 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 sensitivities 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.

Figure 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 (Figure 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 well with observational measurements. Finally, the time integral of v(t), $h(t)={h}_{0}+\int v(t){dt}$, 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 parameter, 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/$\cos \theta$ is multiplied to each projected height, where θ is the longitudinal separation angle between the source region viewed from SDO and the limb of the observer (STEREO-A or STEREO-B) by simply assuming that the eruptions are radial. Table 1 lists the parameters characterizing CME kinematics for all 60 CME events.

We also analyze flare signatures in CME source regions to infer the rate of magnetic reconnection using SDO observations. Magnetic reconnection occurring in the corona forms flare loops and releases energy in these loops; accelerated particles or thermal conduction travel along newly reconnected field lines (flare loops) and deposit energy at their footpoints in the chromosphere, causing the brightenings there and thus forming the flare ribbons in optical and ultraviolet wavelengths (Forbes & Priest 1984; Poletto & Kopp 1986; Longcope & Klimchuk 2015). Therefore, magnetic reconnection, which occurs in the corona yet can be hardly measured there, is mapped in the lower atmosphere by flare radiation, and the reconnection rate is measured by summing up photospheric magnetic fluxes covered by spreading flare ribbons. This method has been widely used to measure the magnetic reconnection rate (e.g., Isobe et al. 2002; Qiu et al. 2002, 2004; 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 the 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 footpoints 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 a threshold is chosen to be above the mean intensity of the AR 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 the 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 Φ_r 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 (Figure 1(e)) sweeping through the magnetic fields is given in Figure 1(f), where the colors indicate the flux reconnected in different time intervals (see color bar). Among the 60 CME-flare events in our database, we analyze flare ribbon evolution and measure the reconnection fluxes using the 1600 (304) Å passband in 26 (16) events, respectively, while in the remaining 18 events of weak flares reconnection flux is not measured, because contamination of emissions by erupting filaments or post-flare loops is difficult to separate from flare ribbon emissions. For the 42 flares, the measured total reconnection flux Φ_r is in the range of 1.5 × 10²⁰–5.5 × 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 important properties, i.e., the length of the ribbons along the interface of the positive and negative magnetic polarities (polarity inversion line [PIL]), L_R, and the average distance of the flare ribbons to the PIL, D. The same example of SOL2012-07-12T16:53 is displayed in Figure 3. The ribbon pixels in the positive and negative polarities are perpendicularly projected to the PIL, respectively, thus giving the corresponding lengths along the PIL, L₊ and L₋. The ribbon length is the average of L₊ and L₋, i.e., L_R = (L₊+L₋)/2. The average perpendicular distance of the ribbon pixels to the PIL is the ribbon distance D. For this flare, L_R and D have values of 103 and 23 Mm, respectively. Measurements of these geometric properties are used to estimate energetics in the reconnecting current sheet (CS) in the corona (Section 5).

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The selected 60 CME-flare events were observed from 2010 August to 2013 December, 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. Figure 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 the MSU website.⁸

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With these plots, we study the initial height of the CMEs and for how far CMEs are accelerated. Histograms of the deprojected heights of the CME fronts are given in Figures 5(a)–(c). The initial heights of the CME fronts (${h}_{00}\equiv {h}_{0}/\cos \theta$) primarily range from 0.4 to 1.0 R_⊙ above the solar surface, with a median value of 0.6 R_⊙ (Figure 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 (h_{max_acc}) between 0.5 and 1.9 R_⊙, with a median value of 1.0 R_⊙ (Figure 5(b)). The distance between the two heights of h₀₀ and h_{max_acc} ranges from 0.15 to 1.2 R_⊙, with a median value of 0.4 R_⊙ (Figure 5(c)). The red curves in Figure 5 are events originating from ARs (see Table 1), which exhibit very similar height (distance) distributions.

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The distributions of the acceleration properties from the fitted curves (Figure 4(c)) are shown in Figures 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 lognormal distributions (Figures 5(d) and (e)), similar to Bein et al. (2011). The peak acceleration a_pk and duration of the acceleration τ_a are anticorrelated with a Pearson correlation coefficient R = −0.91, and their relationship can be described by a power law ${a}_{{pk}}={10}^{4.3}{\tau }_{a}^{-1.2}$ (Figure 5(f)). These results are consistent with previous studies (Zhang & Dere 2006; Vršnak et al. 2007; Bein et al. 2011).

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 cycles 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 properties of CME kinematics, illustrated in Figure 5, do not depend on the phase of the solar cycle.

Out of the 60 CMEs, 42 have reconnection properties unambiguously measured using flare ribbon signatures. Figures 6(a) and (b) display the histograms of the mean perpendicular distance D from the ribbon to the PIL and the mean flare ribbon length L_R 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 L_R are similar between AR and QS, both centering at around 80 Mm. Interestingly, when comparing D with the CME initial heights h₀₀ (Figure 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 altitude 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.

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Using flare radiation signatures and magnetograms, we have measured reconnection flux and reconnection rate. The peak reconnection rate (${\dot{{\rm{\Phi }}}}_{{pk}}$) spans over two orders of magnitude, from 6 × 10¹⁶ to 6 × 10¹⁸ Mx s⁻¹. In Figure 7(a), we compare ${\dot{{\rm{\Phi }}}}_{{pk}}$ with the peak CME acceleration (a_pk). 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 ${\dot{{\rm{\Phi }}}}_{{pk}}$ and a_pk is 0.75, and the ${\dot{{\rm{\Phi }}}}_{{pk}}$–a_pk relation can be well fitted to a power law ${a}_{{pk}}={10}^{2.78}{{\dot{{\rm{\Phi }}}}_{{pk}}}^{0.56}$, with ${\dot{{\rm{\Phi }}}}_{{pk}}$ in units of 10¹⁸ 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.

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Previous studies have shown that the maximum velocities v_max of fast CMEs are positively correlated with the total reconnection flux Φ_r (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 Figure 7(b). We notice that, for the relatively fast CMEs with v_max ≳ 600 km s⁻¹ (Howard et al. 1985; Gopalswamy et al. 2000), their maximum velocity v_max is positively correlated with the total reconnection flux Φ_r, similar to previous findings. Here v_max can be linearly scaled with the reconnection flux (R = 0.75) with v_max = 0.86Φ_r + 0.73, where v_max has units of 10³ km s⁻¹ and Φ_r has units of 10²² 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 reconnection 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 significant 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.

Figure 2 suggests that, on the timescale of a few minutes dictated by the observing cadence of CMEs, the CME acceleration a(t) and flare reconnection rate ${\dot{{\rm{\Phi }}}}_{r}(t)$ 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 ${\dot{{\rm{\Phi }}}}_{r}(t)$. The analysis yields the time lag of CME acceleration with respect to flare reconnection ${\rm{\Delta }}\tau \equiv {t}_{a}-{t}_{r}$ and the maximum correlation coefficient R_{max_a_r} between a(t) and ${\dot{{\rm{\Phi }}}}_{r}(t)$ at Δτ. Figure 8 presents these results for the 42 events with reconnection flux measurements. R_{max_a_r} lies within 0.68–0.99 and peaks at ∼0.9, revealing a strong correlation between a(t) and ${\dot{{\rm{\Phi }}}}_{r}(t)$.

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Meanwhile, the measured time lag Δτ in Figure 8(b) ranges between −20 and 20 minutes and appears to form three groups roughly centered at −10, 0, and 10 minutes. Since 5 minutes is the synoptic cadence of the EUVI and COR1 observations, we consider that CME acceleration leads flare reconnection for 11 events with Δτ < −5 minutes, flare reconnection and CME acceleration are simultaneous for 19 events with −5 ≤ Δτ ≤ 5 minutes, and flare reconnection leads CME acceleration for the remaining 12 events of Δτ > 5 minutes. The median and standard deviation of Δτ of these three groups are −10 ± 2.9, 1.2 ± 2.6, and 10 ± 2.8 minutes, respectively, consistent with the histogram in Figure 8(b). The corresponding widths of the three peaks at ∼5–6 minutes are less than the 10-minute separation between adjacent peaks, suggesting the robustness of the finding.

Examples of the three groups in Figure 8(b) are given in Figure 9. (I) Among the first group of 11 events, the C8.7 flare of SOL2011-06-21T03:27 (Figure 9(a)) corresponds to one of the strongest flares in this group. For this eruption, the CME appears to accelerate ∼12 minutes ahead of the reconnection rate. A similar event can be found in Song et al. (2018). (II) SOL2010-08-01T08:56 (Figure 9(b)) is an example among the 19 events where the a(t) evolve simultaneously with ${\dot{{\rm{\Phi }}}}_{r}(t)$. (III) SOL2011-12-26T20:31 (Figure 9(c)) belongs to the third group. In this event, the acceleration profile falls behind the reconnection rate by around 12 minutes.

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As we compare the properties of magnetic reconnection and CME kinematics among these three groups, we find that all acceleration-led 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 at ∼0.4 × 10¹⁸ Mx s⁻¹, more than twice that of the acceleration-led events. We find no significant differences among the three populations, in other properties, such as the CME initial height.

The time derivative of the GOES SXR profile has often been 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, $\dot{{X}_{r}}(t)$, and the reconnection rate, ${\dot{{\rm{\Phi }}}}_{r}(t)$, and CME acceleration, a(t) (Figure 10).

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The relationship of $\dot{{X}_{r}}(t)$ and ${\dot{{\rm{\Phi }}}}_{r}(t)$ is shown in Figures 10(a) and (b). Only 22 of the 42 events exhibit correlation R_{max_Xd_r} greater than 0.6 (Figure 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 t_Xd − t_r suggests delays of $\dot{{X}_{r}}(t)$ with respect to ${\dot{{\rm{\Phi }}}}_{r}(t)$ by 1–5 minutes with an average of 2.9 minutes (Figure 10(b)).

Similarly, Figures 10(c) and (d) give the relationship of a(t) to $\dot{{X}_{r}}(t)$. The same 22 events exhibit a good correlation (${R}_{\max \_a\_{Xd}}\gt 0.6$). But the distribution (Figure 10(c)) appears to be flatter than the previous two (Figures 8(a) and 10(a)) and gives poorer correlation. Again, among the 22 events, the distribution of their time difference ${t}_{a}-{t}_{{Xd}}$ (Figure 10(d)) still displays three peaks, though shifted by about 3 minutes, due to the delay of $\dot{{X}_{r}}(t)$ in Figure 10(b).

There are several reasons for the overall poor correlation using the time derivative of the GOES SXR light curve $\dot{{X}_{r}}(t)$. After the peak SXR emission, $\dot{{X}_{r}}(t)$ 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 Figures 2 and 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.

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 ${t}_{a\_{st}}$ or that of flare reconnection rate ${t}_{r\_{st}}$ 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 minutes, similar to the time cadence of the CME observation. Figure 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 ${\rm{\Delta }}{\tau }_{{st}}\equiv {t}_{a\_{st}}-{t}_{r\_{st}}$ are primarily within ±25 minutes and have a median value of −1.7 minutes. The number of events for Δτ_st < −5 minutes, $| {\rm{\Delta }}{\tau }_{{st}}| \leqslant 5\,\,\mathrm{minutes}$, and Δτ_st > 5 minutes is 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).

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Figure 11(b) displays a scatter plot of Δτ_st with respect to the magnitude of GOES X-ray in 1–8 Å for 35 out of the 42 events (the remaining 7 events are not included owing to the presence of simultaneous strong emission from other regions or unavailability of GOES data). The scatter plot can also be divided into three groups. For 13 events with $| {\rm{\Delta }}{\tau }_{{st}}| \leqslant 5\,\,\mathrm{minutes}$, 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 nine events with earlier flare reconnection (Δτ_st > 5 minutes) 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 remaining 13 events where CME acceleration begins earlier than flare reconnection (Δτ_st < −5 minutes), the amount of time lag $| {\rm{\Delta }}{\tau }_{{st}}|$ is roughly anticorrelated with the flare SXR peak flux, i.e., shorter time differences for stronger flares. The 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 minutes apart (Figure 8(b)). The distribution of the difference in the start times is slightly asymmetric (Figure 11(a)), with a few more events in which CME acceleration rises earlier than the flare reconnection. In both cases, we find that acceleration-led events are associated with lower reconnection rates.

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 evolution, 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 amount of work done by the reconnection electric field in the CS. Our major findings are summarized as follows:

• 1.  
  A strong correlation (${R}_{\max \_a\_r}\gtrsim 0.7$) exists between the CME acceleration and the reconnection rate (Figure 8(a)), regardless of whether CMEs are fast or slow. The CME peak acceleration shows a power-law scaling with the peak reconnection rate (Figure 7(a)). A positive correlation is also found between the maximum speed of CMEs and the total reconnection flux (Figure 7(b)), but only in relatively fast CMEs (v_max ≳ 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 profiles from rise to decay, and the temporal correlation between the two is much stronger than the correlation between either of them and the time derivative of the GOES SXR light curve. For the studied 42 events, the distribution of the time lag of the CME acceleration with respect to the reconnection rate (${\rm{\Delta }}\tau \equiv {t}_{a}-{t}_{r}$) displays a symmetric distribution with three peaks at −10.0 ± 2.9 minutes (11 events), 1.2 ± 2.6 minutes (19), and 10.0 ± 2.8 minutes (12), respectively (Figure 8(b)). For a comparison, the distribution of the time lag of their start times (${\rm{\Delta }}{\tau }_{{st}}\equiv {t}_{a\_{st}}-{t}_{r\_{st}}$) is slightly asymmetric (Figure 11(a)), with a few more events where acceleration begins earlier than the flare reconnection. On average, the peak reconnection rate of the acceleration-led population is smaller than that of the other two populations.
• 3.  
  The CME total mechanical energy E_cme displays a good correlation (R ∼ 0.6) with the estimated work W_r done by the reconnection electric field in the CS. E_cme−W_r can be fitted to a power-law function with the power-law index of ∼1/3 (Figure 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; Pal et al. 2018; Tschernitz 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 a_pk–τ_a scaling indicates that, statistically speaking, an event with smaller peak acceleration (and also a smaller peak reconnection rate) tends to be accelerated for a 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.

Our analysis reveals a good correlation between the CME mechanical energy and the estimated electrodynamic work W_r done by the reconnection electric field in the CS, especially for the relatively fast CMEs (Figure 13). For events with W_r ≳ 2 × 10²⁴ J (X and M flares; Figure 13(e)), W_r is larger than or comparable to E_cme 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, E_cme is 1–2 orders of magnitude larger than W_r. This large ratio of ${E}_{\mathrm{cme}}/{W}_{r}$ 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 either are undetectable by current instrumentation or require different analysis methodologies (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 E_cme–W_r scaling (Figure 13) may also shed light on the increased association rate between CMEs and flare 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 CS(s) can either be 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 W_r ≳ E_cme, 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 energies, the CME energy, flare energy, and free magnetic energy including W_r will be conducted in future studies.

Our unique data set 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 Figure 9). Our analysis reveals the presence of all three populations, namely, the acceleration-led, the simultaneous, and the reconnection-led events, and adjacent populations are separated by about 10 minutes.

These results may be discussed with respect to some eruption models. For example, in the framework of a 2D 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 either 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-led 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-led 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 (Figure 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 (Figure 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 minutes) of CME observations. To probe the "trigger" of the eruption in the future study, it is crucial to explore new methods, identify 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).