Observations of Turbulent Magnetic Reconnection Within a Solar Current Sheet

Magnetic reconnection is a fundamental physical process in various astrophysical, space, and laboratory environments. Many pieces of evidence for magnetic reconnection have been uncovered. However, its specific processes that could be fragmented and turbulent have been short of direct observational evidence. Here, we present observations of a super-hot current sheet during SOL2017-09-10T X8.2-class solar flare that display the fragmented and turbulent nature of magnetic reconnection. As bilateral plasmas converge toward the current sheet, significant plasma heating and non-thermal motions are detected therein. Two oppositely directed outflow jets are intermittently expelled out of the fragmenting current sheet, whose intensity shows a power-law distribution in spatial frequency domain. The intensity and velocity of the sunward outflow jets also display a power-law distribution in temporal frequency domain. The length-to-width ratio of the current sheet is estimated to be larger than theoretical threshold of and thus ensures occurrence of tearing mode instability. The observations therefore suggest fragmented and turbulent magnetic reconnection occurring in the long stretching current sheet.


INTRODUCTION
Magnetic reconnection, referring to dissipation and connectivity change of magnetic field, is capable of powering plasma heating, plasma motions, and particle acceleration in relativistic jets (Bloom et al. 2011), accretion disks (Balbus & Hawley 1998), solar and stellar flares (Sturrock 1966), and magnetospheres (Phan et al. 2006). In the past decades, abundant evidence for magnetic reconnection has been disclosed including in situ measurements near the Earth and remote sensing observations such as cusp-shaped flare loops (Masuda et al. 1994), inflows and downflows near the reconnection region (Yokoyama et al. 2001;Savage & McKenzie 2011;Takasao et al. 2012;Liu et al. 2013;Liu 2013;Xue et al. 2016), double hard X-ray coronal sources (Sui & Holman 2003), and changes of connectivity of coronal loops (Su et al. 2013;Yang et al. 2015;Li et al. 2016).
Unfortunately, the specific processes involved in magnetic reconnection, in particular what occur in the reconnection region, remain mysterious. Theoretically, magnetic reconnection is believed to take place in a localised region, i.e., the so-called current sheet, that has enhanced resistivity (Priest 2014;Yamada et al. 2010). In the Sweet-Parker model, the current sheet is limited to a long and thin region, in which the reconnection proceeds steadily but too slowly to interpret the real energy release rate. Through invoking slow-mode shocks extending from a shortened Sweet-Parker current sheet, the Petschek model is able to significantly boost the reconnection rate (Petschek 1964). Nevertheless, the current sheet width in the Petschek model is of ion inertial Electronic address: xincheng@nju.edu.cn scale, which can hardly match the detectable width in observations. Therefore, it was proposed that the current sheet can be fragmented into many magnetic islands by tearing mode instability (Furth et al. 1963;Shibata & Tanuma 2001) and develops turbulence to achieve the fast reconnection (Lazarian & Vishniac 1999). However, such a picture has been short of direct observational evidence although documented by numerical simulations (Kowal et al. 2009;Shen et al. 2011;Bárta et al. 2011) and indicated by various indirect observations such as simultaneous intermittent plasmoid ejections and hard X-ray/radio bursts (Asai et al. 2004;Nishizuka et al. 2009;Takasao et al. 2016), vortex above flare arcades (McKenzie 2013;Scott et al. 2016), and complex transition region line profiles with bright cores and broad wings (Innes et al. 2015).
In this study, we present a detailed analysis of a limb solar eruption on 2017 September 10 that produced an X8.2-class flare (SOL2017-09-10T16:06UT 1 ) and a fast coronal mass ejection (CME). In particular, the presence of a thin and long hot plasma sheet underneath an erupting CME fits perfectly into the current sheet structure, as predicted in the theoretical model (Lin & Forbes 2000), and the dynamic behaviours of the plasma within and around the current sheet provide direct and solid evidence of a turbulent and intermittent nature of magnetic reconnection.

INSTRUMENTS
The data sets are primarily from Solar Dynamics Observatory (SDO; Pesnell et al. 2012). The Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board SDO images the solar corona with a spatial resolution of 0.6 arcsec per pixel and cadence of 12 seconds at 7 Extreme Ultraviolet (EUV) passbands. Here, we used the AIA data with a cadence of 24 seconds that have the normal exposure time. The data with a very short exposure time, in particular during the flare, usually have large uncertainties in intensity that can influence the differential emission measure (DEM) calculations and Fast Fourier Transform (FFT) analyses. The X-Ray Telescope (XRT; Golub et al. 2007) and EUV Imaging Spectrometer (EIS; Culhane et al. 2007) on board Hinode (Kosugi et al. 2007) provide the X-ray images and EUV spectra in the wavelength ranges of 170-210Å (short) and 250-290Å (long) with a spectral resolution of 0.0223Å pixel −1 , respectively. The Geostationary Operational Environmental Satellite (GOES) records the soft X-ray 1-8Å flux from the flare. In addition, the K-Cor instrument installed at the Mauna Loa Solar Observatory 2 and the Large Angle and Spectrometric Coronagraph (LASCO; Brueckner et al. 1995) on board the Solar and Heliospheric Observatory (SOHO) observe the white-light images of the CME and its trailing current sheet.

Hot Flux Rope and Induced Super-hot Current
Sheet The early phase of the flare/CME eruption was fully captured by the AIA. At ∼15:35 UT, a filament is activated to rise up. After ∼15 min, it initiates the eruption of a nearby loop-like structure. Shortly afterwards, 2 https://www2.hao.ucar.edu/mlso/mlso-home-page the loop-like structure quickly expands and escapes away from the solar surface. Simultaneously, the overlying field constraining the loop-like structure is stretched outwards. At ∼15:53 UT, the loop-like structure ascends to a height of 90 Mm and appears as a well defined bubble consisting of a ring-shaped envelop and a low emission cavity, both of which are visible at most EUV and X-ray passbands (top panel of Figure 1a). An elongated bright structure connecting the bottom of the bubble and the top of the flare loops is observed. These features basically conform to the classic picture of eruptive flares (Sturrock 1966;Shibata et al. 1995;Chen 2011), in which the eruption of a twisted magnetic flux rope leaves behind a long and narrow current sheet (Lin & Forbes 2000). The bubble is most likely an edge-on manifestation of the forming flux rope as its axis is mostly along the line-of-sight (Cheng et al. 2011). The differential emission measure (DEM) analyses show that the cavity of the bubble has a low emission measure (EM∼10 26 cm −5 ), though the temperature is relatively high (∼10 MK). By contrast, the bubble envelope (or the ring) and the current sheet have a much higher emission measure (∼10 27.5 cm −5 ) and an even higher temperature (∼13 MK). Such a temperature structure highly resembles the numerical results of the erupting flux rope energised by the reconnection in its trailing current sheet (Mei et al. 2012).
As the bubble escapes from the lower corona, the current sheet is further heated and extended. Its lower end ascends to a height of at least ∼100 Mm around the flare peak time of ∼16:15 UT (Figure 1b). The EM maps at different temperatures document that the extended current sheet mainly contains high temperature plasma (Figure 1b), which is also confirmed by the EIS  Fe XXIV 192.03 and 255.11Å lines (with the formation temperature of ∼18 MK). The plasma therein is primarily distributed near the temperature of 20 MK with the total EM of 1-5×10 27 cm −5 (Figure 1c), which is similar to the temperature of supra-arcade downflows that are frequently observed when the current sheet is observed face-on (Hanneman & Reeves 2014). The corresponding density is calculated to be ∼0.6-1.3×10 9 cm −3 assuming a depth of 30 Mm (the size of the bubble) at the height of ∼100-200 Mm. Based on the distribution of the total EM along the direction perpendicular to the current sheet, the average width of the current sheet is estimated to be ∼10 Mm at the height of ∼150 Mm (Figure 1c), slightly larger than the width estimated by Savage et al. (2010).

Fragmented and Turbulent Current Sheet
The EUV 171Å observations disclose that the cool plasma (∼1 MK) on both sides converges into the current sheet (Figure 2a). Shortly afterwards, the plasma is strikingly heated and becomes visible in the AIA higher temperature passbands such as 193Å and 131Å (10-20 MK). The average velocity of the converging motion is ∼100 km s −1 in the early phase (15:55-16:00 UT) and subsequently decreases to ∼20 km s −1 , similar to previous estimations Zhu et al. 2016;Li et al. 2017;Wang et al. 2017). The initial and faster inflows are possibly driven by the restoring force of the magnetic field, which was pushed aside by the erupting bubble before ∼15:54 UT. Besides the plasma heating, the Fe XXIV 192.03Å line also displays a significant non-thermal broadening in the current sheet. The line width implies a non-thermal velocity of ∼100-150 km s −1 after subtracting the thermal velocity corresponding to a formation temperature of 18 MK (Figure 2b and 2c). Such large non-thermal velocity strongly indicates the existence of turbulent motions in the current sheet (also see Ciaravella & Raymond 2008;Doschek et al. 2014;Warren et al. 2018). It is also supported by the fact that the 193Å intensity variation along the current sheet presents a fluctuation, which shows a power-law distribution in spatial frequency domain after Fast Fourier Transform (FFT) (Figure 3d and 3e). The spectral index is estimated to be -1.16±0.22 (Figure 3f).
The turbulent current sheet indicates that the sunward reconnection outflow jets, probably corresponding to magnetic islands expelled from the lower end of the current sheet, will show a power-law behaviour. Figure  3a and attached movie clearly show that the jets are intermittently shot out during the reconnection process. Each jet has an "Eiffel Tower" shape initially. Within a period of 2-5 min, probably driven by magnetic tension (Forbes & Acton 1996;Priest & Forbes 2002), each jet gradually becomes to be cusp-shaped, and then continuously shrinks to a flare loop. The 193Å intensities in the outflow regions also present intermittent fluctuations (Figure 3b and 3c). The FFT analysis shows that the temporal variation of the intensity (e.g., along the dashed line in Figure 3b) does obey the power law distribution with a spectral index around -1.60 (Figure 3d), very close to the spectral index of the turbulent current sheet (e.g., Bárta et al. 2011;Shen et al. 2011). It confirms our conjecture that the current sheet has been fragmented into different scaled structures, strongly suggestive of the existence of turbulence, with which the outflow jets are widely distributed in energies and sizes. Further evidence for a fragmented and turbulent reconnection is that the intensity variations at the other flaring regions also present the power law distribution with spectral indices ranging from -1.2 to -1.8, quite different from that in the quiescent and pre-flare regions (see Figure 11-15 in Appendix). It is worthy of noticing that supra-arcade downflows may directly correspond to the sunward outflow jets (McKenzie 2000;Savage & McKenzie 2011;Reeves et al. 2015) or be structures caused by Rayleigh Taylor instabilities in the outflow region (Guo et al. 2014).
We find that the velocity of the sunward outflow jets also presents a dispersed distribution. The heights of the jets are measured through manually tracking their trajectories (as shown by Figure 16 in Appendix). Almost all outflow jets have a large initial velocity but quickly slow down ( Figure 3e). The initial velocities are diversely distributed, ranging from 100 to 800 km s −1 (Figure 3f and Figure 16), even in a short time period (16:00-16:30 UT), similar to previous estimations (Savage & McKenzie 2011). Interestingly, the FFT analysis indicates that the initial velocities also have a power law spectrum with a spectral index of -0.35 (Figure 3g). It implies that the reconnection that drives the outflow jets proceeds with a varying reconnection rate, proba-bly modulated by turbulence. Taking an average value (20 km s −1 ) of the inflow velocities near the flare peak time (16:00-16:15 UT), the reconnection rate (the ratio of the inflow velocity to the outflow velocity) is estimated to range from 0.003 to 0.2. If the current sheet is fragmented into magnetic islands of different sizes (Shibata & Tanuma 2001), different reconnection rates and thus different kinetic energies of the outflow jets can be achieved. Moreover, the decelerations also have a wide distribution with its maximum up to 2000 m s −2 (Figure 16), indicating that the upward magnetic pressure gradient force also varies with time that resists the downward magnetic tension and the Sun's gravity.

Largely Extended White-light Current Sheet
The K-Cor instrument of the Mauna Loa Solar Observatory provides the white-light images of the largely extended current sheet at its later phase. At 17:12 UT, the lower end of the current sheet is seen to joint the tip of the cusp-shaped flare loops and is located at a height of ∼140 Mm (Figure 4a), similar to the value measured in the EUV data. The apparent width of the current sheet is ∼25 Mm, and the lower limit of the apparent length is 400 Mm (Figure 4b). It corresponds to a maximal reconnection rate of ∼0.06, which, similar to the previous estimations (Savage et al. 2010;Ling et al. 2014;Seaton et al. 2017), is still smaller than the maximum value derived above. In fact, the original current sheet could be fragmented into magnetic islands due to tearing mode instability. Then, the real length of magnetic islands involved in each elementary reconnection process could be much smaller. This is proved by the fact that the lengthto-width ratio (>16) of the current sheet is much larger than the theoretical threshold of tearing mode instability (2π) (Furth et al. 1963). The high-speed anti-sunward moving blobs also provide strong evidence for existence of magnetic islands. Figure 4c shows that the blobs are intermittently formed in the current sheet at the height of ∼200 Mm. The initial velocities are ∼400 km s −1 and then gradually increase. Note that, the width of the current sheet derived in the K corona is about 2.5 times larger than that in the EUV passbands. However, both are still much smaller than the values measured previously in the LASCO/C2 white-light coronagraph (∼100 Mm at 2 R (Lin et al. 2005(Lin et al. , 2009(Lin et al. , 2015Ciaravella & Raymond 2008)). Interestingly, the EUV current sheet is found to be located in the middle of the white-light sheet, implying that the former is closer to the dissipation layer and thus has a higher temperature. Theoretically, the width of the diffusion layer is only tens of km for Petschek-type magnetic reconnection with an anomalous resistivity. However, in observations, the apparent width of the current sheet can be seriously widened by turbulence, as well as slow-mode shock compression and projection effects (Ciaravella & Raymond 2008;Lin et al. 2015).

SUMMARY AND DISCUSSIONS
In the models of flux-rope-induced CME/flare eruptions (Shibata et al. 1995;Chen 2011), a pre-existing flux rope escapes away from the solar surface due to loss of equilibrium (Lin & Forbes 2000), leading to the formation of a CME and a flare at almost the same time (Zhang et al. 2001;Cheng et al. 2011). Magnetic reconnection acts as strong coupling between the CME and the flare as indicated by the simultaneity between the evolution of the CME velocity and the variation of the flare emission (Zhang et al. 2001). The linear bright feature in the wake of the erupting flux rope has been argued to be the induced current sheet, where electric current is enhanced and magnetic field is dissipated (Lin et al. 2015). Previous observations of the current sheet are mostly limited by the wavelength window that only responds to relatively narrow and low temperatures and/or the field of view that is not large enough (Lin et al. 2005(Lin et al. , 2009Ciaravella et al. 2003;Ciaravella & Raymond 2008;Savage et al. 2010;Ling et al. 2014;Seaton et al. 2017). Therefore, studies based on these observations are mostly speculative in particular on the origin of the current sheet and its relation to the CME and flare. Moreover, the observations in those works could not provide further information on the detailed physical processes occurring in the current sheet, therefore it has seldom been addressed what kind of reconnection it is.
In this study, we present a solar limb eruption event, which displays a distinct picture of the CME/flare eruption with unprecedented clarity. Observations with a continuous field of view from 1 to 30 R and multiwavelengths including the white-light, EUV, and X-rays enable us to reveal the origin of and specific processes involved in magnetic reconnection. We successfully detect almost all ingredients predicted by models during a single eruption including the erupting hot flux rope, super-hot current sheet, cusp-shaped flare loops, inflows, and high-speed sunward and anti-sunward outflow jets, some of which have been detected in previous observations (Savage et al. 2010;Ling et al. 2014;Seaton et al. 2017;Yan et al. 2018;Liu et al. 2018). The high temperature of the flux rope envelope and the cusp-shaped flare loops probably originates from the collision of the outflow jets with the local dense plasma and/or the direct heating by slow-mode shocks at both ends of the current sheet ). The high temperature of the cur-rent sheet, however, requires a local heating by magnetic energy dissipation inside the current sheet itself.
The turbulent behaviour of energy release in the current sheet is also revealed. A high Lundquist number, suggested by a large length-to-width ratio (>16) of the current sheet, leads to the generation of magnetic islands due to tearing mode instability (Furth et al. 1963), which subsequently appear as intermittent sunward outflow jets and anti-sunward moving blobs when shot out of the current sheet. Simultaneously, the turbulence develops in the current sheet (Strauss 1988;Lazarian & Vishniac 1999). On the one hand, its effect helps achieve anomalous resistivity to boost magnetic dissipation rate. On the other hand, it may mediate the formation of magnetic islands with their size and energy presenting a power law distribution. This process finally makes the intensity and velocity of the sunward outflow jets exhibit a power law distribution. In particular, the spectral index of the former is found to vary from -1.2 to -1.8, which suggests that the turbulence mediate the reconnection process in the current sheet, resulting the formation of different scaled magnetic islands, consistent with previous numerical results (Kowal et al. 2009;Shen et al. 2011;Bárta et al. 2011). The deviation from the fully developed isotropic turbulence (with a Kolmogorov turbulence spectral index of -5/3) may be due to the role of magnetic field. The significant non-thermal motions shown in the Fe XXIV line also evidence the existence of turbulence. In summary, these observations show that the magnetic reconnection, at least in solar eruptions, does not proceed uniformly in space and time. Instead, the current sheet should be composed of fragmented structures, in which magnetic reconnection dissipates magnetic energy in a turbulent way (Kontar et al. 2017) to heat the plasma and drive the outflow jets.
We are cordially grateful to five anonymous referees for their very meaningful comments and suggestions. We also thank Jun Lin, Zongjun Figure  1c. The red line is the best-fitting of the EM distribution derived by "xrt¯dem¯iterative2.pro". The gray dashed lines represent 100 MC solutions. The EM is calculated by Equation (2) in each temperature bin.
(2004) and later modified by Cheng et al. (2012), is used for reconstructing the DEM. The inputs are observed intensity I i and the temperature response function R i (T ) of the passband i. I i is written as: where DEM denotes the plasma DEM, and δI i is the uncertainty in the intensity I i . The temperature range for doing the inversion is set as 5.5≤ logT ≤ 8.0. The EM is calculated as: where the temperature range of integration is set to be 7.0≤ logT ≤ 7.5. We performed 100 Monte Carlo (MC) solutions through adding a random noise (within the errors of observed intensities) to the intensity I i and then rerunning the routine. The results show that 100 MC solutions are converged in the range of 7.0≤ logT ≤ 7.5 ( Figure 5). The density n in the current sheet is obtained by: where l is the depth of the current sheet. We also take advantage of other two inversion methods independently developed by Hannah & Kontar (2012) and Cheung et al. (2015), respectively. It is found that, the three methods give very similar results. The erupting bubble, in particular its envelope, primarily contains high temperature plasma (Figure 6), while the background and foreground contribute some cool plasma emission. As for the current sheet, the results from the different methods are also consistent with each other, which all present a super-hot ingredient and absence of cool plasma in the current sheet (Figure 7). It is noticed that some discrepancies also exist. The code "xrt¯dem¯iterative2.pro" is able to reconstruct the superhot current sheet with a pretty good clarity. However, in the region outside of the current sheet, it may overestimate the DEM values compared with the other two codes. Nevertheless, we do not think that it influences our results, at least qualitatively. The results are also consistent with Warren et al. (2018)    inversion via the combination of AIA and EIS data and also found that the plasma in the current sheet has temperatures of about 20 MK and distributes in a relatively narrow temperature range. The uncertainties in the DEM results come mainly from the uncertainties in the observed intensities, which are obtained by the routine "aia¯bp¯estimate¯error.pro" in SSW. The uncertainties of the intensities are a result of the uncertainties in the temperature response functions of AIA including non-ionization equilibrium effects (Imada et al. 2011), non-thermal populations of electrons, modifications of dielectronic recombination rates (Summers 1974;Badnell et al. 2003), radiative transfer effects (Judge 2010), and even unknown filling factor. After considering these effects, an uncertainty lower limit of ∼20% for R i (T ) is derived (Judge 2010) and thus can not significantly influence the results (Cheng et al. 2012).
Spectroscopic Analyses: The EIS data are processed via the routine eis prep.pro in the standard EIS software package with corrections for dark current, hot pixels, and cosmic ray hits. It observed the flaring region near the west limb for a period starting before 15:35 UT (flare onset) through 16:53 UT that covers the rise and early decay phases of the flare. The 2 arcsec slit of EIS was used to scan over an area of 240 arcsec × 304 arcsec from west to east with a course step of 3 arcsec, yielding a spatial resolution of 3 arcsec × 1 arcsec. It took about 9 min in each run with an exposure time of 5 s at each step.
Here we used the Fe XXIV 192.03Å line with a formation temperature of 18 MK, in which the current sheet is most clearly visible. The Fe XXIV 192.03Å line is believed to be blended with the Fe XI 192.02Å line (∼1  MK), but the blending could be safely ignored in large flares that contain hot plasmas. This can be verified by checking the relative strength of another line Fe XII 192.39Å (∼1 MK) in the same spectral window, which is clearly separated from the Fe XXIV 192.03Å. Theoretically, the Fe XII 192.39Å line is stronger than the Fe XI 192.02Å line. Therefore, when the emission at 192.02/192.03Å is greater than that at Fe XII 192.39Å, it should be mostly from the hot Fe XXIV 192.03Å line. We examine all of the line profiles around the current sheet region and conclude that the emission is mainly contributed by the Fe XXIV 192.03Å line (also see Warren et al. 2018;Li et al. 2018). In addition, we note that the Fe XXIV 192.03Å line is saturated in some regions (mostly in flare loops) but not in the current sheet region under study. So we just discard those saturated line profiles in our study.
The spectra of some other lines, for example, Fe XXIV 255.11Å (∼18 MK), Fe XXIII 263.76Å (∼14 MK), Fe XXII 253.17Å (∼12 MK), Fe XVI 262.98Å (∼3 MK), and Fe XV 284.16Å (∼2 MK) are also presented ( Figure  8). It is seen that the current sheet is only visible in the high temperature (>12 MK) lines, in particular in Fe XXIV 192.03Å, which is consistent with the AIA imaging observations. The Fe XXIV 192.03Å line profiles show a good Gaussian shape, and we implement a single Gaussian fitting to obtain the non-thermal velocity by the formula where W is the full width at half maximum of the spectral line, λ is the line wavelength, c is the speed of light, k is the Boltzmann constant, T i is the ion temperature, and M is the ion mass. The instrumental width of EIS (2.5 pixels, or 0.056Å) is also subtracted. Here we adopt a fixed thermal temperature of T i = T max = 18 MK. For comparison, we also use a DEM-weighted average temperature which is place-dependent to derive ξ and find that the results are quite similar. The values are also consistent with that independently derived by Warren et al. (2018). Please see Li et al. (2018) for some selected Fe XXIV 192.03Å line profiles and resulting fitting results. Fragmentation of the current sheet: The fragmentation of the current sheet is also examined at the different passbands and different times, as shown in Figure 9 and 10. It can be seen that the spatial variation of the 193Å and 131Å intensity (along the current sheet) presents a power-law behaviour in spatial frequency domain (0.1-1.0 Mm −1 ). The spectral index varies from -1.0 to -1.4. This type of fluctuation is also known as red "noise", which is an intrinsic property of a random physical process, most likely due to turbulence, that can be described by a power-law spectrum with a negative slope (Vaughan 2005;Inglis et al. 2015;Ning 2017). It indicates that the current sheet has been fragmented into different scaled structures, most likely correspond to magnetic islands of different sizes. As shown in Figure 9b and 10b, the AIA 193Å and 131Å intensity has been detrended with a moving average of 10 Mm in order to remove the feature of the intensity decrease as away from the flare region. We also test the different moving average values (5-20 Mm) and find that derived spec-tral index is not seriously influenced. It is also worthy of noticing that, for the detrended data, the power in the low spatial frequency (e.g., <0.1 Mm −1 ) can be artificially suppressed (Gruber et al. 2011), but which is not used here. Of course, as mentioned above, the AIA 193 A and 131Å intensity also include an uncertainty that mainly caused by non-linear effects of the AIA response function. The uncertainty may have somewhat effect on the spectral index .
Intermittency and velocity diversity of the outflow jets: We also inspect the power spectrum of the temporal variations of the AIA 193Å and 131Å intensity at many other locations. Figure 11 shows two slices that we used for creating the time-distance plots. We find that the temporal variations of the intensity at almost all locations do display a power law distribution with spectral index distributing in the range of -1.2 to -1.8 (e.g., Figure 12 and Figure 13). By contrast, for the quiescent regions and pre-flare regions, the spectrum is flat, which denotes white noise that is nearly frequency-independent and mainly originates from random signals (e.g., Figure  14 and Figure 15). Similar to the spatial frequency analysis, the non-linear effects of the AIA passbands also influence the spectral index in the temporal frequency analysis . Note that, the cadence of the AIA data is not exactly uniform, but which is found to be smaller than 0.05%. After a carefully testing, we find that whether the non-uniformity is corrected or not does not significantly influence the FFT results.
Using the time-distance plot of the AIA 193Å running difference images along the direction of the current sheet, we identified manually the trajectories of the sunward outflow jets, as shown in Figure 16a. The initial speed is derived as an average of the first three points of the measured outflow speeds. The histogram distributions of the initial velocities and accelerations of the jets are displayed in Figure 16b and 16c. One can clearly see that both of them have a wide distribution.
Height of the lower end and X-point of the current sheet: The heights of the CME bubble are measured in the AIA field of view. Applying the first order numerical derivative, the velocity as a function of time is derived ( Figure 17). One can see that the CME bubble experiences a slow rise phase of ∼10 min with an average speed of ∼70 km s −1 and a fast acceleration phase with an acceleration of ∼2200 m s −2 in the AIA field of view. The CME finally reaches a speed of over 3000 km s −1 when leaving the LASCO field of view 3 .
The lower end of the current sheet is estimated to be at the height of ∼100 Mm above the solar surface (∼1100 arcsecs) at 16:15 UT, where the outflow jets are expelled. One hour later (17:15 UT), the lower end is also seen by the white-light K coronagraph. The height is determined to be ∼140 Mm. Considering that the lower end of the current sheet has an ascending motion as the CME erupts, its height will increase by 54 Mm in one hour if assuming a velocity of 15 km s −1 (Mei et al. 2012). It roughly agrees with the difference between the heights derived in the EUV and white-light passbands at different instants.
The theoretical model of flux-rope-induced CME/flare (Lin & Forbes 2000;Mei et al. 2012) also predicts an   Figure 11. (b) and (c) The normalised 193Å intensity variations as a function of time at the two outflow regions indicated by S1 and S2 in panel a. It is also detrended with a moving average of 60 min in order to remove the feature of the decay reconnection process. (d) and (e) The power spectral densities of the intensities at S1 and S2 with the oblique lines indicating the power-law fitting to the range of 1-15 mHz.  X-shaped null point existing in the current sheet. Magnetic islands are expected to run away from the null point along two opposite directions, manifesting as sunward outflow jets and anti-sunward fast moving blobs (e.g., Song et al. 2012;Chae et al. 2017), respectively. The jets and blobs have initial heights of ∼100 Mm and ∼180 Mm, respectively. It indicates that the height of the Xshaped null point is in the range of 100-180 Mm. Uncertainty in the reconnection rate: The reconnection rate is calculated as the ratio of the inflow velocity to the outflow velocity. We consider that the initial speed of the outflow jets is equivalent to the outflow speed. The error of the initial speed is about 100 km s −1 . Thus, the uncertainty in the reconnection rate can be up to 50% when considering the initial velocities of 100 to 800 km s −1 in the time period of 16:00-16:30 UT. If taking an average outflow speed of ∼300 km s −1 and the inflow speed of 20 km s −1 , the average reconnection rate is about 0.07±0.03.
Uncertainty in the length of the current sheet:  We estimate the length of the current sheet based on the distributions of the brightness along the direction perpendicular to the current sheet (Figure 4a). Figure  4b shows that the brightness distributions at three slices have a similar profile with an FWHM being about 25 Mm. It is found that the FWHM is nearly uniform in between the two slices located at 840 Mm and 1240 Mm, respectively. Outside this region, the FWHM gets larger. Thus, the distance between the two slices is regarded as the length of the current sheet. Note that such a length is a lower limit. On the other hand, the LASCO observa-tions show that the current sheet may even extend to a height of 8 R at 17:12 UT, i.e., the edge of the C2 field of view where the blobs are still seen to move along the stretched bright structure by the erupting CME ( Figure  18). It corresponds to a length of 4900 Mm. Such a length can be regarded an upper limit for the length of the current sheet. If the width remains to be 25 Mm, the upper limit of the length-to-width ratio for the current sheet is ∼200. Whatever the case may be, the length-to width-ratio is much larger than the theoretical threshold for tearing mode instability (2π; Samtaney et al. 2009).