© The Authors 2023

1. Introduction

Solar eruptions, such as solar flares and coronal mass ejections (CMEs), are catastrophic energy-conversion phenomena that can cause severe space weather that impacts heavily on advanced technological systems in modern society. It is well established that the solar magnetic field plays a fundamental role in such eruptions (Forbes et al. 2006; Chen 2011; Shibata & Magara 2011; Cheng et al. 2017; Guo et al. 2017), and thus it is important to understand the pre-eruptive structure of the magnetic field for a reliable prediction of solar eruptions. In addition, solar eruption is believed to be a drastic release of the free energy stored in the complex, unstable magnetic field in the solar corona; thus, understanding the initiation mechanism of eruption is also crucial for a physics-based forecast of eruptions (Kusano et al. 2020).

A notable magnetic structure that holds the central position in the study of solar eruptions is the magnetic flux rope (MFR, Kuperus & Raadu 1974; Chen 1989; Titov & Démoulin 1999; Amari et al. 2014). A MFR refers to a coherent group of twisted magnetic flux winding around a central axis, and is believed to exist commonly in the corona, and in the whole heliosphere. It is of great interest to the study of eruption initiation owing to the two well-known ideal magnetohydrodynamics (MHD) instabilities of the MFR, namely the kink instability (KI, Hood & Priest 1981; Török et al. 2004, 2010; Török & Kliem 2005) and the torus instability (TI, Kliem & Török 2006), which can result in a sudden loss of equilibrium of a pre-eruption MFR and lead to eruptions. The twist degree of the MFR (denoted 𝒯, i.e., the winding number of magnetic field lines around the axis) and the decay index of the strapping field (n, quantifying the spatial decreasing speed of the overlying magnetic field) are controlling parameters of the KI and TI of MFR, respectively. Evolution of the photosphere slowly drives a MFR to the unstable regime when these control parameters exceed their critical values, and an eruption is triggered through these instabilities.

Since these ideal MHD models of solar eruptions are based on MFR, once there is evidence indicating the existence of MFR prior to an eruption, it is often considered that the eruption could be triggered by the MFR instabilities. Our recent survey of the major flares (above GOES M5.0) from 2011 to 2017 with coronal magnetic field extrapolations from vector magnetograms taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO, Pesnell et al. 2012) shows nearly 90% of the events possess pre-flare MFRs (Duan et al. 2019, 2021a), which indicates that the pre-existence of a MFR is rather common for major flares. Furthermore, by calculating the controlling parameters T_w and n for each of these events, it is found that many events have parameters exceeding their thresholds for triggering the MFR instabilities. However, over half of the MFR-possessing events cannot be explained fully by the MFR instabilities since for these events both of the parameters before flare are apparently below their thresholds for triggering the MFR instabilities.

In this paper we present a study of the first on-disk X-class flare of solar cycle 25, for which there is clear evidence of a pre-existing MFR, but it is not likely the MFR instabilities that triggered the eruption, as supported by both extrapolations of coronal magnetic field and analysis of time profile of the rising filament height. We further found that the pre-flare evolution of the current density shows progressive thinning of a vertical current layer on top of the flare PIL, which suggests that a vertical current sheet forms before the eruption as driven by the photospheric motions. This hints that the reconnection may have triggered the eruption. Study of the filament height evolution suggests that once triggered, the MFR immediately runs into the domain of TI and should be also driven by TI in addition to the flare reconnection.

2. Data and method

Data from the SDO are mainly used in this study. The Atmospheric Imaging Assembly (AIA, Lemen et al. 2012) on board the SDO provides seven extreme ultraviolet (EUV) filtergrams that cover the temperature from 10⁵ K to 10⁷ K, with a spatial resolution of 1.2 arcsec (i.e., two pixels) and a cadence of 12 s. The Hα data from the Global Oscillation Network Group (GONG) are also used to show the filament with a spatial resolution of 1 arcsec. In addition, the EUVI images from STEREO-A is used to determine the height of the filament around the eruption onset time by triangulation with the AIA images.

The HMI instrument (Schou et al. 2012) on SDO provides vector magnetograms with different products, and one of them is the Space-weather HMI Active Region Patch (SHARP, Bobra et al. 2014) data which is suitable for extrapolation in Cartesian coordinates. The SHARP data has effective spatial and temporal resolutions of ∼1 arcsec and 12 min, respectively. It has been resolved with 180° ambiguity using the minimum energy method and transformed into a heliographic Cylindrical Equal-Area (CEA) projection centered on the patch via the Lambert method with the projection effect corrected.

We use the CESE–MHD–NLFFF extrapolation code developed by Jiang & Feng (2013) to reconstruct the coronal magnetic field from the photospheric field as provided by the SHARP data. The raw data are preprocessed (Jiang & Feng 2014) to reduce the noise and the Lorentz force before being put into the code. The CESE–MHD–NLFFF code uses an advanced space-time conservation-element and solution-element (CESE) scheme (Jiang et al. 2010) to solve a set of modified MHD equations with a friction force and a zero-β approximation, seeking approximately force-free equilibrium for a given vector magnetogram based on an MHD-relaxation approach. It is widely used in reconstructing different magnetic structures corresponding to the SDO observations (Jiang & Feng 2013, 2014; Duan et al. 2017, 2021b,a,2022; Zou et al. 2019, 2020), and shows a good quality of extrapolations with reasonably small metrics that measure the force-freeness and divergence-freeness of the field.

To identify MFRs in the extrapolated field, we calculate the magnetic twist number T_w (Berger & Prior 2006) with a fast code proposed by Liu et al. (2016). For a given magnetic field line, T_w is defined as

$$\begin{array}{c}\hfill T_w={\displaystyle {\int }_L\frac{(\mathrm{\nabla }\times \mathit{B})·\mathit{B}}{4\pi B^2}\mathrm{d}l,}\end{array}$$(1)

where the integral is taken along the field line between its two footpoints, both of which are anchored at the photosphere. We note that T_w is not the exact number of turns that field lines wind a common axis, but it can provide a good approximation of two closely neighboring field lines winding around each other, and the particular field line with the maximum local twist number |T_w|_max can be taken as a reliable proxy of the MFR axis (Liu et al. 2016; Duan et al. 2019).

Since |T_w|_max merely measures the twist at an infinitesimal radius around the MFR axis, a measurement of the large-scale twist rather than only a local twist should be used to a more comprehensive judgement of KI. Thus, we use two methods to quantify the large-scale twist in this paper, as we did in Duan et al. (2022). In the first way, a flux-weighted average of the twist number was defined as

$$\begin{array}{c}\hfill {(T_w)}_{\mathrm{mean}}=\frac{{\int }_{S,T_w\ge 1}{B}_n{T}_w\mathrm{d}s}{{\int }_{S,T_w\ge 1}{B}_n\mathrm{d}s},\end{array}$$(2)

where S and B_n denote a cross section of the MFR and the magnetic field component normal to the cross-sectional slice, respectively. We restrict the integration with the area of T_w ≥ 1 since the MFR is defined by this threshold and the studied MFR here has positive twist numbers. In the second method, we calculate the winding number directly for each field line (denoted by 𝒯, which is different from T_w) around the axis using the standard equation of Berger & Prior (2006),

$$\begin{array}{c}\hfill \mathcal{T}=\frac{1}{2\pi }{\displaystyle {\int }_L\mathit{T}(l)·\mathit{V}(l)\times \frac{\mathrm{d}\mathit{V}(l)}{\mathrm{d}l}\mathrm{d}l,}\end{array}$$(3)

where l is the arc length from a reference starting point on the axis curve, T(l) is the unit vector tangent to the axis, and V(l) denotes a unit vector normal to T(l) and pointing from the axis curve to the target field line. To give a reasonable estimate of the average value of the winding number (i.e., the large-scale twist), we also calculated the flux-weighted average of the winding number,

$$\begin{array}{c}\hfill {\mathcal{T}}_{\mathrm{mean}}=\frac{{\int }_{S,T_w\ge 1}{B}_n\mathcal{T}\mathrm{d}s}{{\int }_{S,T_w\ge 1}{B}_n\mathrm{d}s}·\end{array}$$(4)

To evaluate the condition of TI, we calculate the decay index of the strapping field of the MFR. It is defined as

$$\begin{array}{c}\hfill n_z=-\frac{\mathrm{d}log(B)}{\mathrm{d}log(z)},\end{array}$$(5)

where B and z denote the strapping magnetic field and the radial distance (or height) from the solar surface, respectively. Apparently, this formula is valid only for those MFRs that erupt radially (i.e., vertically) and have strapping force in the opposite radial direction. However, non-radial filament eruptions are often observed (McCauley et al. 2015); some of them even significantly deviate from the radial direction. Thus, we recommend a more accurate way to calculate the decay index, which was first proposed in Duan et al. (2019). Briefly speaking, the decay index n is computed along an oblique line matching the eruption direction as

$$\begin{array}{c}\hfill n=-\frac{\mathrm{d}log(B_{\mathrm{p}})}{\mathrm{d}log(r)}·\end{array}$$(6)

Here r is the distance between the surface and the apex of the MFR axis along the eruptive direction and B_p refers to the poloidal flux; the product between the current of the rope and B_p can produce an effective strapping force in the opposite direction of the eruption. It is decomposed from the magnetic strapping field, which is extrapolated with the potential field model (for a detailed description of the method, see Duan et al. 2019). In this paper we use both of the methods (see Eqs. (5) and (6)) to calculate the decay index.

3. Results

3.1. Overview of the event

The active region NOAA 12887 (i.e., AR 12887) rotated from the far side of the Sun to the disk on 2021 October 22, and produced many flares during its passage on the disk in the following days. In particular, when it was close to the central meridian on 2021 October 28 (located at S28W01 on the solar disk), the AR had developed to a complex βγ-type sunspots system and generated multiple flares, including five C-class and two M-class flares (an M1.4 and M2.2 peaking at 07:40 UT and 10:28 UT, respectively), and the largest one, an X1.0 flare (peaking at 15:35 UT), which is the one that interests us. This X1.0 flare is also the first X-class flare observed on solar disk in solar cycle 25 as an eruptive flare accompanied with a CME.

Figure 1 (and its supplementary animation) presents the SDO and STEREO-A observations of the flare eruption in different EUV channels. As seen in the AIA 304 Å (denoted by the arrows in Fig. 1c) and also the Hα (Fig. 2b) images, there was clearly a J-shaped filament that existed well before the flare. The filament existed without significant variation at least from the beginning of the day, and suggests the pre-existence of a stable MFR. This filament ran roughly along the main polarity inversion line (PIL; i.e., the core site where the flare took place), and the X1.0 flare was associated with the eruption of this J-shaped filament system. The flare initiated at 15:22 UT, reaching its peak impulsively within about ten minutes, and the flare ribbons expanded along the filament toward both the east and south directions. Immediately after onset of the flare, the middle of the straight part of the J-shaped filament first rose rapidly, which was followed by eruption of the whole filament (as denoted by arrows in the middle panels of Fig. 1) with dark material ejected quickly from the flare site (see the animation for whole eruption). This eruption resulted in a CME with a wide angular width of around 270° and an average speed of 502 km s⁻¹, which was detected by SOHO/LASCO C2 coronagraph at 15:48 UT¹. We note that during the eruption, there was no obvious kink motion (i.e., with a helical shape) of the erupting filament, suggesting that the eruption was not likely triggered by the KI.

Fig. 1. Observation of the X1.0 flare and the filament eruption. (a) Angular locations of the Sun, the flare site, and STEREO, with respect to the Earth. (b) GOES soft X-ray flux. (c)–(f) Observations of the filament motion during the eruption from SDO/AIA and STEREO-A/EUVI with wavelengths of 304 Å, 171 Å, 131 Å, and 195 Å, respectively. The first row displays a clear J-shaped filament that remains stable before the flare onset. The second row shows that the filament starts to rise up quickly. The third row presents the eruption of the filament and the flare ribbons. An animation of SDO/AIA observation with cadence of 1 min is attached.

3.2. Coronal magnetic flux rope

To confirm the pre-existence of the MFR, we extrapolated the pre-flare coronal magnetic fields of a time series from 13:00 UT to 15:12 UT with time cadence of 12 min. The quality of force-freeness and divergence-freeness of the extrapolated field was checked with two groups of metrics. One group is named CWsin and ⟨|f_i|⟩, which are commonly used in the literature (e.g., Schrijver et al. 2006; DeRosa et al. 2009; Jiang & Feng 2013). They are, respectively, the mean sine of the angle between current density J and magnetic field B, as weighted by J, and the normalized divergence error. The other is E_∇ × B and E_{∇ ⋅ B}, which are, respectively, the average ratios of the residual Lorentz force and the nonphysical force (F = B∇⋅B, as introduced by the non-zero ∇ ⋅ B) to the sum of the magnitudes of the two component forces (i.e., the magnetic tension force and magnetic pressure-gradient force; Jiang & Feng 2012; Malanushenko et al. 2014). Although less used than CWsin and ⟨|f_i|⟩, these two metrics are introduced for a more physical meaning by directly quantifying the residual force in the extrapolated field (see the appendix of Duan et al. 2022 for detailed descriptions of all these metrics). Among them, the CWsin and E_∇ × B measure the force-freeness of the field, while the ⟨|f_i|⟩ and E_{∇ ⋅ B} estimate the divergence-freeness of the field. Here for all the extrapolated fields, we calculated the average and rms values of these metrics for the whole volume and the subdomain containing only the flux rope, respectively, and the results are shown in Table 1. We can see that all of the metrics are highly consistent with our previous works (Jiang & Feng 2013; Duan et al. 2017, 2021b, 2022). It should be noted that the extrapolated field is not accurately force-free, mainly because the photospheric field is generally not force-free, which conflicts with the basic assmuption of force-free field modeling. For example, the CWsin = 0.27 implies an average misalignment angle of 16° between the current density and magnetic field. This value is on the same level as that from other currently avaiable NLFFF codes for ARs, which give CWsin in a typical range of 0.2 − 0.4 (e.g., DeRosa et al. 2009, 2015; Schrijver et al. 2006, 2008). For the residual force, as quantified by E_∇ × B and E_{∇ ⋅ B}, it is smaller than the magnetic pressure and tension force by an order of magnitude.

From the reconstructed field, we found a large-scale MFR with the T_w of its axis kept larger than 2.0. To compare the reconstructed MFR with the observational filament, we show observations by SDO/AIA 304 Å and Hα from Cerro Tololo Inter-American Observatory in Figs. 2a and b, respectively. Since the filament can be observed all the time before its eruption without much variation from the start of October 28, here we only display the time (15:12 UT for AIA 304 Å and 15:10 UT for Hα) when the filament can be seen most clearly. Figure 2c presents the sampled reconstructed magnetic field lines (colored thick curves) at 13:24 UT. We note that at 13:24 UT the T_w of the MFR axis reaches its maximum value of ∼4.0. In Fig. 2c the field lines are overlaid on the AIA image of panel a, and such comparison clearly demonstrates that the MFR almost matches perfectly with the filament system. Figure 2d shows the magnetic dips at 13:24 UT. We compute the location of dips from a 3D magnetic field according to their definition (i.e., the location with B_z = 0 and B ⋅ ∇B_z ≥ 0) and trace the parts of the field lines that extend from the dips up to a height of 300 km (which is a typical scale height in prominence; Guo et al. 2010; Zuccarello et al. 2016) to simulate the location of filament, and it shows that the magnetic dips closely match the filaments system, as the MFR does.

Fig. 2. Observations of the filament and the NLFFF reconstruction of the MFR. (a) SDO/AIA 304 Å image at 15:12 UT. (b) Hα image from Cerro Tololo Inter-American Observatory at 15:10 UT. (c) Sampled field lines (in different colors) from the reconstructed magnetic field at 13:24 UT. (d) Segments of magnetic field lines that extend from magnetic dips to a scale height of 300 km (cyan lines) at 13:24 UT.

Figure 3 shows both the largest ((T_w)_max and 𝒯_max) and flux-weighted average values ((T_w)_mean and 𝒯_mean) of the twist number and winding number of the flux rope. As expected, there are systematic differences between T_w and 𝒯. In addition, the averaged winding number that quantifies the large-scale twist of the MFR is below the smallest threshold for KI, namely 1.25 (Hood & Priest 1981), suggesting that KI cannot be triggered.

Fig. 3. Evolution of the twist number Tw and the winding number 𝒯, including both their largest value and mean value.

Figures 4a and c present the sampled reconstructed magnetic field lines at two representative times, 13:24 UT and 14:48 UT, respectively, when the reconstructed MFR can be most clearly shown. Figures 4b and d show vertical cross sections of the MFR whose locations are given by the yellow and green lines in panels a and c, respectively. The arrows on the slice show the directions of the transverse field components, from which we can see that in both panels the arrows show that the poloidal flux of the rope forms spirals centered at the axis of MFR (denoted by the thick red lines, which are also the field lines in the MFR with the largest T_w). Values of the decay index calculated from different positions with the two methods (the radial definition n_z and the oblique definition n) are labeled in panels b and d. In panel b, slices A and B correspond to the yellow and green lines in panel a, and the decay indices are computed at the points where the yellow and green lines intersect with the MFR, respectively. Similarly, the decay index labeled in panel d is calculated at the point of the intersection between the green line and the MFR in panel c. Here we have n (n_z) with 0.89 (0.30), 0.33 (0.19), and 0.60 (0.19) for the three points, while the corresponding heights of the MFR axis are 3.33, 8.00, and 12.43 in units of arcsecond (or 720 km), respectively. Such low decay index values at the MFR axis are far below the canonical threshold (∼1.5) of TI, and also below the most typical range of 1.5 ± 0.2 as derived in many theoretical, numerical, and laboratorial investigations (Kliem & Török 2006; Fan & Gibson 2007; Török & Kliem 2007; Aulanier et al. 2010; Démoulin & Aulanier 2010; Fan 2010; Myers et al. 2015; Inoue et al. 2014, 2018; McCauley et al. 2015; Zuccarello et al. 2015; Alt et al. 2021) and in some statistical studies of flare events (Duan et al. 2019, 2021a).

Fig. 4. Observations of the filament and the NLFFF reconstruction of the MFR. (a) Sampled field lines (in different colors) from the reconstructed magnetic field at 13:24 UT. (b) Two vertical cross sections of the MFR whose locations are denoted by the yellow and green lines in panel a. (c) Same as (a), but for 14:48 UT. (d) Vertical cross section of the MFR located at the position given by the green line in panel c. The arrows in both (b) and (d) show the directions of the transverse magnetic field on the slices, and they form rings centered at the red thick line, which is expected as the axis of the MFR. The decay index calculated at the axis of the MFR is denoted in each slice. (e) Evolution of the heights of the MFR axis and the magnetic dips at their highest point in the section corresponding to the earliest rising part of the filament during its eruption.

Figure 4e further shows the evolution of the heights of MFR axis and magnetic dips from 13:00 UT to 15:12 UT. The MFR axis is identified using exactly the same method as followed in Duan et al. (2019; i.e., it is the field line in the MFR with the largest twist number T_w). Then we tracked the highest point of the axis in the section corresponding to the earliest rising part of the filament during its eruption. As can be seen, the height increases with time overall, but from 13:48 UT to 15:12 UT it shows oscillation from around 5 to 9 Mm, which is likely owing to the uncertainty of the NLFFF extrapolations (of ∼ ± 2 Mm). The magnetic dips, which are calculated from the NLFFF data, have a height of around 8 Mm on average. As is often assumed, the filament material is supported by magnetic dips, and thus the height of the dips can be taken as an approximation of the upper limit of the filament height. All these heights at all times are far below the TI critical height of ∼25 Mm (see the profile of the decay index of the strapping field as studied in Sect. 3.3), suggesting that TI is not likely the trigger mechanism of eruption in this event. It is worth noting that at some times the dips are slightly higher than the MFR axis by around 2 Mm. This is owing to the complexity of the MFR axis, which is not simply arched (as shown in the idealized model of MFR; e.g., Zuccarello et al. 2016) but undulated, and thus is itself dipped at some locations (see Fig. 4b).

3.3. Kinematics of the erupting features

We further analyze the kinematic evolutions of the eruptive filament and its overlying loops, as well as their timing relations with the evolutions of the flare emission, and the results are shown in Fig. 5 (and the supplementary animation). Specifically, Fig. 5a presents the GOES soft X-ray flux (black line). Regarding that the GOES soft X-ray flux is taken for the full disk and may include a contribution from other regions, we also plot the source-integrated AIA 131 Å flux to represent the hot flare emission as restricted within the studied AR. These light curves confirm that the onset time of the flare impulsive phase (or fast reconnection) is 15:22 UT (as denoted by the pink dashed line).

Fig. 5. Velocity and acceleration of the filament eruption. (a) Evolutions of the GOES soft X-ray flux (dark solid line) and the source-integrated AIA 131 Å flux (red solid line) from 14:20 UT to 16:00 UT. (b) Stack plot (or Jmap) of the 304 Å intensities along slit 1, as denoted in Fig. 1c1, showing the fast rise of the filament. The dashed blue line tracks the leading edge of the erupting filament. (c) Temporal evolutions of the velocity and acceleration of the eruptive filaments as computed from the dashed blue line in panel b. (d) Stack plot along slit 2, as denoted in Fig. 1c1, which tracks mainly the slow rise of the filament before the eruption onset. (e) The velocity and acceleration for the slow rise of the filament are estimated from the dashed blue line in panel d. In all the panels, the vertical dashed line (in pink) denotes the time of 15:22 UT. An animation for the SDO/AIA 171 Å and 304 Å with a cadence of 12 s is attached (without the light curves).

Figures 5b and c show time-distance evolution and the estimated speed (and acceleration) in slit 1 from 304 Å, as denoted in Fig. 1c1, which is selected to track most clearly the fast ejection of the filament material. In addition, Figs. 5d and e show those for slit 2, as denoted in Fig. 1c1, to track mainly the slow rise of the filament before the eruption onset. The filament undergoes a slow rise from around 14:40 UT to the flare onset (15:22 UT) with speed increased mildly from almost zero to a few km s⁻¹; we note that the acceleration is very low (around 0.01 km s⁻²; see Fig. 5e), which is close to the quasi-static evolution speed as driven by the photosphere (e.g., lower than the photospheric sound speed). After 15:22 UT, the filament was impulsively accelerated to a speed of ∼600 km s⁻¹ within around eight minutes (Fig. 5c). Thus, the start time of the filament eruption is in agreement with the abrupt increase of both the GOES soft X-ray and the AIA 131 Å light curves.

To determine more precisely the height of the filament around the eruption onset time, we used a triangulation approach (Thompson 2009) by combining the AIA and EUVI images, and the results of the highest point (which is also roughly the middle point) of the filament are shown in Fig. 6c. As the selection of the same highest point in both the AIA and EUVI images is done manually, we performed the computation multiple times, and the uncertainty of the estimated heights are shown by the error bars in the plot, which is around ±2 Mm. For comparison, the heights of the MFR axis at approximately the highest point of the filament for times of 15:00 UT and 15:12 UT derived from the extrapolated NLFFFs are denoted by the red crosses in the plot, which are found to be consistent with the heights derived from the triangulation approach (in particular at time near 15:12 UT). In the slow rise phase until 15:20 UT, the average rising speed of the filament is around 6 km s⁻¹, while at 15:22:30 UT the filament has already been accelerated to a speed of over 37 km s⁻¹. As shown in Fig. 6d, we compute the decay index of the strapping field (i.e., the horizontal component of the potential field, using time of 15:12 UT). The decay index at the height of the filament remains smaller than 1, at least until 15:22 UT when the acceleration of the filament starts. This agrees with our analysis based on the NLFFF reconstruction that the trigger of the eruption is not TI. It also shows that once triggered, the MFR quickly rises into the TI domain, after which the eruption should be driven by TI in addition to the reconnection. The peak acceleration, as shown in Fig. 5, reaches 2.7 km s⁻² (the real value should be higher, bearing in mind the projected effect). A theoretical analysis by Vršnak (2008) suggests that without reconnection, an MFR cannot be accelerated in such an impulsive way.

Fig. 6. Height evolution of the filament as determined by triangulation method combining SDO/AIA (a) with STEREO/EUVI (b) images. The highest point of the filament is denoted by the small circles in both the AIA and EUVI images. (c) Evolution of the height and the typical velocity. The uncertainty in the estimation of the height is denoted by the error bars. The two red crosses denote the heights of the MFR derived from the NLFFF extrapolations for time of 15:00 UT and 15:12 UT, respectively. The dashed lines shows the critical height of TI using the canonical threshold (1.5) of decay index, and the gray region shows the range of heights with decay indexes from 1.3 to 1.7. (d) Profile of the decay index of the strapping field. The heights of the filament shown in (c) are also denoted on the profile by the times symbols (×).

3.4. Suggestion of reconnection as the initiation mechanism

As the above analysis shows that the eruption cannot be triggered by TI, here we suggest the reconnection-based mechanism as its trigger, and give further evidence. Recently, using a sufficiently high-accuracy MHD simulation, Jiang et al. (2021) established a fundamental mechanism of solar eruption initiation: a bipolar field driven by slow shearing motion at the photosphere can form an internal current sheet in a quasi-static way, which is followed by fast magnetic reconnection (in the current sheet) that triggers and drives the eruption (see Jiang et al. 2021 for more details of the process). There are two pieces of evidence suggesting that the studied event follows this reconnection-based scenario. First, the extrapolated magnetic fields before the eruption suggests formation of a current sheet. As shown in Fig. 7, a vertical, thin current layer with a high value of jΔ/B ∼ 0.2 (where j = ∇ × B is the current density and Δ the grid resolution) is seen at the middle section of the MFR. We note that jΔ/B is a useful parameter to show the current sheet, and its value can indicate the thickness of the current layer (a higher value indicates a thinner layer; see Jiang et al. 2016, 2021). From Fig. 7c it can be seen that the current layer has a thickness of around 2Δ. This current layer extends upward from the central part of the flare PIL, and becomes progressively thinner with time (see Figs. 7d–f). Although this current layer is somewhat thicker than can be regarded as a true current sheet, it is likely to be thinned with further shearing of the field, eventually being a true current sheet until the flare onset. Second, there is continuous photospheric shearing motion before the eruption, which can help to build up the current sheet. Figure 8 shows the photospheric flows as derived by the DAVE4VM method (Schuck 2008) from the time sequence vector magnetograms. As can be seen, although the structure of the flow is complex, the shearing motion (e.g., eastward flow in the north and westward flow in the south) along the PIL under the main branch of the filament (i.e., the core region where the eruption starts) is clearly identified (see the large arrows).

Fig. 7. Thinning of a vertical current layer as derived from the NLFFF extrapolations. (a) 3D iso-surface (in green) of jΔ/B = 0.2 (i.e., a thin current layer on top of the flare PIL). The black lines show sampled magnetic field lines of the MFR; most of these field lines cross through the current layer. (b) 3D view of the current layer. (c) Vertical slice cutting perpendicularly through the current layer at the largest value of jΔ/B. The arrows show magnetic field vectors on the slice. (d)–(f) Time evolution of the jΔ/B in a vertical cross section as denoted by the red line in (a). The arrows in the different panels give the same location of the current layer.

Fig. 8. Photospheric velocity field before the eruption onset. The three panels show three different times with cadence of one hour. The background shows the magnetogram of Bz and small arrows show the horizontal velocity field (white in the negative polarity and black in the positive polarity). The red contour lines overlaid show the location of the initial flare ribbons observed by AIA 1600 Å at time of 15:25:51 UT. In the first panel the blue thick curve gives the location of the filament (or MFR), and the large green arrows denote the shearing motions of the polarities.

4. Conclusions

In this paper we focus on the initiation mechanism of the first on-disk X-class flare as recorded in solar cycle 25. This flare is accompanied by a filament eruption and results in a moderate CME. The coronal NLFFF reconstructions from the photospheric vector magnetograms reveal that there is a well-defined coronal MFR, with configuration highly consistent with the J-shaped filament, existing for a long period before the flare. During the eruption, the entire filament erupts, which indicates the eruption of the underlying MFR. However, by a quantitative analysis of the extrapolated magnetic field and the observed slow rise phase of the filament immediately before its eruption, we found that the MFR is confined in a height that is too low to trigger the TI, which is often assumed to play the key role in CME initiation of a pre-flare MFR.

On the other hand, the evolution of the current density in the extrapolated magnetic fields shows progressive thinning of a vertical current layer on top of the flare PIL, which hints that a vertical current sheet may form before the eruption. Meanwhile, there is continuous shearing motion along the PIL under the main branch of the filament that can drive the coronal field to form such a current sheet. As such, we suggest that the event follows the reconnection-based initiation mechanism as recently established using a high-accuracy MHD simulation (Jiang et al. 2021): the photosphere shearing motion can build up a current sheet in a quasi-static way, and fast magnetic reconnection in the current sheet triggers the eruption. As accelerated by the reconnection, the filament rises impulsively at the onset of the flare. Then the filament quickly rises into the TI domain and should be further driven by TI in addition to the reconnection, attaining a fast acceleration.

Nevertheless, it should be noted that we still lack a solid indication of the pre-flare current sheet since our analysis is based on the NLFFF extrapolations, which has inherent limitations. We have never seen reports of NLFFF extrapolation of coronal current sheet in the literature. The limitations may come from either the force-free assumption or the particular numerical techniques (see, e.g., Low 2013; Yeates 2022). For example, the force-free assumption might fail if there is a non-force-free current sheet in which the Lorentz force is balanced by gas pressure gradient, and since the force-free field assumes a smooth solution (while a true current sheet is a discontinuity), this constitutes a weak solution of the MHD equation. It is also possible that a current sheet exists, but the grid resolution of the extrapolation is not sufficiently high to capture the current sheet. Future investigation of this event will be carried out by high-resolution data-driven MHD simulations (Jiang et al. 2022) to study how a current sheet is built up as driven by the photospheric motions along with the presence of the MFR.

Acknowledgments

This work is supported by National Natural Science Foundation of China (NSFC) U2031108, Guangdong Basic and Applied Basic Research Foundation (2021A1515011430), and Yunnan Key Laboratory of Solar Physics and Space Science under the number YNSPCC202213. C.J. acknowledges support by NSFC 42174200, Guangdong Basic and Applied Basic Research Foundation (2023B1515040021), and Shenzhen Science and Technology Program (Grant No. RCJC20210609104422048). The computational work of the NLFFF extrapolations was carried out on TianHe-1(A), National Supercomputer Center in Tianjin, China. Data from observations are courtesy of NASA/SDO and Cerro Tololo Inter-American Observatory. We are very grateful to the reviewer for helpful comments and suggestions that improved the paper.

References

All Tables

All Figures

Fig. 1. Observation of the X1.0 flare and the filament eruption. (a) Angular locations of the Sun, the flare site, and STEREO, with respect to the Earth. (b) GOES soft X-ray flux. (c)–(f) Observations of the filament motion during the eruption from SDO/AIA and STEREO-A/EUVI with wavelengths of 304 Å, 171 Å, 131 Å, and 195 Å, respectively. The first row displays a clear J-shaped filament that remains stable before the flare onset. The second row shows that the filament starts to rise up quickly. The third row presents the eruption of the filament and the flare ribbons. An animation of SDO/AIA observation with cadence of 1 min is attached.

In the text

Fig. 2. Observations of the filament and the NLFFF reconstruction of the MFR. (a) SDO/AIA 304 Å image at 15:12 UT. (b) Hα image from Cerro Tololo Inter-American Observatory at 15:10 UT. (c) Sampled field lines (in different colors) from the reconstructed magnetic field at 13:24 UT. (d) Segments of magnetic field lines that extend from magnetic dips to a scale height of 300 km (cyan lines) at 13:24 UT.

In the text

	Fig. 3. Evolution of the twist number Tw and the winding number 𝒯, including both their largest value and mean value.
In the text

Fig. 4. Observations of the filament and the NLFFF reconstruction of the MFR. (a) Sampled field lines (in different colors) from the reconstructed magnetic field at 13:24 UT. (b) Two vertical cross sections of the MFR whose locations are denoted by the yellow and green lines in panel a. (c) Same as (a), but for 14:48 UT. (d) Vertical cross section of the MFR located at the position given by the green line in panel c. The arrows in both (b) and (d) show the directions of the transverse magnetic field on the slices, and they form rings centered at the red thick line, which is expected as the axis of the MFR. The decay index calculated at the axis of the MFR is denoted in each slice. (e) Evolution of the heights of the MFR axis and the magnetic dips at their highest point in the section corresponding to the earliest rising part of the filament during its eruption.

In the text

Fig. 5. Velocity and acceleration of the filament eruption. (a) Evolutions of the GOES soft X-ray flux (dark solid line) and the source-integrated AIA 131 Å flux (red solid line) from 14:20 UT to 16:00 UT. (b) Stack plot (or Jmap) of the 304 Å intensities along slit 1, as denoted in Fig. 1c1, showing the fast rise of the filament. The dashed blue line tracks the leading edge of the erupting filament. (c) Temporal evolutions of the velocity and acceleration of the eruptive filaments as computed from the dashed blue line in panel b. (d) Stack plot along slit 2, as denoted in Fig. 1c1, which tracks mainly the slow rise of the filament before the eruption onset. (e) The velocity and acceleration for the slow rise of the filament are estimated from the dashed blue line in panel d. In all the panels, the vertical dashed line (in pink) denotes the time of 15:22 UT. An animation for the SDO/AIA 171 Å and 304 Å with a cadence of 12 s is attached (without the light curves).

In the text

Fig. 6. Height evolution of the filament as determined by triangulation method combining SDO/AIA (a) with STEREO/EUVI (b) images. The highest point of the filament is denoted by the small circles in both the AIA and EUVI images. (c) Evolution of the height and the typical velocity. The uncertainty in the estimation of the height is denoted by the error bars. The two red crosses denote the heights of the MFR derived from the NLFFF extrapolations for time of 15:00 UT and 15:12 UT, respectively. The dashed lines shows the critical height of TI using the canonical threshold (1.5) of decay index, and the gray region shows the range of heights with decay indexes from 1.3 to 1.7. (d) Profile of the decay index of the strapping field. The heights of the filament shown in (c) are also denoted on the profile by the times symbols (×).

In the text

Fig. 7. Thinning of a vertical current layer as derived from the NLFFF extrapolations. (a) 3D iso-surface (in green) of jΔ/B = 0.2 (i.e., a thin current layer on top of the flare PIL). The black lines show sampled magnetic field lines of the MFR; most of these field lines cross through the current layer. (b) 3D view of the current layer. (c) Vertical slice cutting perpendicularly through the current layer at the largest value of jΔ/B. The arrows show magnetic field vectors on the slice. (d)–(f) Time evolution of the jΔ/B in a vertical cross section as denoted by the red line in (a). The arrows in the different panels give the same location of the current layer.

In the text

Fig. 8. Photospheric velocity field before the eruption onset. The three panels show three different times with cadence of one hour. The background shows the magnetogram of Bz and small arrows show the horizontal velocity field (white in the negative polarity and black in the positive polarity). The red contour lines overlaid show the location of the initial flare ribbons observed by AIA 1600 Å at time of 15:25:51 UT. In the first panel the blue thick curve gives the location of the filament (or MFR), and the large green arrows denote the shearing motions of the polarities.

In the text