The Initiation Mechanism of the First On-disk X-Class Flare of Solar Cycle 25

The active region NOAA 12887 (i.e., AR 12887) rotated from the back 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 $\beta\gamma$-type sunspots system, and generated multiple flares, including five C-class ones, two M-class ones (an M1.4 and M2.2 peaking at 07:40 UT and 10:28 UT, respectively), and the largest one of X1.0 (peaking at 15:35 UT), which is of our interest. 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 Figure 1c) and also the H$\alpha$ (Figure 2b) images, there was clearly a J-shaped filament existing 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 run 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 10 minutes, and the flare ribbons expanded along the filament towards 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 middle panels of Figure 1) with dark materials ejected fast from the flare site (see the animation for whole eruption). This eruption resulted in a CME with a wide angular width of around $270^{\circ}$ and an average speed of 502 km s^-1, which was detected by SOHO/LASCO C2 coronagraph at 15:48 UT ¹¹1http://helio.gmu.edu/seeds/lasco.php. 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 is not likely triggered by the KI.

To confirm the pre-existence of the MFR, we extrapolate the pre-flare coronal magnetic fields of a time series from 13:00 UT to 15:12 UT with time cadence of 12 minutes. The quality of force-freeness and divergence-freeness of the extrapolated field has been checked with two groups of metrics. One group is named as CWsin and $\langle|f_{i}|\rangle$, which are commonly used in the literature (e.g., Schrijver et al. 2006; DeRosa et al. 2009; Jiang & Feng 2013). They are, respectively, 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 $E_{\nabla\times\mathbf{B}}$ and $E_{\nabla\cdot\mathbf{B}}$, which are, respectively, the average ratios of the residual Lorentz force and the nonphysical force ($F=B\nabla\cdot\mathbf{B}$, as introduced by the non-zero $\nabla\cdot\mathbf{B}$) 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 $\langle|f_{i}|\rangle$, these two metrics are introduced for a more physically meaning by directly quantifying the residual force in the extrapolated field (one can refer to the Appendix of Duan et al. (2022) for detailed descriptions of all these metrics). Among them, the CWsin and $E_{\nabla\times\mathbf{B}}$ measure the force-freeness of the field, while the $\langle|f_{i}|\rangle$ and $E_{\nabla\cdot\mathbf{B}}$ 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 $16^{\circ}$ between the current density and magnetic field. This value is on the same level with that from other currently avaiable NLFFF codes for ARs, which give CWsin in a typical range of $0.2\sim 0.4$ (e.g., DeRosa et al. 2009, 2015; Schrijver et al. 2006, 2008). For the residual force, as quantified by $E_{\nabla\times\mathbf{B}}$ and $E_{\nabla\cdot\mathbf{B}}$, 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 H$\alpha$ from Cerro Tololo Inter-American Observatory in Figure 2(a) 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 H$\alpha$) when the filament can be seen most clearly. Figure 2(c) presents the sampled reconstructed magnetic field lines (the colored thick curves) at 13:24 UT. Note that at 13:24 UT, the $T_{w}$ of the MFR axis reaches its maximum value of $\sim 4.0$. In Figure 2(c) 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 2(d) shows the magnetic dips at time of 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 ${\mathbf{B}}\cdot\nabla B_{z}\geq 0$) 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 highly matches with the filaments system, as the MFR does.

Figure 3 shows both the largest ($(T_{w})_{max}$ and $\mathcal{T}_{max}$) and flux-weighted average values ($(T_{w})_{mean}$ and $\mathcal{T}_{mean}$) of the twist number and winding number of the flux rope. As expected, there are systematic differences between $T_{w}$ and $\mathcal{T}$. In addition, the averaged winding number that quantify the large-scale twist of the MFR are below the smallest threshold for KI, namely 1.25 (Hood & Priest 1981), suggesting that KI cannot be triggered.

Figure 4(a) and (c) present the sampled reconstructed magnetic field lines (the colored thick curves) at two representative times, 13:24 UT and 14:48 UT, respectively, when the reconstructed MFR can be most clearly shown. Figure 4(b) and (d) show vertical cross sections of the MFR whose locations are marked by the yellow and green lines in the 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 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 line 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 on (b) and (d). In panel (b), slice A and B correspond to the yellow and green lines on panel (a), and the decay indices are computed at the points where the yellow and green lines intersect with the MFR, respectively. Similarly, decay index labeled in panel (d) is calculated at the point of the intersection between the green line and the MFR on 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’s axis are $3.33$, $8.00$ and $12.43$ with unit of arcsecond (or 720 km), separately. Such low values of decay index at the MFR’s axis are far below the canonical threshold ($\sim 1.5$) of TI, and also below the most typical range of $1.5\pm 0.2$ 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) as well as some statistical studies of flare events (Duan et al. 2019, 2021a).

Figure 4(e) 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 done 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 $\sim\pm 2$ Mm). The magnetic dips, which are calculated from the NLFFF data, have the 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 time are far below the TI critical height of $\sim 25$ Mm (see in Figure 6 the profile of the decay index of the strapping field), 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, for example, Zuccarello et al. (2016)) but undulated and thus is itself dipped at some locations (see Figure 4(b)).

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 Figure 5 (and the supplementary animation). Specifically, Figure 5(a) presents the GOES soft X-ray flux (the 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).

Figure 5(b) and (c) show time-distance evolution and the estimated speed (and acceleration) in slit 1 from the 304 Å as denoted in Figure 1(c1), which is selected to track most clearly the fast ejection of the filament material. In addition, Figure 5(d) and (e) show those for slit 2 as denoted in Figure 1(c1) 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 (note that the acceleration is very small of around $0.01$ km s^-2, see Figure 5e), which is close to the quasi-static evolution speed as driven by the photosphere (e.g., smaller than the photospheric sound speed). After 15:22 UT, the filament was impulsively accelerated to a speed of $\sim 600$ km s^-1 within around 8 minutes (Figure 5c). Thus, the start time of the filament eruption is in accordance with the abrupt increasing 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 use 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 Figure 6(c). As the selection of the same highest point in both the AIA and EUVI images is done manually, we have performed multiple times of computation and the uncertainty of the estimated heights are shown by the error bars in the plot, which is around $\pm 2$ 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 ones 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 Figure 6(d), 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 being triggered, the MFR quickly rises into the TI domain, and after then the eruption should be driven by TI in addition to the reconnection. The peak acceleration, as shown in Figure 5(c), 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.

As the above analysis shows that the eruption cannot be triggered by TI, here we suggest the reconnection-based mechanism as its trigger with further evidences. 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 evidences suggesting that the studied event follows this reconnection-based scenario. Firstly, the extrapolated magnetic fields before the eruption suggests formation of a current sheet. As shown in Figure 7, a vertical, thin current layer with a high value of $j\Delta/B\sim 0.2$ (where ${\mathbf{j}}=\nabla\times\mathbf{B}$ is the current density and $\Delta$ the grid resolution) is seen at the middle section of the MFR. Note that $j\Delta/B$ is a useful parameter to show current sheet and its value can indicate the thickness of the current layer (higher value indicates thinner layer, see Jiang et al. 2016, 2021). From Figure 7c, it can be seen that the current layer has a thickness of around $2\Delta$. This current layer extends upward from the central part of the flare PIL, and is becoming progressively thinner with time (see Figure 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.

Secondly, there is continuously 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).