The Evolution of Photospheric Magnetic Fields at the Footpoints of Reconnected Structures in the Solar Atmosphere

Magnetic reconnection is believed to play an important role in the release and conversion of energy among magnetized plasma systems. So far, we have been unable to understand under what conditions magnetic reconnection can take place. Based on observations from the New Vacuum Solar Telescope and the Solar Dynamics Observatory (SDO), we study 16 magnetic reconnection events, and each event has a clear X-type configuration consisting of two sets of atmospheric structures. We focus on 38 footpoints that are relevant to these structures and can be clearly determined. By using SDO/Helioseismic and Magnetic Imager line-of-sight magnetograms, we track the field evolution of these footpoints. Prior to the occurrence of magnetic reconnection, the associated fields at the footpoints underwent convergence and shear motions, and thus became enhanced and complex. During the converging period, the rates of increase of the mean magnetic flux densities (MFDs) at these footpoints are 0.03–0.25 hr−1. While the unsigned mean MFDs are 70–300 G, magnetic reconnection in the solar atmosphere takes place. Subsequently, the photospheric fields of these footpoints diffuse and weaken, with rates of decrease of the MFDs from 0.03 to 0.18 hr−1. These results suggest that, due to the photospheric dynamical evolution at the footpoints, the footpoint MFDs increase from a small value to a large one, and the corresponding atmospheric magnetic fields become complicated and nonpotential; then reconnection happens and it releases the accumulated magnetic field energy. Our study supports the conjecture that magnetic reconnection releases free magnetic energy stored in the nonpotential fields.


Introduction
Magnetic reconnection (Priest & Forbes 2000;Yamada et al. 2010) is a fundamental physical process, including the approach of antiparallel magnetic field lines, a change in magnetic field topology, and the generation of new field lines.During the reconnection process, the stored magnetic field energy is released rapidly and converted into kinetic and thermal energy (Aschwanden 2002;Caspi & Lin 2010;Su et al. 2013;Ashfield & Longcope 2022;Fleishman et al. 2023), resulting in a new equilibrium configuration of lower energy.This mechanism was first proposed and used to explain the energy release in solar flares (Giovanelli 1946(Giovanelli , 1947)).Since the potential (current-free) field is the minimum energy state for the magnetic field, the energy released via magnetic reconnection is widely believed to be the free magnetic energy stored in nonpotential fields with current, defined as the difference between the total magnetic energy and the potential field energy (Gary et al. 1987;Schrijver et al. 2005Schrijver et al. , 2008;;Sun et al. 2012;Gupta et al. 2021).Up to now, there has been no solid evidence from an observational perspective to confirm the conjecture that magnetic reconnection releases the stored free magnetic energy (nonpotential magnetic energy).
Coronal loops (Rosner et al. 1978;Su et al. 2013) and chromospheric fibrils (Hansteen et al. 2006;Mandal et al. 2023) are quite common solar atmospheric structures.Under particular conditions, magnetic reconnection can take place between these structures and cause a change in their connectivity (e.g., Török et al. 2009;Li et al. 2016;Mason et al. 2021;Ding et al. 2022).Various observational studies have revealed the relevance of magnetic reconnection to different kinds of solar phenomena, e.g., flares (Su et al. 2013;Fleishman et al. 2020), extremeultraviolet (EUV) brightenings (Vernazza et al. 1981;Berghmans et al. 2021), jets (Shibata et al. 1992;Bučík et al. 2018), and coronal mass ejections (Masuda et al. 1994;Green et al. 2018).Nevertheless, there is much confusion over the cause of magnetic reconnection.We do not know the values of the magnetic flux densities (MFDs) at the footpoints of reconnected structures.In addition, the complexity and nonpotentiality of the structures are not clear yet.Furthermore, whether magnetic reconnection can take place between any two sets of structures is not understood.
According to the standard magnetic reconnection models (Parker 1957;Sweet 1958;Petschek 1964), the antiparallel field lines on both sides of the reconnection region approach each other, then form an X-type configuration.In the solar atmosphere, the X-type reconnection is defined as the generation of a clear X-configuration, and this X-configuration consists of two sets of independent atmospheric structures (e.g., Yang et al. 2015;Ding et al. 2022).Among the jet events, the inverse Y-shape configuration at the reconnection site has been detected (Shibata et al. 1992;Shen 2021).In a threedimensional (3D) model of magnetic reconnection, the reconnection process displays a continuous slippage of the field lines along each other, and the footpoints of the field lines slip-run at super-Alfvénic speeds along the intersection of the quasi-separatrix layers with the line-tied boundary (Aulanier et al. 2006), indicating that the geometry between the reconnecting structures involves various types (Aulanier et al. 2007;Li & Zhang 2014).
Several parameters from the solar magnetic fields, e.g., magnetic flux, global nonpotentiality, free magnetic energy, etc., have been obtained to study the solar activities (Falconer et al. 2002(Falconer et al. , 2006;;Schrijver 2007;Schrijver et al. 2008;Sun et al. 2015;Panesar et al. 2016;Li et al. 2021b).In this work, we integrate the previous achievements related to X-type reconnection events (e.g., Yang et al. 2015;Srivastava et al. 2019;Ghosh & Tripathi 2020;Ding et al. 2022), and concentrate on 38 footpoints of the reconnected structures among 16 reconnection events with clear X-type configurations (Priest & Forbes 2000;Su et al. 2013).These events are detected by two kinds of instruments: 11 are from the New Vacuum Solar Telescope (NVST; Liu et al. 2014) and five from the Solar Dynamics Observatory (SDO; Pesnell et al. 2012).By employing SDO/Helioseismic and Magnetic Imager (HMI; Schou et al. 2012) line-of-sight (LOS) magnetograms, we track the evolution of photospheric magnetic fields at these footpoints from 48 hr prior to the occurrence of magnetic reconnection to 24 hr after it, and obtain the MFDs associated with these footpoints.In Section 2, we describe the observational data and analytical methods.Section 3 presents the results, and is followed by the conclusions and a brief discussion in Section 4.

Observations
The Hα observations taken in the center of the 6562.8Å channel are obtained from the NVST, which is the primary ground-based solar telescope located by Fuxian Lake in southwest China.The high-resolution Hα data displayed in this work have fields of view (FOVs) of 151″ × 151″ (event 1) and 184″ × 188″ (event 3), with spatial resolutions of 0.″163 and 0.″165, as well as time cadences of 12 s and 11 s, respectively.The Level 1 data are first calibrated by using the raw data (Level 0), involving the subtraction of the dark current and the correction of the flat field.Then the speckle masking method is carried out to derive the Level 1+ data with these calibrated Level 1 data.
Full-disk EUV observations from the SDO/Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) are adopted to comprehend the evolution of magnetic reconnection for events 1-4 with a spatial resolution of 0 6 pixel −1 and a time cadence of 12 s.These EUV wavelength data reflect the emission from plasma at different temperatures in He/Fe lines from the cool chromosphere to hot corona.The LOS magnetograms provided by the SDO/ HMI play a key role in determining the polarities of atmospheric structure footpoints and studying the evolution of the photospheric magnetic field at the footpoints.The magnetograms cover the full solar disk with a pixel size of 0 5 and a cadence of 45 s.
The AIA and HMI data are rotated differentially to reference times (07:00:00 UT on 2014 February 3 for event 1, 12:00:00 UT on 2015 January 9 for event 2, 03:20:00 UT on 2019 November 1 for event 3, and 10:00:00 UT on 2016 February 6 for event 4) by using the standard aia prep.proroutine in the SolarSoftWare package (Freeland & Handy 2012).Then the NVST and SDO images are coaligned by the cross-correlation method with specific characteristics, such as synchronous brightenings, typical concaveconvex structures, special intersection points, etc.

X-type Reconnection Events
We examine all the NVST data from 2012 October 1 to 2022 September 30 and all the reported 3318 articles from 2011 July to 2023 July based on the SDO/AIA data to search for X-type reconnection events.To obtain relatively reliable magnetic fields at the footpoints of the reconnected structures, we first check those events that take place inside a heliocentric angle of 30°.Then, we focus on the footpoints that are relevant to these reconnected structures and can be clearly determined.In addition, the magnetic fields of the footpoints are separated from surrounding ones, and the field evolution at the footpoints can be tracked.Eleven events are obtained from the NVST observations and five from the SDO/ AIA data (see Table 1).

Determination of the Footpoints of Reconnection Structures
To determine the footpoints of these structures, several methods have been employed.First, we coalign HMI photospheric magnetic field data with chromospheric Hα (coronal EUV) images.Then we search for the relations between the magnetic fields and reconnected structures.Several kinds of signals have been used to determine the footpoints, e.g., the photospheric magnetic field polarities, the photospheric brightenings during the reconnection process, the change in the topological connectivity of the reconnected structures, and the drainage positions of the plasmas inside the reconnected structures.To further check the topological connectivity and the footpoint location of the reconnected structures, we employ HMI photospheric vector magnetograms (Hoeksema et al. 2014) to extrapolate 3D magnetic fields of the 16 reconnected events using a nonlinear force-free field (NLFFF) model (Wiegelmann et al. 2006(Wiegelmann et al. , 2012)).Among the 16 events, there are 32 sets of atmospheric structures.Seventeen structures reappear by extrapolating the 3D magnetic fields (see Figures 2(a), 3(a), and Table 1).The topological connectivity and the footpoint location of these extrapolated fields are consistent with the visual structures from the NVST Hα and SDO/AIA images, as well as the HMI LOS magnetograms.

Calculation of the Emission Measure and Temperature of Current Sheets
In AIA Fe lines (94, 131, 171, 193, 211, and 335 Å), the atmospheric structures can be traced by magnetized plasmas.During the magnetic reconnection process, the current sheets display bright features (e.g., Xue et al. 2020;Ding et al. 2022).The emission measure (EM) and temperature of the plasmas inside current sheets in situ can be obtained with the almost simultaneous observations of the six AIA Fe lines via the differential EM (DEM) analysis (Plowman & Caspi 2020).The total EM and temperature are derived from EM = ∫ DEM(T)dT and T = ∫ DEM(T)TdT/EM, respectively.In order to ensure the reliability of the calculated results, the integral intervals are selected as 5.5 = lg(T/K) = 7.0.

Calculation of the Horizontal Velocities of Photospheric Fields
The method of the differential affine velocity estimator (DAVE; Schuck 2006) is applied to derive the horizontal velocities of photospheric fields with the SDO/HMI LOS magnetograms.The window size is set as 10 pixels in DAVE, and the velocity is obtained from the difference between two sets of magnetograms with an interval of 10.5 minutes.

Measurement of the MFDs
To measure reliably the MFD at a footpoint, the noise level σ of the LOS magnetograms is estimated.First of all, we select a 160″ × 160″ region centered on the reconnection site (e.g., Figures 5( a1)-( a4)).In the selected region, there are several small zones in which no obvious magnetic field is detected.The average values of unsigned mean MFDs in these zones can be considered as σ (see Table 1).In subsequent analysis of the footpoint MFDs, unsigned values of less than 20 G (nearly 3σ) are removed.The footpoint fields investigated in this work are all separated from surrounding ones, and the MFDs are measured within the associated magnetic patches.

Results
Figure 1 displays an X-type magnetic reconnection event on 2014 February 3 (event 1).This event takes place at the edge of active region (AR) 11967 (Figure 1(a)).Prior to the occurrence of magnetic reconnection, there are two sets of atmospheric structures (red and white dotted lines in Figure 1(b)), and the field directions of the two structures are opposite.When they meet, an X-type configuration forms between them and a bright current sheet is detected in the AIA 171 Å observation (Figure 1(c)).After that, new field lines are generated (purple and cyan dotted lines in Figure 1(d)).We further investigate the thermal properties of plasmas inside the reconnecting current sheet.The EM and temperature maps are exhibited in Figures 1(e) and (f), respectively.Figure 1(g) displays the DEM distributions for the current sheet.Inside the current sheet, the peak mean temperature reaches 5.77 MK and the corresponding mean EM is 5.16 × 10 28 cm −5 .During the reconnection period, the mean temperature of the current sheet exhibits a rapid ascent and descent (Figure 1

(h)).
To reveal the photospheric magnetic field properties of the reconnection structures, we examine the LOS magnetograms from 48 hr prior to the occurrence of magnetic reconnection to 24 hr after it.Figures 1(i)-(k) display the magnetic field evolution of the footpoint P1 (Figure 1(b)).Before the reconnection, the magnetic fields associated with P1 undergo continuous convergence and shear motions with a duration of about 2.5 hr (an animation is available), and thus become enhanced and complex.Meanwhile, the mean MFDs at P1 increase from 140 ± 15 G to 230 ± 20 G (Figure 1(l)), and the rate of increase of the MFD is 0.25 ± 0.05 hr −1 .After the occurrence of magnetic reconnection, the photospheric fields at P1 begin to diffuse and weaken (Figure 1(k)), and this evolution lasts for around 2 hr.The MFDs decrease from 230 ± 20 G to 150 ± 15 G with a rate of decrease of 0.17 ± 0.03 hr −1 (Figure 1(l)).
Figure 2 demonstrates the magnetic reconnection event (Event 2) that occurred near AR 11257 on 2015 January 9 (Figure 2(a)).The reconnection process is displayed in Figures 2(b)-(d), and the EM and temperature results inside the reconnecting current sheet are shown in Figures 2(e)-(h).The evolution of photospheric magnetic fields at the footpoint P2 (see Figure 2(b)) is tracked (Figures 2(i)-(k)).Similarly, prior to the occurrence of magnetic reconnection, the associated magnetic fields also involve the convergence and shear motions (an animation is available), resulting in the increase in the mean MFDs at P2 (Figure 2(l)).After the reconnection, the photospheric fields become diffuse (Figure 2(k)) and the corresponding MFDs decrease (Figure 2(l)).
Figure 3 is similar to Figures 1 and 2, but for event 3, which happened in the quiet Sun (QS) on 2019 November 1 (Figure 3(a)).The details of the magnetic reconnection process and the physical properties inside the reconnecting current sheet can be found in Figures 3(b)-(d) and (e)-(h), respectively.From Figures 3(i)-(k), we notice that the photospheric magnetic field evolution at the footpoint P3 (Figure 3(b)) is similar to that at P1 and P2 (an animation is available).In addition, the mean MFDs at P3 also increase and decrease before and after the reconnection, separately (Figure 3(l)).
Another magnetic reconnection event (event 4) took place in the QS on 2016 February 6 (Figure 4 Comparing the unsigned distributions of the footpoints with those of the selected FOVs, we notice that the MFD values of the footpoints are concentrated in a small range, e.g., from several tens of gauss to 400 G.

Discussion and Conclusions
In this study, we use the NVST and SDO observations to investigate 16 X-type magnetic reconnection events with wellidentified X-type configurations, and track the evolution of photospheric magnetic fields at the 38 footpoints of the reconnected structures among these events (some of the footpoint magnetic fields of the structures cannot be distinguished from the background ones).Prior to the occurrence of magnetic reconnection, the observations indicate that the convergence motion (with durations of 3-15 hr) of photospheric magnetic fields contributes to the accumulation of flux of the same polarity, resulting in the enhancement of the mean MFDs at the footpoints.Based on high-resolution observations, we have measured the unsigned mean MFDs of the 38 footpoints.The rates of increase of the MFDs during the converging period are 0.03-0.25 hr −1 (see Table 1), and the amplitudes increase by 40%-90%.During the reconnection process, the MFDs of the 38 footpoints are from 70 G to 300 G, and 60% of the MFD values are between 100 G and 200 G. Subsequently, the fields at the footpoints diffuse and weaken, and this evolution lasts for 2-10 hr.The rates of decrease of the MFDs are 0.03-0.18hr −1 , with the amplitudes decreasing by 30% to 60%.To our knowledge, the MFDs at the footpoints of reconnected structures are rarely studied.Recently, Xue et al. (2021) have reported one event about the enhancement of MFDs at the footpoints prior to the occurrence of magnetic reconnection.We reexamine this event, and measure the MFDs also.The two MFD values are similar.We understand that the HMI LOS magnetic field is a function of observing angle (location on the disk) and inclination angle of the magnetic vector (Schou et al. 2012).To reduce the magnetic field uncertainty, all the investigated footpoints are within 30°of the heliocentric angle.According to the observations, the increase or decrease in the footpoint MFDs in 72 hr manifests as the continuous converging or diffuse motions of the associated magnetic patches, indicating that the changes in the MFDs result from a real evolutionary trend rather than the alignment or inclination of the magnetic field lines with the LOS (Hoeksema et al. 2014;Schuck et al. 2016).
The photospheric flows will result in the deformation of atmospheric magnetic fields, e.g., shearing (twisting) magnetic field lines, and transfer energy to the fields (Roudier et al. 2008;Yamada et al. 2010;Liu & Schuck 2012;Vekstein 2016;Chintzoglou et al. 2019).As a result of the horizontal flows, Roudier et al. (2008) have revealed an increase in the shear below the point where the filament eruption starts and a decrease in shear after the eruption, and they conclude that the shear pumps the energy to the atmospheric structure.Largescale flows in the direction opposite to the differential rotation can create strong shear along the magnetic polarity inversion line of a filament channel, which influences the stability of the structure and contributes to the eruption of the filament (Roudier et al. 2018;Wollmann et al. 2020).
During convergence motion, more field lines from surrounding distributed fields are introduced into a local region.The contact and interaction of these field lines will enhance the complexity of the associated magnetic fields (Parker 1972;van Ballegooijen & Martens 1989;Török & Kliem 2005).Meanwhile, the fields become nonpotential and energetic (Shimizu et al. 2014).As revealed in previous studies, highly twisted (Rust & Kumar 1996;Titov & Démoulin 1999) or sheared (Bobra et al. 2008;Roudier et al. 2008;Wollmann et al. 2020) magnetic flux rope typically suggests strong complexity and nonpotentiality, as well as more free magnetic energy of the fields (Yamada et al. 2010).In this study, the sigmoid-like structure (Rust & Kumar 1996) in Figure 4  magnetic reconnection may be triggered easily in a nonpotential environment.
To estimate tentatively the magnetic energy accumulated during the convergence motion, we consider event 2 as an example.In this event, the two reconnected structures are simple, and the 3D magnetic fields corresponding to them are reconstructed (see L1 and L2 in Figure 2(a)).The magnetic free energy (B f ) can be calculated as (Schrijver 2007;Sun et  where E N , E P , B N , and B P denote the NLFFF energy, the potential field energy, the magnetic field strength from the NLFFF extrapolation, and the potential field strength, respectively. V represents the volume of the magnetic fields of the structures.We assume that the magnetic flux of the structure is a conserved quantity during the converging process, and the magnetic fluxes of L1 and L2 are estimated to be 8.23 × 10 17 Mx and 1.27 × 10 18 Mx, separately.We compute the total free energy B f1 of the two structures at 17:34:09 UT and B f2 at 20:34:09 UT.B f1 and B f2 are ∼2.29 × 10 26 and ∼5.47 × 10 26 erg, respectively, and the accumulated energy is ∼3.18 × 10 26 erg.Chromospheric fibrils are ubiquitous in the solar atmosphere (Vernazza et al. 1981;Tsiropoula et al. 2012).The interaction between the fibrils is inevitable and common (e.g., Yang et al. 2015;Ding et al. 2022;Yan et al. 2022).However, based on 10 yr (from 2012 October 1 to 2022 September 30) highresolution chromospheric data from the NVST, we detect fewer than 15 events with explicit X-type reconnection between the fibrils (Zhang et al. 2023).Such rare examples indicate that the occurrence of magnetic reconnection should satisfy several physical conditions, e.g., enlarged MFDs at the footpoints of atmospheric structures, enhanced nonpotentiality and complexity of magnetic fields, antiparallel magnetic field lines, etc. Certainly, it is also possible that we omit small-scale and lowenergy events because of the limited resolution of the instrument.
In summary, the analysis manifests that during the photospheric dynamical evolution process, the MFDs at the footpoints increase from a small value to a large one, and the complexity and nonpotentiality of corresponding atmospheric magnetic fields are gradually accumulated, as well as the free magnetic energy (Gary et al. 1987;Schrijver et al. 2005).While magnetic reconnection is triggered between two sets of antiparallel magnetic field lines, the stored magnetic energy is released and the topological connectivity is changed (Priest & Forbes 2000;Schrijver et al. 2005;Yamada et al. 2010;Sun et al. 2012).Eventually, the associated fields at the footpoints gradually diffuse and weaken.These results support the conjecture that magnetic reconnection releases the free magnetic energy stored in the nonpotential fields.To comprehend the nature of magnetic reconnection, more highresolution observations are necessary.

Figure 1 .
Figure 1.The X-type magnetic reconnection event on 2014 February 3 (event 1).Panels (a) and (i)-(k): the SDO/HMI LOS magnetograms.Panels (b) and (d): the NVST observations in the center of the Hα line.Panel (c): the SDO/AIA EUV image in 171 Å wavelength.Panels (e) and (f): EM (e) and temperature (f) maps derived from the DEM analysis method.The cyan square in panel (a), the green one in panel (b), and the red one in panel (c) outline the FOVs in panels (b)-(d), (i)-(k), and (e)-(f), separately.The red solid curves in panels (b) and (d) are the contours of the SDO/HMI LOS magnetograms at +400 G, and the blue ones in panels (b), (d), and (i)-(k) are the contours of the magnetograms at −400 G.The red and white dotted lines in panels (b), (e), and (f) display two independent atmospheric structures prior to the occurrence of magnetic reconnection, respectively, while the purple and cyan ones in panels (d)-(f) show the newly formed structures after the reconnection.The green rectangles in panels (c), (e), and (f) exhibit the current sheet.The red arrows in panels (i) and (k) represent the horizontal velocities obtained by the DAVE method.Panel (g): DEM distributions for the current sheet.The red curves are the optimum DEM distributions while the black curves are the results of 100 Monte Carlo simulations.Panel (h): the mean temperature curve of the current sheet.Panel (l): The unsigned mean MFDs of the fields associated with P1.The black solid histogram shows the measured MFD values, and the black dotted ones display the error bars.The vertical black, red, and green lines represent the times of panels (i)-(k), separately, and the MFD values of these lines are obtained within the areas circled by the dotted curves of corresponding colors.To display the relationship between the photospheric dynamical evolution and the occurrence of magnetic reconnection, an animation of the HMI/LOS magnetograms and the NVST Hα observations is available.The duration of this animation is 7 s.The first 2 s of the animation show a zoom from the full solar disk image to the green box region in panel (b), covering a duration from 2014 February 2 11:03:25 UT to 20:28:55 UT.The next 3 s display the photospheric field evolution associated with P1 from 2014 February 2 20:48:25 UT to 2014 February 3 07:12:25 UT.Then the FOV of the magnetograms enlarges from the green box region to the cyan box region in panel (b).At 5 s in the animation, the atmospheric structure corresponding to P1 is shown by red dashes, and the animation switches from the SDO/HMI LOS magnetograms to the NVST Hα observations superimposed with contours of the magnetogram (2014 February 3 07:12:25 UT).In the final 2 s of the animation, the FOV reduces to the red box region in panel (c) to highlight the change in connectivity of atmospheric structures, and this sequence runs from 2014 February 3 07:12:25 UT to 07:24:56 UT. (An animation of this figure is available.)

Figure 2 .
Figure 2. Similar to Figure 1, but for event 2 (2015 January 9).The red (L1) and white (L2) solid lines in panel (a) are the magnetic field lines from NLFFF extrapolation.An animation of the HMI/LOS magnetograms from 2015 January 9 12:07:54 UT to 2015 January 10 06:00:24 UT, showing the evolution of photospheric magnetic fields at the footpoint (P2) before and after reconnection, is available.The duration of this animation is 2 s. (An animation of this figure is available.) (a)).Figures 4(b)-(d) show the change in the topological connectivity of the atmospheric structures during the magnetic reconnection process, and Figures 4(e1)-(e4) display the photospheric magnetic field evolution at the footpoint P4.Prior to the occurrence of magnetic reconnection, the footpoint magnetic fields also experience the convergence and shear motions (Figure 4(e1)), which make the fields enhanced and complex.Moreover, the rotating motion of the associated fields is detected (Figures 4(e2)-(e4)), and lasts for around 7 hr with a rotation angle of 25°.7 hr −1 .Meanwhile, by checking the SDO/AIA EUV observations (Figures 4(f1)-(g4)), we can find that the feature of the corresponding atmospheric structure changes and deforms (an animation is available).Figures 5(a1)-(a4) display the magnetic fields of the footpoints relevant to events 1-4, respectively, with FOVs of 160″ × 160″.The red and blue dotted lines in each panel correspond to the reconnection structures mentioned above.Figures 5(b1)-(b4) show the footpoints of events 1-4 (P1, P2, and P3 are not included, as they have been displayed before and the corresponding MFDs have been obtained), and Figures 5(c1)-(c4) exhibit the unsigned MFD distributions of magnetic patches at the footpoints and of the selected FOVs.

Figure 3 .
Figure 3. Similar to Figure 1, but for event 3 (2019 November 1).The white solid lines in panel (a) are the magnetic field lines from NLFFF extrapolation.An animation of the HMI/LOS magnetograms from 2019 October 31 08:46:57 UT to 2019 November 1 13:32:41 UT, showing the evolution of photospheric magnetic fields at the footpoint (P3) before and after reconnection, is available.The duration of this animation is 2 s. (An animation of this figure is available.)

Figure 4 .
Figure 4.The evolution of the footpoint magnetic field and the deformation of the corresponding atmospheric structure.Panels (a) and (e1)-(e4): the SDO/HMI LOS magnetograms.Panels (b)-(d) and (f1)-(f4): the SDO/AIA EUV images in 171 Å wavelength.Panels (g1)-(g4): the SDO/AIA 304 Å images.The cyan square in panel (a) outlines the FOV in panels (b)-(d) and (f1)-(g4), and the green one in panel (b) the FOV in panels (e1)-(e4).The green dotted lines in panels (b), (f1)-(f4), and (g1)-(g4), and the white one in panel (b), display two independent atmospheric structures prior to the occurrence of magnetic reconnection, respectively, while the purple and cyan ones in panel (d) show the newly formed structures after the reconnection.The green rectangle in panel (c) exhibits the current sheet.The red arrows in panel (e1) represent the horizontal velocities obtained by the DAVE method.The cyan arrows in panels (e2)-(e4), the yellow one in panel (e3), and the pink one in panel (e4) are used to mark the rotating motion of the footpoint field.To exhibit the evolution of photospheric magnetic fields at the footpoint P4 and the deformation of the corresponding atmospheric structure, an animation of the HMI/LOS magnetograms (left panel, from 2016 February 6 06:04:09 UT to 20:02:39 UT) and the AIA 171 Å images (right panel, from 2016 February 6 13:20:10 UT to 20:20:10 UT) is available.The duration of this animation is 2 s. (An animation of this figure is available.) (b) (see the green dotted line) shows the nonpotential feature.Checking the magnetic field (see Figures 4(e1)-(e4)) and imaging observations (see Figures 4(f1)-(g4)), we find that the deformation of the structure is consistent with the field evolution at the footpoint (van Ballegooijen & Martens 1989;Chen et al. 2019).A statistical study has indicated that the occurrence of magnetic reconnection is more frequent in ARs with strongly nonpotential atmospheric fields(Schrijver et al. 2005), hinting that

Table 1
Lists of 16 X-type Magnetic Reconnection Events and Associated Measured Parameters Note.NAR = near an AR, FP = footpoint.