Preliminary Discussion on the Current Sheet

The current sheet is a characteristic structure of magnetic energy dissipation during the magnetic reconnection process. So far, the width and depth of the current sheet are still indefinite. Here we investigate 64 current sheets observed by four telescopes from 1999 to 2022, and all of them have been well identified in the previous literature. In each current sheet, three width values are obtained at the quartering points. Based on these investigated cases, we obtain 192 values, which are in a wide range from hundreds to tens of thousands of kilometers. By calculating the pixel width (PW: the ratio of the current sheet width to the pixel resolution of corresponding observed data) of these current sheets, we find that more than 80% of the PW values concentrate on 2–4 pixels, indicating that the widths of the current sheets are dependent strongly on the instrument resolutions and all the sheets have no observable three-dimensional information. To interpret this result, we suggest that there are two probabilities. One is that the width of the current sheet is smaller than the instrument resolution, and the other is that the detected current sheet is only a small segment of the real one. Furthermore, there is another possible scenario. The so-called current sheet is just an emission-enhanced region.


Introduction
Magnetic reconnection (Priest & Forbes 2000;Yamada et al. 2010) is a fundamental and efficient mechanism of magnetic field energy release in magnetized plasma systems (Spitkovsky 2006;Ripperda et al. 2020).In solar physics, it is widely accepted that this mechanism is associated with various activities, such as extreme-ultraviolet (EUV) brightenings (Su et al. 2013;Berghmans et al. 2021), jets (Shibata et al. 1992;Bučík et al. 2018), and coronal mass ejections (CMEs; Masuda et al. 1994;Green et al. 2018).According to the classical magnetic reconnection models (Parker 1957;Sweet 1958;Petschek 1964), two sets of antiparallel magnetic field lines approach each other, then break and reconnect within a current sheet, resulting in the change of topological connectivity (Yamada et al. 2010;Takasao et al. 2012;French et al. 2020).In this process, magnetic energy is rapidly released and converted to other forms, e.g., plasma thermal and kinetic energy (Aschwanden et al. 2017;Phan et al. 2020).
The "current sheet" is first proposed to be a thin sheet-or plane-like current structure (Giovanelli 1947).The scale, especially the width or thickness, of the current sheet is an important physical property describing the dynamical process of particles within the sheet (Sergeev et al. 1990;Siversky & Zharkova 2009;Yamada et al. 2010).The width can be obtained with imaging observations.Based on the Large Angle Spectroscopic Coronagraph (LASCO; Brueckner et al. 1995) onboard the Solar and Heliospheric Observatory (SOHO; Domingo et al. 1995), a narrow bright feature was observed behind a CME and interpreted as a current sheet (Ciaravella & Raymond 2008).The current sheet width was measured to be 30-60 Mm.As for a current sheet detected by the Hinode X-ray Telescope, its width is estimated to be 4-5 Mm (Savage et al. 2010).By using the EUV data from the Solar Dynamics Observatory (SDO; Pesnell et al. 2012)/Atmospheric Imaging Assembly (AIA; Lemen et al. 2012), a current sheet above a postflare arcade system was observed.To deduce the sheet width, Seaton et al. (2017) combined the algorithmic image processing and visual inspection, and yielded a range of 1.7-3.8Mm.Studies on some small-scale magnetic reconnection events have revealed that the widths of current sheets can be less than 1 Mm, e.g., 0.42 Mm (Yang et al. 2015)  EUV observations, a current sheet was detected, and a width range of 0.34-0.64Mm was obtained (Xue et al. 2018).
Although the current sheet in the magnetic reconnection process has been generally accepted in space science (Burch et al. 2016;Schwartz et al. 2021) and astrophysics (Ciaravella & Raymond 2008;Fleishman et al. 2020), the observable current sheets always exhibit a bright line-like structure instead of a sheet-like one.Up to now, some basic parameters about the current sheet, e.g., the width and depth, are indefinite and debatable.Moreover, we do not know the relation between the detected current sheet and the real one.Furthermore, the reconnection electric field property of the current sheet is still beyond our understanding.
In this study, by integrating the previous achievements related to the current sheet, we analyze 64 well-identified current sheets.These current sheets were detected by four instruments during 1999-2022, including 12 from SOHO, 48 from SDO, 2 from NVST, and 2 from IRIS (see Table 1).Based on the observation data from these instruments, the widths of these current sheets are obtained.Considering the difference in the pixel resolutions of data products, we propose a new parameter, i.e., pixel width (PW), defined as the ratio of the current sheet width to the pixel resolution of corresponding observations, to better describe the physical property of the current sheets.

Observations
The LASCO developed for the SOHO mission images the solar corona from 1.1 to 30 R e .The C2 is one of the three coronagraphs of the LASCO and covers the range from 2.3 to 6.0 R e .The spatial resolution is 11 9 pixel −1 , with a typical cadence of 12 minutes between frames (e.g., case 1 in Figure 2(a) and other cases observed by the LASCO in Table 1).The SDO/AIA obtains full-disk multiband EUV observations of the solar atmosphere, including 94,131,171,193,211,304, and 335 Å wavelength, with the spatial sampling and the time cadence of 0 6 pixel −1 and 12 s, respectively (e.g., case 2 in Figure 2(b) and other cases observed by the AIA in Table 1).The Hα observations taken in the center of 6562.8Å channel are obtained from the NVST.The highresolution Hα data of case 3 have a field of view (FOV) of 154″ × 154″, with a spatial resolution of 0″165 per pixel and a time cadence of 12 s.The IRIS provides imaging observations with the slit-jaw imager (SJI) instrument.Case 4 is exhibited with the SJI 1400 Å observations, which are taken with a pixel resolution of 0″33 and a cadence of 66 s.Other cases observed by the NVST and SJI can be found in Table 1.
To obtain sufficient samples for the study, we checked all of the published literature based on the data of the SOHO, SDO, NVST, and IRIS.The numbers of the literature associated with the SOHO/LACSO, SDO/AIA, NVST Hα, and IRIS/SJI are 2327, 3318, 233, and 943, respectively, and the publication dates are from 1995 December to 2023 August, from 2011 July to 2023 August, from 2014 October to 2023 August, and from 2014 March to 2023 August.

Results
The spherical grid graphs in Figures 1(a) and (b) denote the solar surface, and the 64 marks represent the projection locations of the centers of the current sheets during the magnetic reconnection process.The SOHO/LASCO cases (see the red "o" marks in Figure 1(a)) are located at 2.5-4 solar radii (R e ).On the other hand, the current sheets observed by the  Figure 2 exhibits four current sheets observed by the four devices mentioned above.The corresponding magnetic reconnection events take place on 2003 November 5 (case 1), 2012 January 1 (case 2), 2014 October 3 (case 3), and 2016 August 8 (case 4), separately.Case 1 is displayed with a SOHO/LASCO C2 image (Figure 2(a)).An elongated bright structure can be detected, and the red square outlines the position of the brightest region of the structure, which is represented as a current sheet.To measure the width of a current sheet, we make three perpendicular slits at the quartering points in the current sheet, e.g., cut1, cut2, and cut3 in Figure 2. The intensity distributions along the perpendicular slits are obtained, and a simple Gaussian fit of the normalized intensity is conducted.The FWHM of the Gaussian profile is calculated and considered as the width of the current sheet (see Figure 3).Based on 64 current sheet cases, we obtain 192 width values.The width values of the cases detected by the SOHO/LASCO, SDO/ AIA, NVST Hα, and IRIS/SJI are 15-45, 0.5-2.5, 0.4-0.5, and 0.5-0.8Mm, respectively (see Figure 4(a) and Table 1).By employing these obtained width values, we compute the PWs of these current sheets.From Figure 4(b), we notice that the PW values range from 1 to 5 pixels, and more than 80% of the values concentrate on a small range of 2-4 pixels.
To illustrate the current sheet structure, several schematic diagrams are exhibited in Figure 5.The blue and cyan curves denote the magnetic field lines, and the red thin sheet-like structures show the current sheet.The large-scale reconnection electric fields are based on the typical Sweet-Parker magnetic reconnection model (Parker 1957;Sweet 1958).The extent in the length (Y-axis) and depth directions (Z-axis) of the current sheet is larger than that in the width direction (X-axis).While the direction of the line of sight (LOS) is parallel to that of the electric fields (Z-axis), the current sheet presents an elongated line-like structure (see Figure 5(a)).While the LOS direction is vertical to the electric field one, the current sheet is expected as a broad sheet-like structure (see Figures 5(b)-(d) and the attached animation).

Discussion
In this work, we investigate 64 current sheets observed by four instruments, and the obtained widths of these current sheets are in a wide range from hundreds to tens of thousands of kilometers.Compared with the theoretical width of a current sheet, i.e., the proton Larmor radius, which is about tens of meters (Litvinenko 1996;Wood & Neukirch 2005), these obtained values are far larger than the theoretical one.By calculating the PWs of these current sheets, we find that most of the PW values are centered in 2-4 pixels, indicating that the widths of the current sheets are dependent strongly on the instrument resolutions.Therefore, it is possible that the real width of the current sheet is smaller than the instrument resolution.
As for the width of an observed current sheet, several physical factors will affect the obtained values, e.g., the thermal conduction front (Yokoyama & Shibata 2001;Takasao et al. 2015) and the plasmoids embedded in the current sheet (Innes et al. 2015).In the MHD simulation of a solar flare, Yokoyama & Shibata (2001) made a perpendicular slit across the reconnection region to obtain the one-dimensional current density and temperature plot.They found that the width of the hot region was broader than that of the current region, and this result has also been revealed by Takasao et al. (2015), indicating that the real current sheet is narrower than the observed bright structure.Among large aspect-ratio current sheets, the plasmoids have been detected within the sheets (Ciaravella & Raymond 2008;Guo et al. 2013).By employing the IRIS observations, combined with a simulation of magnetic reconnection, Innes et al. (2015) suggested that the occurrence   of the fast reconnection during small-scale events resulted from the instability of plasmoids.These plasmoids within current sheets may also manifest as a thick current sheet.
Solar magnetic fields are traced by kinds of atmospheric structures, e.g., chromospheric fibrils (Yang et al. 2015;Rutten et al. 2019), solar filaments (Li et al. 2016a;Joshi et al. 2023), and coronal loops (Su et al. 2013;Seaton et al. 2017).Under particular circumstances, the current sheets are generated between the atmospheric structures, which have antiparallel magnetic fields (Li et al. 2016b;Longcope et al. 2018;Ding et al. 2022).In the solar atmosphere, we cannot expect that the reconnection electric field directions of the current sheets are always parallel to the LOS one (e.g., Xue et al. 2020;Harden et al. 2021).If the electric field direction is vertical to the LOS one, the current sheet is expected to be a sheet-like structure (see Figures 5(b)-(d)).In the study of numerical simulation, Shiota et al. (2005) calculated three-dimensional views of a CME and the associated flare arcades.The calculated images indicate that the reconnection region also shows a sheet-like structure, while the electric field direction is vertical to the LOS one.However, by checking those investigated cases shown in Figure 1, we do not observe the sheet-like structure, and the current sheets always display a line-like structure (see Figure 5(a)).To interpret this result, several possibilities are proposed as follows.
One possible condition is that the included angle between the electric field direction of the observed current sheets and the LOS one is small enough, and thus the projection widths of the current sheets depend mainly on the narrow line-like region (e.g., Figure 5(a)).Furthermore, the observed current sheet is an emission-enhanced region (Chae et al. 2017;Patel et al. 2020), and the emission intensity is related to the plasma temperature or density (Plowman & Caspi 2020;Bemporad et al. 2022).For the region where the magnetic reconnection is violent, more plasma flows are introduced into the reconnection layer and more magnetic field energy is released to heat the plasmas (Mackay et al. 2010;Takasao et al. 2012), which contributes to a brightened region of strong emission (Humphries & Morgan 2021;Cheng et al. 2023).In other segments of the current sheet, however, the emission is weak and decays quickly (see Figures 5(a) and (b)).Due to the observation limitation of the instruments, only the strong emission region is detected, and the detected current sheet is a small segment of the real one.Certainly, the current sheet may be very thin except near an X-type neutral point (Giovanelli 1946(Giovanelli , 1948;;Dungey 1958), and the detector cannot observe the signal away from the X-point, as the increased emission of the thin segment of the current sheet is very weak.
In the reconnection region, the plasmas couple complexly with magnetic and electric fields (Yamada et al. 2010).At the X-point where the magnetic field is zero, the plasmas will be accelerated along the reconnection electric field (Kulsrud et al. 2005).We anticipate that some substructures related to the moving plasmas should be observed, e.g., the sawtooth structures in Figure 5(c).Nevertheless, no such structure has been detected yet (see Figure 6).Moreover, the reconnection electric field may be nonuniform within the current sheet, and the electric field intensity in the current sheet center is stronger than that on both ends of the sheet.At this condition, the current sheet must manifest as a shuttle-like structure (see Figure 5(d)).Unfortunately, this structure has not been observed either, indicating that the reconnection electric field property of the current sheet has not been demonstrated.
The consistently adopted evidence about a current sheet in observations is a bright structure between two sets of antiparallel magnetic field lines during their approaching and squeezing process in the solar atmosphere.Based on the achievement integration method, we reexamine 64 current sheets that have been well-identified in the previous literature over the past 24 yr.It is noteworthy that the PWs of these sheets are around 2-4 pixels, implying that these sheets have no observable three-dimensional information.To determine the properties of the bright structure, which is now considered as a current sheet, we suggest that two factors are indispensable.The first one is the three-dimensional characteristics, and the second is the reconnection electric field property.At the present stage, the observations can only tell us that the bright structure is only an emission-enhanced region in the solar atmosphere, and cannot confirm this structure as a current sheet.To comprehend the nature of the "current sheet" and the release of magnetic field energy, more higher resolution observations and dedicated laboratory experiments on magnetic reconnection are necessary.

Figure 1 .
Figure 1.Current sheets observed by four telescopes.The spherical grid graphs in panels (a) and (b) denote the solar surface.The red "o" marks in panel (a) represent the current sheets detected by the SOHO/LASCO, and the blue "×," green "+," and black " * " ones in panel (b) denote the current sheets observed by the SDO/AIA, NVST Hα, and IRIS/SJI, respectively.These marks indicate the projection locations of the centers of these current sheets.The three small black boxes in panel (b) outline the FOVs of cases 2-4 displayed in Figures 2(b)-(d), separately.
Figure 2(b) shows case 2 with an SDO/AIA 171 Å observation, and the current sheet is developed between two sets of atmospheric structures.Figure 2(c) (Figure 2(d)) is similar to Figure 2(b) but for case 3 (4) with an NVST Hα (an IRIS/SJI 1400 Å) image.

Figure 2 .
Figure 2. Four current sheets.Panel (a), the SOHO/LASCO C2 image.Panel (b), the SDO/AIA EUV data in 171 Å wavelength.Panel (c), the NVST observation in the center of the Hα line.Panel (d), the IRIS SJI 1400 Å image.The red rectangles in panels (a)-(d) denote the positions of the current sheets.The cut1, cut2, and cut3 are the perpendicular slits on the current sheets, and the widths of the sheets are measured at these slits.

Figure 3 .
Figure 3.The widths of cases 1-4.Panels (a1)-(d3), normalized intensities along the perpendicular slits (cut1, cut2, and cut3) in Figure 2. The black curves denote the results of the Gaussian fit of the intensities, and the blue lines represent the FWHM of Gaussian profiles.

Figure 4 .
Figure 4. Statistical properties of the current sheets.Panels (a) and (b), width (panel (a)) and PW (panel (b)) histograms of the current sheets.

Figure 5 .
Figure 5. Schematic diagrams illustrating the current sheet structure.Panels (a) and (b), reconnecting current sheets in which the electric field direction is parallel (panel (a)) and vertical (panel (b)) to the LOS one, respectively.The current sheets in panels (a) and (b) are based on the observed data and statistical results, and the gradient color of the current sheets corresponds to the intensity of plasma emission.Panels (c) and (d), similar to panel (b), but from anticipation.The substructures related to the moving plasmas form sawtooth structures (panel (c)), and the nonuniform electric fields contribute to a shuttle-like structure (panel (d)).To show the three-dimensional views of the observed sheet structure, an animation of a rotating sheet-like structure (see panels (a) and (b)) without the field lines is available.The duration of this animation is 1 s.(An animation of this figure is available.)

Figure 6 .
Figure 6.Emission intensities of current sheets (cases 1 and 4).Panel (a), the SOHO/LASCO C2 image.Panel (b), the IRIS SJI 1400 Å image.The X-and Y-axis in panels (c) and (d) represent the length and width directions of the current sheets, respectively.The mesh surfaces denote the normalized intensities (Z-axis) within the green rectangles in panels (a) and (b).
measured by employing the New Vacuum Solar Telescope (NVST; Liu et al. 2014) Hα images.Furthermore, based on the Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014)

Table 1
List of 64 Current Sheets and the Obtained Widths