First Determination in the Extended Corona of the 2D Thermal Evolution of a Current Sheet after a Solar Eruption

For the first time the evolution of the coronal reconfiguration after a coronal mass ejection (CME) was observed by the multichannel Metis Coronagraph on board the ESA–Solar Orbiter mission. The images acquired in visible light (VL) between 3.0 and 5.4 R ⊙ show the formation after a CME of a bright elongated radial feature interpreted as a post-CME current sheet (CS). The unique combination of VL and UV images allowed the time evolution of multiple plasma physical parameters inside and outside the CS region to be mapped in 2D for the first time. The CS electron temperature reached peak values higher than 1 MK, more than twice as high as the surrounding corona. An elongated vertical diffusion region, characterized as a region of much higher thermal pressure and lower magnetic pressure, is observed to slowly propagate outward during 13 hr of observations. Inside this region the Alfvénic Mach number is of the order of M A ≃ 0.02–0.11, the plasma β is close to unity, and the level of turbulence is higher than in the surrounding corona, but decreases slowly with time. All these results provide one of the most complete pictures of these features, and support the idea of a magnetic reconnection coupled with turbulence, thus allowing significant heating of the local plasma, despite the weakness of involved coronal magnetic fields in the considered altitude range.


Introduction
As originally pointed out by Lin & Forbes (2000), the catastrophic loss of equilibrium in a magnetic configuration including a current-carrying magnetic flux rope triggers a solar eruption that develops a solar flare, eruptive prominence, and coronal mass ejection (CME).Rapid thrusting of the flux rope as a result of the loss of equilibrium stretches the closed coronal magnetic field severely, and two magnetic fields of opposite polarity behind the flux rope move toward each other, producing a magnetically neutral region (called a current sheet, CS).Magnetic reconnection (MR) taking place inside the CS diffuses the magnetic field and converts the magnetic energy into heating and kinetic energy of plasma, as well as the nonthermal energy of the energetic particles accelerated by MR.In this process, the dynamic behavior of the CS is governed by two competing factors: disrupting magnetic field stretches the MR configuration outward, helping the CS develop, and MR tends to erode the CS.In principle, the timescale of the former is short compared to that of the latter in a realistic coronal environment.Therefore, a long CS could be expected in a major eruption (see detailed discussions of Lin 2002;Lin et al. 2003).
In addition to its great length, both observations and theories indicate that the CME-flare CS is also orders of magnitude thicker than expected (see, e.g., Lin et al. 2015;Lin & Ni 2018).Theoretical studies indicated that the tearing mode instability always occurs in a long CS (Furth et al. 1963;Priest & Forbes 2000), invoking the production of magnetic islands in the CS.Numerical experiments demonstrated that the MR inflow keeps squeezing the CS until turbulence is triggered by the tearing mode, and the turbulent structures in the CS offer extra pressure to balance the compression of the MR inflow (e.g., see Bárta et al. 2011;Shen et al. 2011;Mei et al. 2012;Ni et al. 2015;Takahashi et al. 2017;Ye et al. 2019).Observations confirmed that the CME-flare CS is apparently thick compared to the expectation in the framework of the classical theory about MR (see Lin et al. 2015;Lin & Ni 2018, and references therein).Therefore, the formation of a CME-flare CS is characterized by at least three important phases.First, a typical eruption develops a long CS connecting the CME to the associated flare; second, the CS formed in this way is fairly thick; and third, many structures of various sizes occur in the CS, which allows MR to take place at a reasonably fast rate even though the CS is very thick.
From the observational point of view, the evolution of post-CME CSs has been studied in a few cases in the inner corona with EUV spectrometers (e.g., Innes et al. 2003;Wang et al. 2007;Landi et al. 2012;Li et al. 2018;Warren et al. 2018), mostly because the study of these features requires the occurrence of a limb event observed off-limb in order to reduce as much as possible the complications in the analysis related to the line-of-sight integration effects.Thanks to spectroscopic observations, these works found that the elemental composition of CS plasma is similar to that of the surrounding corona, supporting the interpretation that the higher temperatures in the CS are due to the fact that the reconnection brings the magnetic field and the plasma into the CS from the surrounding corona, and that the plasma in the CS is heated locally by MR to high temperature.Hence, the highertemperature plasma detected in the corona is not entirely related to outflows from an MR site located at lower altitudes.Also, spectroscopic observations provided evidence for large nonthermal velocities, supporting the idea of MR coupled with plasma turbulence (see the review by Lazarian et al. 2015, for the role of turbulence in MR).
Many more CSs (mostly associated with flares and supraarcade downflows) have been studied in the inner corona with the analysis of EUV images acquired in different filters by disk imagers (e.g., Reeves & Golub 2011;Savage et al. 2012;Cheng et al. 2018;Chitta et al. 2021;Lu et al. 2022), and then combined with the so-called differential emission measure technique to get temperature measurements (see, e.g., Hannah & Kontar 2012, and references therein).Nevertheless, after the occurrence of the CME-flare phenomenon the MR is expected to proceed at rising altitudes, and hence the EUV observations can provide information only about the early phases of the post-CME-flare reconfiguration in the inner corona.Higher up, in the extended corona unique information has been obtained so far with classical visible light (VL) coronagraphs, which observed many post-CME CSs allowing even for statistical studies (Webb & Vourlidas 2016).These works (e.g., Lin et al. 2005;Vrsnak et al. 2009) demonstrate that post-CME CSs have an unexpectedly long lifetime (even a few days), are significantly broadened (see review by Lin et al. 2015), and are characterized by the propagation of plasmoids and blobs (Ko et al. 2003;Riley et al. 2007;Patel et al. 2020), a phenomenon likely related to the occurrence of plasmoidinduced fractal reconnection (Shibata & Tanuma 2001;Bárta et al. 2010).Thanks to the availability of observations from multiple viewpoints, a few post-CME CSs have been also studied in 3D (Patsourakos & Vourlidas 2011).
Interestingly, many of these features have been observed also by the UV Coronagraph Spectrometer (UVCS; Kohl et al. 1995) on board the Solar and Heliospheric Observatory (SOHO), the only UV spectrometer built over the last decades capable of observing the outer solar corona.The UVCS observations allowed us to discover that, unexpectedly, inside these features the plasma is heated to temperatures (up to ∼6 MK) usually never reached at the heliocentric distances (typically above 1.5 R e ) of observation (Ciaravella et al. 2002(Ciaravella et al. , 2003;;Bemporad et al. 2006).Thanks to UV data, this demonstrated unambiguously that some (but not all; see Ciaravella et al. 2013) of the radial features observed after CMEs in the VL coronagraphs are intrinsically different from the other stationary structures of the solar corona, and are associated with a physical process heating the coronal plasma for days after the transient event (Bemporad et al. 2006), most likely post-CME MR associated with plasma turbulence (Bemporad 2008).Nevertheless, given the limited field of view of the UVCS spectrometer, providing observations at fixed altitudes, it was impossible from these data to characterize the full thermodynamic evolution of the post-CME CSs, and to distinguish between spatial and temporal evolution.
These results are obtained in this work for the first time, thanks to the availability of multiwavelength imaging observations of a CS provided by Metis (Antonucci et al. 2020;Fineschi et al. 2020) that allowed us to study the time evolution of its physical parameters in 2D for the first time.In Section 2, the post-CME CS phenomena and the multichannel coronagraphs used in this work are described.Physical parameter distributions of the CS obtained from observations are shown in Section 3. The turbulence that occurred in the CS is analyzed in Section 4. Discussion and conclusions are given in Section 5.

Available Observations
As described in Bemporad et al. (2022), the event under study occurred on 2012 February 12-13 and was observed by many instruments, such as the Solar Orbiter (SO)/Metis and SOHO/Large Angle and Spectrometric Coronagraph Experiment (LASCO) C2 coronagraphs (Brueckner et al. 1995).On 2021 February 12-13 the SO spacecraft was at a heliocentric distance of 0.5 au, and the separation angle between the SO and Earth was around 161°.6.The Metis coronagraph provided 1024 × 1024 pix 2 VL images and 512 × 512 pix 2 UV Lyα images with spatial scales of 20 3 pix −1 and 40 8 pix −1 , respectively.The field of view (FoV) of the Metis coronagraph is from 3.0 to 5.4 R e .The LASCO C2 coronagraph on board SOHO has an FoV from 2.1 to 6.0 R e .
The Metis instrument observed a radial CS structure in both VL and UV channels after the CME that started on 2021 February 12; this event was not associated with any solar flare.Cyan arrows from the left to right panels of Figure 1 mark a faint CME front, a bright elongated CS, and a blob.In Figure 1, different panels show the base ratio images (normalized to the pre-event background at 12:30 UT on 2021 February 12) of Metis in the VL polarized-brightness (pB; top row) and UV Lyα (middle row), as well as the LASCO C2 total-brightness (tB; bottom row) images after subtraction of the monthly minimum background image.The CS first appeared at around 00:11 UT on 2021 February 13 in the LASCO FoV and lasted about 13 hr.As shown in the middle panels of Figure 1, the CS appears as an intensity enhancement in the pB image and a dimming in the UV Lyα image, which may be due to higher plasma temperatures along the CS and or to the so-called Doppler dimming effect caused by the higher radial speeds (Noci et al. 1987).A cut showing the VL and UV intensity distributions across the CS is provided in Bemporad et al.
(2022, see their Figure 8).With the elongation of the CS, a collimated plasma blob appeared in the Metis FoV on 2021 February 13 at around 6:35 UT to 10:00 UT, subsequently.The blob is relatively bright in both the VL and UV images and was also observed by LASCO coronagraph (right panels in Figure 1).
From a comparison between the VL and UV emission distributions across the blob, Bemporad et al. (2022) concluded that the emission in the UV Lyα line is mostly due to the collisional rather than radiative excitation of H atoms.Moreover, from the apparent different location of the blob in the VL and UV channels, it was inferred that the plasma temperature across the blob is not uniform, but is larger at the base of the blob and then decreases from the bottom to the top of the blob.The additional heating could be provided by magnetic reconnection that occurs just below the blob being responsible also for its observed acceleration (see Bemporad et al. 2022, for more details).Unlike other events reported in the literature, only one blob was observed propagating along the post-CME CS in this case.

Current Sheet Plasma Parameters
The determination of plasma physical parameters inside the CS requires the successive measurement of different quantities, such as the plasma velocities, densities, and temperatures; these are explained in the following subsections.

Current Sheet Plasma Kinematics
The unresolved small-scale outflow plasma motions along the CS cannot be tracked in the available images, hence this is usually done by tracking the motions of larger-scale plasma blobs propagating along the CS (e.g., Ko et al. 2003;Lin et al. 2005).Here, by tracking the positions of the blob observed in Metis UV and LASCO C2, the unprojected propagation speed of the blob along the CS can be calculated.The positions of the blob are determined from the locations of the peak values of the radial intensity profiles along the CS by Gaussian fitting.Temporal evolution of the blob positions as derived from Metis UV (blue triangles) and LASCO C2 (red circles) is shown in the left panel of Figure 2. The apparent average speeds are obtained by linear fitting of the positions at different observation times, which are (194 ± 4) km s −1 in Metis UV and (216 ± 4) km s −1 in LASCO C2.Due to the effect of projection on the plane of the sky (PoS), these speeds can be considered as the projected outflow speed of the CS plasma from different observational perspectives.Note that projection effects could also be responsible for the blob appearing to propagate nearby but outside the CS.As shown by the evolution of the CME flux rope, this CS was most likely oriented almost parallel to the line of sight, but the CS has a given thickness, and it is not expected to have a perfectly planar shape, hence different branches of the same CS could appear projected at different positions on the PoS, thus explaining the apparent propagation of the blob outside the CS.Combining the longitudes of two satellites, SO and SOHO, and their PoS in Carrington coordinates during this event, the unprojected speed and propagation longitude of the blob are determined as v out ; (219 ± 12) km s −1 and θ ; (150 ± 8)°, respectively (in agreement with previous measurements by Bemporad et al. 2022).
To measure the speed of inflows toward the CS we adopted the method commonly used in previous works (e.g., Vrsnak et al. 2009;Lu et al. 2022).In particular, we tracked the CS inflows, building a time-distance diagram as shown in the right panel of Figure 2. The time-distance diagram is composed of intensity slices extracted perpendicularly to the CS and taken from successive LASCO C2 running difference images.The inflow pattern can be clearly seen and is outlined by two yellow dashed lines.The inflow speed derived from the linear fitting of these two lines is v in ; (24.7 ± 0.5) km s −1 .It is worth noting that there is another feature in the time-distance diagram, which appears at around 08:00.It could be considered as the inflow, but after we compared the time-distance slice with the original LASCO data, we found that the feature was actually caused by a blob moving outward along an elongated structure, i.e., it corresponds to the outflow signature of the elongated structure.The elongated structure, seen in the LASCO C2 with the projection effect, is just below and is inclined to the CS we are interested in, so we exclude the false signal from our inflow measurement.
Once the inflow speed v in and outflow speed v out of the CS have been determined, by assuming that v out is representative of the local Alfvén speed v A , and that v in is representative of the inflow toward the reconnection region, the Alfvénic Mach number can be calculated as M A = v in /v out ; 0.11 ± 0.01.This is a very important parameter and is closely related to the reconnection rate and the local plasma magnetic diffusivity η (see, e.g., Lin & Forbes 2000) as v in = η/d for a CS with thickness d.
According to the existing magnetic reconnection theory of the CS, the formation of the blob is generally believed to be related to the development of tearing mode instabilities in the CS (Priest & Forbes 2000).For the tearing mode instability, the lower limit to the apparent value d min of the CS thickness can be expressed as (see Lin et al. 2015) where λ = 2π/k is the wavelength of the turbulence, k is the wavenumber, and α is a power exponent relating to different boundary conditions and different modes of the tearing (Pritchett et al. 1980;Priest 1985).The λ parameter is measured here from the Metis observation by assuming it to be comparable with the extent of the blob parallel to the CS (see Figure 19 in Lin et al. 2015).From the Metis UV image acquired at 8:22 UT (right panel in Figure 1), it turns out that λ ≈ (0.44 ± 0.04) R e using Gaussian fitting of the UV emission distribution.As we are going to show, if the value of d min is further assumed to be equal to the minimum value of the CS thickness measured from the pB and thermal pressure distribution perpendicular to the CS, then Equation (1) can be inverted to measure the α parameter.This can provide very interesting information about possible physical processes occurring in the CS; results will be discussed in Section 3.5.

Current Sheet Densities
The plasma densities inside the CS can be determined from the VL images.In general, the VL radiation in the corona comes from the contributions of the K-, F-, and E-coronas.The radiation mechanism of the K-corona is the Thompson scattering of photospheric light by free electrons, and this component is partially linearly polarized.On the other hand, the F-corona arises from the scattering of interplanetary dust, which can be assumed to be mostly unpolarized.The E-corona comes from the radiation of the coronal plasma emitted by atomic processes, mainly distributed at small heliocentric distances, usually less than 2 R e .Therefore, the pB emission observed by Metis can be assumed to come entirely from the K-corona.
According to the Thompson scattering theory, the pB intensity only depends on the integration of electron number density n e along the line of sight (LoS) and some scattering geometrical functions, which can be expressed as a function of the heliocentric distance r.The intensity I pB (ρ) of pB located at the projected distance ρ on the PoS is defined as the difference between the tangential K t and the radial polarization K r components of the K-corona (van de Hulst 1950;Billings 1966;Hayes et al. 2001): where C is a conversion coefficient,  and  are geometrical factors, and r = z r 2 2 represents the LoS coordinate.The electron number density of the corona near the CS is estimated from Metis VL by applying two different methods.One is based on the assumption of single-electron Thompson scattering (Quémerais & Lamy 2002).The total LoS-integrated intensity I pB can be expressed as an integral along the LoS of the single-electron scattering intensity I e times the electron number density n e , where 〈...〉 here denotes the average value along the LoS, and L (ρ) corresponds to LoS extent of the plasma emitting region at the distance ρ.From the above expression, given the singleelectron scattering intensity on the PoS (z = 0) and the plasma LoS extent L, the average number density can be estimated from the observed integrated intensity.
Another method is the so-called van de Hulst inversion technique (van de Hulst 1950), which assumes that the density is axisymmetric and can be expressed in polynomial form, n e (r) = ∑ k α k r − k .The density distribution can be obtained by substituting the polynomial expression for n e into Equation (2) and by fitting it with the observed pB intensities.Fitting results are more robust by taking the form of a fourth-order polynomial (k = 1-4) (Hayes et al. 2001).
Here we combined the above two methods to take into account the fact that, unlike in the nearby corona, in the CS the plasma is expected to be more concentrated on the PoS and not significantly extended along the LoS, hence the pB inversion technique assuming an axisymmetric distribution is no longer applicable in this region.Hence, we first determined the radial distribution of density in the nearby corona with the standard inversion technique.Then, by using Equation (3) we derived the function L(ρ), providing the average depth along the LoS of the emitting plasma as a function of the projected distance ρ.Finally, we assumed the same function L(ρ) to hold not only in the nearby corona, but also inside the CS, and derived pixelby-pixel the quantity 〈n e 〉 based on Equation (3) from the observed pB values.This method (different from the standard van de Hulst inversion technique) allowed us to derive in each image the 2D density distribution pixel-by-pixel, thus preserving possible inhomogeneities in the radial direction (which would be washed out by the standard inversion method).The derived values of L(ρ) in the Metis FoV range from L = (3.15± 0.09) R e at ρ = 3.0 R e up to L = (6.14 ± 0.44) R e at ρ = 5.4 R e ; these uncertainties on L have been propagated following the standard error theory in the rest of the analysis.
The resulting temporal evolution of the 2D distribution of the electron number densities inside the CS and in the nearby corona is shown in Figure 3. Similar to the pB images, the narrow and elongated CS structure can be clearly seen, with higher electron number densities than near the corona.In particular, in Figure 4 the left panel shows the density profiles extracted perpendicular to the CS at the heliocentric distance of 4.0 R e with different colors for different times, and the right panel is the profile along and inside the CS observed at 6:30 UT.Pink and blue shadows represent measurement errors, originating from the uncertainty of LoS estimation.The peak of densities inside the CS at 4.0 R e reaches over 1.5 × 10 5 cm −3 at 8:30 UT.The radial profile of densities along the CS shows a decrease from 3.0 × 10 5 cm −3 at 3 R e to 6.0 × 10 4 cm −3 at 5.5 R e , a trend similar to that of the nearby corona.As a reference, the radial profile of the coronal density derived by Gibson et al. (1999) in coronal streamers is shown in the right panel, represented by a blue line.
Interestingly, the 2D density maps (Figure 3) and 1D density profiles (Figure 4) show that in the first 6 hr after the CME the CS is elongating from the lower to the higher altitudes, and in these first phases the CS becomes approximately twice as dense as the surrounding corona.Then, after reaching the peak density at 08:30 UT, it starts to become thinner and thinner with time.The densities both in the CS and in the nearby corona decrease with time, but the contrast in CS density with respect to the nearby corona remains approximately the same, suggesting that the plasma compression going on inside the CS is approximately the same at different times.This evolution is better quantified later on in this work.

Current Sheet Temperatures
The VL and UV images provided by Metis can be combined to derive, under some assumptions, the 2D distribution of solar wind speeds on the PoS by taking into account the LoS integration across the optically thin coronal plasma.This method, called the full-inversion Doppler dimming technique,   Gibson et al. (1999).
is based on the Doppler dimming process (Withbroe et al. 1982;Noci et al. 1987) and mainly starts from the measurements of the plasma density derived from VL with van de Hulst inversion to synthesize the expected UV Lyα intensity without outflows, and then adjusts the outflow speed to get an agreement between the observed and the synthesized UV emissions (see Dolei et al. 2018, 2019, andreferences therein).This method is currently applied to Metis data to measure the outflow speed in large-scale coronal features, such as streamers (Romoli et al. 2021) and coronal holes (Telloni et al. 2023).A second method, called the quick-inversion Doppler dimming technique (first proposed by Withbroe et al. 1982), takes the direct ratio between the VL and UV images by assuming that the LoS density distribution (which is the main plasma physical quantity varying along the LoS) simplifies in the ratio, and then adjusts the outflow speed to find an agreement with the observed ratio.This method was tested successfully with the combined analysis of UVCS and LASCO observations of the solar wind (Bemporad 2017), with numerical MHD simulations (Bemporad et al. 2021), and was also applied to the observations of a CME (Bemporad 2022).
The main difference is that the first method requires a predetermination of the plasma densities, while the second one is independent of the density measurements.Because, as mentioned, the coronal densities are usually derived under the assumption of an axisymmetric distribution, and because this assumption cannot be applied during and after CMEs, the quick-inversion method is more suitable for the analysis of impulsive/transient phenomena.Moreover, this method, which is usually employed to measure the solar wind speed after the assumption of coronal plasma temperatures (Bemporad 2017;Bemporad et al. 2021), is more suitable to be adapted for the analysis of transients whose speeds are more easily derived from the sequence of coronagraphic images, thus allowing one to measure the plasma temperatures inside these transients (see Bemporad 2022).For these reasons, here the CS plasma temperatures have been derived with the quick-inversion technique briefly summarized below.
Under the assumption that the observed Lyα is entirely due to resonant scattering of chromospheric emission centered at wavelength λ 0 , and by assuming that the main plasma physical quantity varying along the LOS is the electron density n e , the total intensity ( ) r I res of UV Lyα images at the projected distance ρ on the POS can be written as In the above expression H res is a constant quantity, K res contains the H ionization fraction R H [T e (ρ)] related to the electron temperature T e , and D(V 0 ) is the Doppler dimming coefficient related to the outflow speed V 0 and given by where σ disk and σ cor are the 1/e half-widths of the chromospheric and coronal excitation and absorption profiles.By simplifying also Equation (2), the total VL intensity I pB (ρ) can be written as where H pB is a constant quantity and K pB is a geometric factor.
Combining the expressions in Equations ( 4) and (6), the H ionization fraction R H can be expressed explicitly as between the UV and VL intensities.
To do this pixel-by-pixel and exposure-by-exposure, the Metis UV images have been rescaled to the VL size, hence from 512 × 512 pix 2 to 1024 × 1024 pix 2 , coaligned with pB images to the same location of the center of the Sun, and averaged with the same time cadence.The temperature distribution of the CS and nearby corona have been derived from the Metis VL and UV image ratios by further assuming a uniform speed distribution equal to the outflow speed of the blob.Figure 5 shows the resulting temporal evolution of the 2D distribution of the electron temperatures.Narrow and hightemperature CS structures can be seen to form in the observed distance range between 3.0 and 5.5 R e .Similar to Figure 4, Figure 6 shows the temperature profiles perpendicular (left panel) and parallel (right panel) to the CS.The error represented by shadows in the figure is mainly due to the uncertainty in measuring the solar wind speed.As a reference, the radial profile of the coronal temperature derived by Gibson et al. (1999) in coronal streamers by assuming hydrostatic equilibrium is shown in the right panel, represented by a red line.
Results show for the first time that a higher-temperature region gradually evolves in the post-CME corona, moving up from the inner to the outer regions, with the formation of a fanshaped feature that can be seen around 9:30 UT.During the observation interval the measured peak temperature inside the CS first increases and then decreases with time.The electron temperature along the CS reached up to 10 6 K, which is lower than the typical temperatures measured by previous authors inside post-CME CSs, but still significantly higher by almost a factor of 2 than typical values expected for the surrounding corona at these heliocentric distances, as shown by the comparison with the reference profile of Gibson et al. (1999).
Because we have only a few exposures with the blob falling inside the Metis coronagraph FoV, we had to assume a constant value of v out = v A with height all along the observed CS.Moreover, the standard Doppler dimming technique (Dolei et al. 2018) cannot be applied here to measure the outflow speed, because the post-CME coronal temperatures are also unknown.Hence, there is no way to measure the outflow speed   Gibson et al. (1999).
in the post-CME corona near the CS, and we can only place constraints.For these reasons, the velocity distribution of the CS and the post-CME environment surrounding the CS is assumed to be equal to the outflow speed of the blob and uniformly distributed.Statistically, the post-CME speed is expected to be smaller than the measured speed of the CME front of ∼250 km s −1 , as we derived from a comparison between the speeds of the CME core and front measured in a series of slow CME events reported by Ying et al. (2023).We obtained that on average the ratio between these two speeds is between 0.3 and 1.5 in a distance range between 1.7 and 3 R e .Thus, considering the speed of the CME core as an upper limit for the post-CME plasma speed, it is reasonable to assume, at least for this event, that the speed of the post-CME corona is similar to the CS velocity, with a ratio between the post-CME speed and the speed of the CME front around 0.86, hence in the above range.

Thermal and Magnetic Pressures
Once the 2D distributions of the electron number density n e and temperature T e of the CS are obtained, we can derive the distribution of plasma thermal pressure P th .For a fully ionized hydrogen plasma (n e ; n p , hence n = 2n e ) in a thermal equilibrium (T e = T p ) the thermal pressure is given by where k B (erg K −1 ) is the Boltzmann constant.Notice that the thermal equilibrium hypothesis does not necessarily hold in the solar corona in the observed altitude range (see, e.g., Kohl et al. 2006), but since we are unable to measure the temperatures of the two species, it is the only possible hypothesis here.Figure 7 shows the evolution of the thermal pressure distribution of the CS with time, while profiles of P th across and along the CS are displayed in Figure 8 (left and right panels, respectively).The peak of thermal pressure inside the CS first increases and then decreases, reaching the value of 4 × 10 −5 dyn cm −2 .In the radial direction, the thermal pressure in the CS decreases from 1.0 × 10 −4 to 1.5 × 10 −5 dyn cm −2 with increasing heliocentric distance.
Considering the CS as a stationary feature and applying the same analysis as performed by Susino et al. (2013), it is possible to assume a balance between the total plasma pressure (P tot ) inside and outside the CS, with P tot given by the sum of the thermal (P th ) and magnetic (P mag ) pressures, hence where B is magnetic field strength and μ is the plasma magnetic permeability.The magnetic field inside the macroscopic CS structure can be measured by assuming that the outflow speed of the blob is locally equal to the Alfvén speed v A in the ambient surrounding plasma that is being reconnected in multiple small-scale regions (see Bemporad 2008), hence Once the magnetic field strength inside the CS is obtained, the magnetic pressure and total pressure inside the CS can be calculated.Based on the assumption of pressure balance, and given the thermal pressure outside the CS, the distributions of magnetic pressure and magnetic field strength outside the CS can also be obtained from Equation (10).Notice that, because in this work we assumed an Alfvén speed v out = v A constant with height inside the CS, the combination of the above two equations provides plasma temperatures roughly inversely proportional to the measured density n e , in agreement with the fact that the temperature due to reconnection does not depend on the magnetic field alone, but also on the ratio of magnetic energy density to particle density.In the CS, the time evolution of temperatures will also be related to possible other (i.e., not associated with reconnection events) thermal energy gains (e.g., by propagating waves or thermal conduction) and losses (e.g., by thermal conduction and radiative cooling), but the lack of further information on the CS plasma conditions prevents us from quantifying these processes.
The resulting temporal evolution of the magnetic field distribution is shown in Figure 9, while Figure 10 shows the profiles of the magnetic field perpendicular to the CS at 4.0 R e at different times (left panel), and the radial profiles extracted along the CS and near the corona (right panel).The red line represents the reference profile of coronal magnetic fields derived by Dulk & McLean (1978), used by many authors as a reference profile for coronal magnetic field values.As expected, the magnetic field strength is lower inside the CS than outside, due to magnetic field dissipation via MR.Minimum values inside the CS decrease with time from around 0.04 G to 0.035 G.In the radial direction the magnetic field decreases inside and outside the CS with increasing heliocentric distance from around 0.06 G to 0.025 G and from 0.08 G to 0.03 G, respectively.The values we measured in the nearby corona are lower than those provided by Dulk & McLean (1978), but the radial trend is very similar; the difference could be due to the transit of the CME, which evacuated most of the pre-CME corona.To our knowledge, this is the first time that 2D maps of magnetic fields inside and outside a post-CME CS have been derived from observations.Furthermore, from the thermal and magnetic pressures the plasma β parameter can also be estimated as The temporal evolution of the 2D distribution and radial profiles of β are shown in Figures 11 and 12, respectively.It can be seen that the higher-temperature region has a higher plasma beta than nearby corona, which is close to 1 inside the CS but is below 0.2 outside.Later on, when the highertemperature region leaves the instrument's FoV, the plasma β starts to settle down to more typical coronal values.These results indicate that the thermal pressure inside the diffusion region (DR) is comparable with the magnetic pressure, while in the nearby corona the magnetic pressure dominates.This also supports the detection of turbulence inside the CS found by previous authors (e.g., Bemporad 2008;Ye et al. 2019) and also found here (see below).

Current Sheet Thickness
The apparent thickness of the CS is always an important parameter in CS research, not only in observations but also in simulations.This parameter is usually measured from the width of bright radial features observed in the VL coronagraphs.Nevertheless, this method could provide an overestimate of the real thickness of the actual DR, not only because of projection effects, but also because the extent of the DR is not necessarily  coincident with the extent of the higher-density region (see discussion by Lin et al. 2015, and references therein).A better estimate at least of what is called the "thermal halo" around the DR (i.e., the region where the thermal energy is diffused by the thermal conduction; see, e.g., Seaton & Forbes 2009;Reeves et al. 2010) can be obtained from the extent of the region of higher temperature or of higher thermal pressure perpendicular to the CS (Figure 8), as was done in previous works (Ciaravella et al. 2003;Bemporad et al. 2006;Susino et al. 2013) and is also done here.
In particular, by Gaussian fitting the profiles of pB and thermal pressure in the direction perpendicular to the CS we measured the FWHM of the CS at different times, and the results are shown in Figure 13.As mentioned above, during the observation sequence one blob appeared in the FoV of Metis, so the FWHM measurement results do not include frames with blobs.Blue and red lines represent the FWHM fitting results from pB and thermal pressure, respectively, which have consistent evolutionary trends.It can be seen that the width of the CS decreases with time, from around 0.2 to 0.08 R e .Under the assumption of the development of tearing instability in the CS, it is possible now to combine the measured blob size (assumed representative of the wavelength of turbulence λ) and the Alfvénic Mach number M A to obtain the value of α in Equation (1).which means that fluctuations in the direction perpendicular to the CS are small (Lin et al. 2015).
Figure 13 also marks the narrowing speed at different times obtained by linear fitting the FWHM evolution, with an average   9, while the red line shows the radial profile of coronal magnetic fields derived by Dulk & McLean (1978).
value of v narrow = (3.88 ± 0.65) km s −1 .This value can be considered as a lower limit for the reconnection inflow speed.Combining it with the measured outflow speed v out of the blob, we estimate the lower limit of Alfvénic Mach number as M A = v narrow /v out ; 0.02 ± 0.006.With this value of the Alfvénic Mach number and the other quantities above, it turns out that α ; 0.14 ; 1/7, in agreement with the lower limit expected for this parameter for a CS with a periodic internal structure (see Lin et al. 2015, and reference therein).

Turbulence in the Current Sheet
Following the analysis previously performed by Cheng et al. (2018) for another event, the turbulence in the CS is analyzed here by applying a fast Fourier transform (FFT) to the radial intensity profiles of Metis VL (tB), UV (Lyα), and electron temperature (T e ) along the CS. Figure 14 shows the results of this analysis.The above-mentioned profiles are extracted along the CS in the region denoted by white dotted lines in Figures 14(A) and (B).Second, the profiles are detrended with a moving interval of 0.2 R e in order to eliminate their characteristic decrease with heliocentric distance, and are normalized to the range of intensity variation of [−1.0, 1.0] (Figures 14(C) and (D)).Third, power spectra of   Using the same processing method, the spectral indices along the CS were obtained at different times.Figure 15 shows the temporal evolution in the power spectral indices along the CS.Black and red solid lines represent the power indices derived from Metis VL (tB) and UV (Lyα), respectively, inside the CS, while the blue line represents the power indices derived from the spatial distribution of the electron temperature.The black and red dashed lines also show the power indices of the reference pre-CME quiet corona outside the CS from Metis VL (tB) and UV (Lyα), respectively, providing a reference for any kind of spurious fluctuation or noise not representative of the CS plasma turbulence.The reference Kolmogorov's value of 5/3 is also marked in Figure 15 as the dotted line.Interestingly, Figure 15 shows that the power indices of VL and UV have the same evolutionary trend, becoming first larger than the reference coronal value and then decreasing to it.
Fluctuations of VL are mapping the density fluctuations related with plasma turbulence, and the resulting evolution of the spectral index can be interpreted as turbulence evolving from inhomogeneous (∼2) to homogeneous (∼5/3).The interpretation of fluctuations in the UV is much more complex because these are due in principle to density, temperature, and nonthermal velocity fluctuations all integrated together.Hence, it is reasonable that the measured power spectral indices from UV are always higher than those from VL, ranging between ∼2.2 and ∼3.3.Moreover in the UV the power spectral indices are larger than the reference corona for a much longer time interval.
It is also very interesting to notice that the temporal evolution of fluctuations in the electron temperatures has a trend similar to that of VL fluctuations (increasing and then decreasing), but the evolution is delayed by approximately 3-4 hr.This is in agreement with the idea that the turbulence helps the diffusion of the magnetic field, and hence increases the heating rate in the CS.

Discussion and Conclusions
As mentioned in the introduction, it is still unclear what is the large-scale evolution in the post-CME CS and how this is related to the unresolved smaller scales where the magnetic reconnections are occurring.Some previous works (Vrsnak et al. 2009;Ko et al. 2010) explained the evolution observed in the VL coronagraphic images and UV spectroscopic observations in the extended corona by assuming that the observed plasma is almost entirely accelerated by a Petshecktype MR region located in the inner corona and then, flowing outward at higher altitudes, is observed in the outer corona.On the other hand, Bemporad (2008) argued that the hightemperature plasma observed in the outer corona could be heated locally in an MR process strongly coupled with turbulence and occurring in multiple small-scale CSs, and resulting in the macroscopic feature observed remotely.Also, Susino et al. (2013) showed that for a specific event the decay of the soft X-ray source located at the top of the post-eruption arcades (likely where the Petsheck-type MR is going on) is not compatible with the much longer lifetime of the hightemperature source observed higher up in the extended corona by UVCS.
Here, thanks to the unique observations acquired by the Metis coronagraph in the VL and UV channels, we were able to infer the 2D time evolution of many fundamental plasma physical parameters (density, temperature, magnetic fields) and also other important plasma quantities (plasma β, Alfvénic Mach number, level of turbulence), providing a full picture of the physical evolution of a post-CME CS.All these quantities and parameters have been measured here at a range of heliocentric distances (between 3 and 5.5 R e ) where these features have never been studied previously.After the CME transit and the standard formation in the VL of a vertically extended and bright feature aligned with the CME, results found here show the transit of an extended higher-temperature region moving slowly outward over 9 hr of observations.This region (which can be interpreted as the DR where the magnetic field is dissipated via reconnection) enters the instrument's FoV at 3 R e around 02:30 UT and leaves it at 5.5 R e around 10:30 UT.Considering that the top of this region appears to propagate at around 120 km s −1 , this corresponds to a vertical extent of this DR of the order of 2.5 R e .As we showed here, inside this vertically extended DR not only are the temperatures about a factor of 2 higher than in the plasma in the surrounding corona, but also the level of turbulence is higher and the turbulence evolves from inhomogeneous to homogeneous.This is suggesting that in the initial phase of formation of the DR the coronal magnetic field dragged by the inflows inside the CS is responsible for the formation of blobs and plasmoids that are moving mostly in a direction parallel to the vertical axis of the post-CME CS, leading to anisotropic turbulence.This is in agreement for instance with the numerical simulations by Ye et al. (2019), and it is also supported here by the value we estimated for the α parameter, which is more representative of a situation where fluctuations in the direction perpendicular to the CS are small.Hence, as also suggested by Cheng et al. (2018), in the initial phases of formation of the DR the magnetic field plays a role in keeping the turbulence at inhomogeneous levels.Nevertheless, later on, as the DR evolves, the turbulence also appears to evolve, becoming more isotropic closer to the coronal reference value.This implies that fluctuations become significant also in the direction perpendicular to the CS, and this is likely the reason why these features appear much broader than expected.This result has never been observed before and never predicted in previous MHD simulations.
The derived physical parameter distributions of the CS were also compared with the results of MHD simulations.One is 3D MHD simulation of prominence-forming coronal flux ropes in spherical geometry by Fan & Liu (2019), taking account of nonadiabatic effects of empirical coronal heating, optically thin radiative cooling, and the field-aligned electron heat conduction.Another one is the 2.5D MHD simulation of magnetic flux-rope formation and eruption by Zhao et al. (2019), considering the effects of radiative cooling, anisotropic thermal conduction along the magnetic field, gravitational stratification, resistivity, and viscosity.The altitude ranges of the simulations are 1.3-1.7 R e and 0.03-0.07R e , respectively.Due to the simulated FoV being smaller than the observation of the CS in this event, only qualitative comparisons are made on the parameter profiles.It can be found that the peaks or valleys in the temperature values across the CS are smoother than in simulations.The reason may be due to LOS integration, CS inclination, and limited instrumental spatial resolution.Nevertheless, the general trend of our profiles is consistent with the MHD simulation.

Figure 1 .
Figure 1.Observations of the CME front (left column), formation of the post-CME CS (middle column), and propagation of the blob (right column) as obtained by Metis pB (top row) and UV (middle row), and LASCO C2 (bottom row) from different perspectives.The top and middle rows show Metis base ratio images, while the bottom row shows the LASCO C2 images after subtraction of the monthly minimum background.Dashed lines and cross symbols indicate the edge and the center of the Sun, respectively.

Figure 2 .
Figure 2. Temporal evolutions of the plasma inflow and outflow of the CS.Left panel: apparent positions of the blob derived from Metis UV (blue) and LASCO C2 (red) by Gaussian fitting.Right panel: the time-distance diagram across the CS derived from LASCO C2.Yellow dashed lines denote the CS inflows.Projected outflow speeds of the blob and the plasma inflow speeds are marked in the panels, which are obtained by linear fitting.

Figure 3 .
Figure 3. Temporal evolution of the 2D distribution of the electron number densities inside the CS and near the corona in the Metis FoV.

Figure 4 .
Figure 4. Time evolution of density profiles.Left panel: profiles extracted perpendicular to the CS at 4.0 R e with different colors for different times.Right panel: density profiles along the CS (black) and in the nearby corona (blue) as measured at 6:30 UT at the locations shown by the two dashed lines in the middle left panel of Figure 3. Colored shadows represent the uncertainties.The red line represents the reference radial profile of the coronal densities derived byGibson et al. (1999).

Figure 5 .
Figure 5. Temporal evolution of the 2D distribution of the CS electron temperature obtained by the pixel-by-pixel quick-inversion method applied to observations of Metis pB and UV.

Figure 6 .
Figure 6.Left panel: profiles of the electron temperature across the CS at 4.0 R e colored by the different observation times.Right panel: temperature profiles along the CS (black) and in the nearby corona (blue) as measured at 6:30 UT at the locations shown by the two dashed lines in the middle left panel of Figure 5.The red line represents the reference radial profile of the coronal temperatures derived byGibson et al. (1999).

Figure 7 .
Figure 7. Temporal evolution of the 2D distribution of the CS thermal pressure derived from the distributions of electron temperature and number density.

Figure 8 .
Figure 8. Profiles of the thermal pressure across the CS (left panel) at 4.0 R e plotted with different colors for different observation times, and at different altitudes (right panel) at 6:30 UT.In the right panel, the thermal pressure profiles are extracted inside the CS (black) and in the nearby corona (blue) at the locations shown by the two dashed lines in the middle left panel of Figure 7.
with λ = 0.44 R e and M A = 0.11, it turns out that

Figure 9 .
Figure 9. Temporal evolution of the 2D distribution of the CS magnetic field derived with the assumption of pressure balance.

Figure 10 .
Figure10.Left panel: profiles of the magnetic field across the CS at 4.0 R e colored with different observation times.Right panel: black and blue lines indicate the magnetic field profiles inside the CS and near the corona at 6:30 UT, respectively, at the locations shown by the two dashed lines in the top left panel of Figure9, while the red line shows the radial profile of coronal magnetic fields derived byDulk & McLean (1978).

Figure 11 .
Figure 11.Temporal evolution of the 2D distribution of the CS plasma β derived from the thermal and magnetic pressure distributions.

Figure 12 .
Figure 12.Profiles of the plasma beta across the CS (left panel) at 4.0 R e colored with different observation times, and along the CS (right panel) at 6:30 UT.

Figure 13 .
Figure 13.Temporal evolution of the CS thickness derived from profiles of the Metis pB (blue line) and thermal pressure (red line) fitted by a Gaussian function.Narrowing speeds obtained by linear fitting are marked in the panel.

Figure 15 .
Figure 15.Temporal evolution of the power spectral indices derived from Metis VL tB (black solid line), UV Lyα (red line), and electron temperature (blue line) along the CS using the FFT method.Black and red dashed lines indicate respectively the VL and UV indices of the pre-CME quiet corona.The Kolmogorov's reference value of 5/3 is denoted by the black dotted line.