High-altitude Spider-type Prominence above the Magnetic Null Point

Rather unique observations of a high-altitude spider-type prominence in 2023 February are presented. The prominence or corresponding filament on the disk was not visible all the time but could appear and disappear in the course of a particular day. However, it persisted during the whole half of a solar rotation, being observable from day to day starting from the east limb of the Sun to the west limb. We show that the prominence was located in sagged coronal field lines just above a coronal magnetic null point. The presence of the null point and magnetic dips above it is confirmed by calculations of the potential magnetic field. The mass of the prominence apparently was appearing due to the condensation of hot coronal plasma after several eruptions that occurred in an active-region complex where the prominence was located. The prominence material flowed down along widely spread large coronal loops as coronal rain and was sometimes swept away by subsequent eruptions.


Introduction
Most prominences could be observed on the disk as dark filaments.They are referred to as "channel prominences" (Martin 2015) because they are located within filament channels along large-scale polarity inversion lines (PILs).Channel prominences usually have distinct features such as spines extended along PILs and barbs protruding from the main body of a prominence and connecting it to the chromosphere.Some prominences are located within active regions adjacent to sunspots.On the limb, they hardly rise above the upper fringe of the chromosphere, so it is more correct to refer to them as active-region filaments because they are observed mostly on the disk (Schmieder 1989).Quiescent prominences have larger size compared to active-region prominences and looser, more diffuse structure (Rompolt 1990).They are more commonly observed in high latitude regions, at latitudes 50° ( Engvold 2015).However, they can also develop at low latitudes or be a global structure occupying both northern and southern hemispheres.There can also be distinguished intermediate-type prominences, which to some extent have the properties of both active-region and quiescent prominences (Martin 1998).Dozens of prominences and filaments exist simultaneously in periods of solar maximum.They may be observed in less numbers at solar minimum too (Zou et al. 2014;Hao et al. 2015).
Quite different from channel prominences are coronal cloud prominences and coronal rain, which are less dense and fainter than channel prominences and recognized mostly above the limb since they are too weak to absorb the background emission to be observable against the disk (Engvold 1976;Stenborg et al. 2008;Martin et al. 2016).Coronal cloud prominences are composed of rarefied cool material suspended up to 200 Mm in the corona.They are also termed as coronal spiders due to their characteristic shapes or funnel prominences because of a characteristic V-shaped structure (Allen et al. 1998;Liu et al. 2012).Coronal cloud prominences have never been observed erupting.Instead, they shrink and disappear within less than a day by drainage along curved trajectories at nearly the freefall speed resembling coronal rain.There is no evidence that coronal cloud prominences are associated with PILs (Engvold 2015).
Highly conductive prominence plasma can rest in a "hammock" formed by concave, upward magnetic field lines, which prevents the matter from dropping into the chromosphere.The upward curvature of the field lines creates conditions for a stable equilibrium.For the first time, such a model for prominence equilibrium was suggested by Menzel (1951).In 1957, Kippenhahn & Schlüter (1957) developed a model, which has become "classical" for many years and universally recognized despite certain difficulties that are unable to be solved.If all significant field sources are located under the photosphere (the field in the corona is potential), sagged field lines can exist only near saddle singular points.For their appearance, at least a quadrupolar magnetic configuration is necessary.Such geometry is often used as a probable magnetic "skeleton" of a prominence (Malherbe & Priest 1983;Demoulin & Priest 1993).Although the quadrupolar configuration for the stable prominence support was proposed by Kippenhahn & Schlüter (1957), it can be considered as the inverse type since the direction of the field in the prominence is opposite to the photospheric field just below the prominence.
Dips are integral parts of magnetic flux ropes, which can exist in the solar corona in equilibrium.Cold dense plasma filling the dips represents the internal fine structure of filaments.Aulanier & Demoulin (1998) and Aulanier et al. (1998) first calculated the distribution of dips within a model force-free flux rope.Each dip was associated with a thread segment filled with dense cold plasma.The length of each segment is determined by the curvature of the field line so that the depth of each dip is ∼1 Mm.Up to this height, the tube can be Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.considered filled with plasma in hydrostatic equilibrium within it.Emphasis on the model is given to filament barbs.They are formed by small parasitic inclusions on both sides of the PIL.Combination of field-line segments with the depth of about 1 Mm around the dips creates a form similar to the shape of a quiescent prominence.Despite the fact that such a model prominence looks like an arch bridge from the side, it is composed of nearly horizontal segments of field lines.
The numerical solution of the system of 3D MHD equations showed the possibility of formation of sagged field lines in arches of the bipolar configuration deformed by shear movements of field-line footpoints near the PIL (Antiochos et al. 1994;DeVore & Antiochos 2000;Aulanier et al. 2002).The footpoints located in the inner part of the arcade, under the dome of the main mass of arches, are carried out by the shear motion from the region of the strong field to areas of weaker field, where the tension and pressure from above, from the rest of the field, are smaller than in the central part.Deformed field lines tend to expand but meet the resistance of the ambient field, under influences of which the resulting shape of the field lines is formed.Sagged field lines in this model are extended roughly along the neutral line and not across it, as in the classical Kippenhahn-Schlüter model.Further displacements of footpoints cause reconnection of the field lines with the field lines of the potential arcade.As a result, helical field lines are created so that the model becomes in some sense similar to flux-rope models.Both flux rope and sheared arcade models describe channel prominences.What type of magnetic field configuration supports coronal cloud prominences is an open question.The V-shaped structure implies the presence of a dip, but whether it is created by sagging of a coronal magnetic field by the falling mass or it exists prior to the prominence formation near a separatrix surface between adjoining coronal loop systems is a question (Martin 2015).
The source of the mass for coronal cloud prominences is not certain yet.There is a tendency for coronal cloud prominences to appear about 1 day after a coronal mass ejection (CME), which assumes that their mass comes from falling back to the Sun material lifted by solar eruptive events (Wang et al. 1999;Lin et al. 2006).Another possibility is the radiative cooling instability in magnetized hot coronal plasma (Karpen & Antiochos 2008).Coronal magnetic field dips play a significant role as falling and condensed material can be accumulated and stored in them (Liu et al. 2012(Liu et al. , 2014)).
In this paper, we analyze rather unique observations of a high-altitude spider-type prominence in 2023 February.We show that the prominence is located in sagged coronal field lines just above a coronal magnetic null point.While the prominence appears and disappears in the course of a particular day, it persists during the whole half of a solar rotation, being observable from day to day starting from the east limb to the west limb.

Observations
We used images taken by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) in different wavelengths and magnetograms taken by the Heliospheric and Magnetic Imager (HMI; Schou et al. 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) for the analysis of the high-altitude spider-type prominence evolution during its passing through the solar disk and the magnetic configuration in which it was suspended.Hα filtergrams from the Cerro Tololo Inter-American Observatory, Chile, incorporated into the National Solar Observatory (NSO)/Global Oscillation Network Group (GONG) were used in addition to the AIA data.The high-altitude prominence appeared at the eastern limb of the Sun close to the equator on 2023 February 8 (Figure 1).It can be classified as a spider-type prominence because its main body did not touch the chromosphere, being rather high in the corona, and was connected to the chromosphere only by numerous thin loops emanating horizontally from the There was a rather intensive eruptive activity in the region to which the prominence belongs.As it became clearer when the region came to the disk, the prominence was located in an active-region complex consisting of two active regions with large, round sunspots of negative polarity, AR3217 and AR3220.Possibly, this eruptive activity supplies the prominence with mass, but it also destroys it from time to time.For example, the prominence was swept after 20:00 UT on February 8 by rising loops on the northern side of it (Figure 1 animation).The prominence material drained down along a large loop to the south from the prominence.Thus, the prominence appeared and disappeared as the region passed through the solar disk (Figure 2).It might be rather referred to as a filament when it was projected onto the disk, but this term is also not very appropriate because the structure was not elongated like most of the channel filaments.
In contrast to many coronal cloud prominences, which are hardly distinguishable on the disk, the studied prominence was quite dense and was observable in several SDO/AIA channels, as well as in the Hα line (Figure 3).However, owing to eruptive activity in the region, the prominence appeared and disappeared both at the limb and on the disk throughout a single day (Figure 4).For this reason, the prominence is observable in some periods of time, while it is absent from images in other periods.Nevertheless, the necessary condition for the prominence formation seems to be persistent during the whole half-rotation period.
The apparent location of the prominence in the active-region complex changes from day to day (Figure 2).On February 13, the prominence was located close to the position of the eastern sunspot of the complex, almost immediately above it.On February 15, the prominence occupied a position about onethird of the distance between the sunspots from the eastern sunspot (Figure 3).On this day, the prominence was located practically at the central meridian.On the following days, when the prominence became visible, its relative position somewhat shifted toward the western sunspot.Such displacement is natural taking into account the height of the prominence of about 100 Mm, when it was observed at the limb, and the projection effect.When the region traveled to the western hemisphere, the projection shifted toward the western sunspot.Every day, the visible position of the prominence relative to the sunspots shifted by about 30″ or 2°in heliocentric coordinates.Of course, the influence of some changes in the structure of the coronal magnetic field and conditions for the prominence formation on the apparent position of the prominence cannot be ruled out.

Coronal Magnetic Field Structure
The structure of coronal loops at the eastern limb suggests quadrupolar configuration of the magnetic field with a null point in the vicinity of the prominence.However, it should be proved by calculations of the coronal magnetic field structure at least in potential (current-free) approximation.Obviously, the photospheric magnetic field data are not available for the time when the prominence was at the limb.The best magnetic data exist for areas close to the central meridian.The active-region complex came there on February 15, and the prominence was observable during half of the day (Figures 4 and 5).For the boundary conditions for solving the Neumann external boundary value problem, we cut a rectangular area around the filament from a full-disk magnetogram, which then was transformed into the array with pixels of equal area (see Filippov 2013 and references therein).Figure 5 presents a fragment of the SDO/AIA image taken in the 211 Å channel and SDO/HMI magnetogram of the same area, which includes the active regions AR3217, AR3220, and the surrounding dispersed magnetic fields.As main sources of the magnetic fields are included in the area, the boundary condition permits the calculation of the coronal potential field up to rather great heights, comparable with the sizes of the area.The major leading negative sunspot of the active region AR3217 (the western sunspot of the complex) is surrounded by a large area with dominating elements of negative polarity.The major leading negative sunspot of the active region AR3220 (the eastern sunspot of the complex) has only several satellite elements of negative polarity and is surrounded by a large area with dominating elements of positive polarity (Figure 5(b)).
Calculated PILs of the potential magnetic field at different heights are shown in Figure 6.At lower heights, the major negative polarities are divided by a rather narrow neck of positive polarity.At the height of 50 Mm, the PILs enclosing the sunspots touch each other and merge into the united PIL.The intersection of PILs denotes a magnetic null point.Indeed, the vertical component of the field is zero at a PIL by definition, while the horizontal components vanish at the intersection of PILs for symmetry reasons.Above the height of 50 Mm, both major areas of negative polarity merge, and only one PIL exists (except the PIL related to a small active region in the southwest corner of the frame).The lowest end of the prominence observed at the limb on February 8 was at 65 Mm, which can mean that the calculated height of the null point is underestimated in the potential-field approximation or the field slightly changed from February 8 to February 15 or the prominence material does not fill the dips too close to the null point, where the field strength is too weak.
While the studied prominence does not look like the channel filaments, it is located at the appropriate PIL (Figure 5(c)).The absence of a vertical component of the coronal field (the field is horizontal) is only one of the necessary conditions for the prominence existence.For the stable equilibrium of a plasma element, the coronal field lines should have the curvature directed upward.The condition for the presence of a dip at a PIL was derived by Aulanier & Demoulin (1998): where the z-axis is assumed to be vertical.We calculated the location of dips at PILs according to the Expression (1) using our potential-field approximation.At lower heights, dips exist only at the periphery of the region, where the reliability of results is low because of the neglecting of fields outside of the cut frame.The sections of PILs where field lines have the upward-directed curvature are marked with small green circles.There are no dips near the projected position of the prominence at lower heights.This is natural that low field lines are convex in the potential magnetic field without any singularity.But just above the null point we may expect the appearance of dips, and this actually takes place (Figure 6(c)).The dips exist at rather extended segments of PILs (Figures 5 and 6) at heights of the prominence observed at the limb.The dips disappear at heights above 115 Mm, the upper boundary of the prominence at the limb.Therefore, the prominence is located in the dips of the coronal magnetic field where at least two necessary conditions of plasma element equilibrium are fulfilled.
The curvature of field lines in dips is determined by the expression (Aulanier & Demoulin 1998) Figure 7 shows the distribution of the curvature radius of field lines along the dipped section of the PIL marked with small green circles in Figure 5(c).It slightly varies along the section except for some spikes caused possibly by numerical errors and uncertainties.An average radius of field-line curvature is about 60 Mm.
There is another method to estimate the field-line curvature using the pendulum model (Luna & Karpen 2012;Zhang et al. 2012).While the prominence blobs are swinging to and fro not where g is the gravitational acceleration.The period of 45 minutes gives the radius of about 55 Mm, which surprisingly agrees well with the calculations of the curvature radius in the potential-field approximation.
Of course, there is a question of how mass fills the existing dips.As it was mentioned before, the complex shows rather    intense eruptive activity.Apart from true eruptions of some small and filaments (presumably flux ropes) presented in the active-region complex, several coronal loops become activated from time to time, increasing their brightness, showing intense motions along them, ascending and disappearing.Thus the material propagation along loops can reach the dips and stay there for some time in a stable or at least metastable state.After eruptions, a lot of plasma can remain in the corona, which gradually condenses and falls down.The connection of the prominence body with far-going coronal loops emanating from it is obvious in the limb observations (Figure 1), but it is observable also in some on-disk observations.Blue arrows in Figure 4 show long coronal loops related to the prominence.These loops can be considered as extensions of short, thin internal threads of the prominence.A longer loop in Figure 5(c) is connected with negative-polarity network elements northwest to the western sunspot.A shorter loop in Figure 5(d) is related to the western sunspot itself.Since the prominence threads are the segments of these loops, it is possible to determine the direction of the magnetic field within it based on the footpoint anchoring of the long coronal loops in photospheric areas of definite polarity.The field is directed from the south to the north.Comparison with the polarities on both sides of the photospheric PIL over which the prominence is located shows that the direction is opposite to the direction of the transverse photospheric field and the prominence can be ascribed to inverse-polarity prominences.However, it is not an inverse-polarity prominence related to a flux rope (Kuperus-Raadu type; Kuperus & Raadu 1974) but is rather the Kippenhahn-Schlüter-type prominence in the quadrupolar magnetic configuration.

Discussion and Conclusions
A high-altitude prominence appeared at the eastern limb of the Sun on 2023 February 8.It may be classified as a coronal cloud prominence or a spider-type prominence.Close inspection of coronal limb images and potential magnetic field calculations showed that the prominence material was located in sagged coronal field lines just above a coronal magnetic null point (Figure 9).While the coronal cloud prominences usually are not observable on the disk as dark absorbing features, as common prominences do, this prominence was clearly visible on the disk but not every day of its passage through the disk.Therefore, this is more a unique case of such events, and it allows one to study in more detail magnetic configuration and conditions for its formation.The prominence appeared and disappeared in the course of a particular day both when it was located above the limb and projected onto the disk; however, it persists during the whole half of the solar rotation, being observable from day to day starting from the east limb to the west limb.Coronal cloud prominences are usually assumed to be not associated with PILs (Engvold 2015), possibly because they are rarely observed on the disk as filaments; this prominence was dense enough to be visible on the disk at least on some days during its passage through the disk.Surprisingly, the prominence on the disk was located directly on the PIL at the height corresponding to the height that was measured when it was previously at the limb.
The dips needed to support the dense plasma in the corona are usually attributed in prominence models to coronal flux ropes or sagged field lines of sheared arcades.There is no evidence of the presence of these structures near the highaltitude prominence in AR3217 and AR3220.Sagged field lines also exist above coronal null points in a fairly small volume, limited in all three dimensions.This volume is located inside one of the eight lobes divided by three separatrix surfaces intersecting at the null point.In projection on a flat surface, the vicinity of the null point looks like a saddle structure.Such saddle structures are observed sometimes on the disk in a pattern of chromospheric fibrils (Filippov 1995; Xue  (Tsuneta 1996;Filippov Shilova 1997;Sun et al. 2014) and at the limb or not far from it in the projection of coronal loops on the plane of the sky (Filippov 1999;Su et al. 2013;Sun et al. 2016;Mason et al. 2019).Saddle-like structures can be recognized in EUV images of the considered active-region complex at the limb and on the disk, which implies the presence of a null point in the corona.Calculations of the coronal potential magnetic field confirm this assumption.
Not every null point in the corona is favorable for the existence of dips.If separatrices of the saddle structure are vertical and horizontal as in the well-known fan-spine configuration with the vertical spine (Shibata 1998;Pariat et al. 2009), despite the presence of curved field lines, their curvature is not directed upward at any point.The vertical spine emerging from the null point merges with a vertical ambient field, field lines of which are open or can be considered as open in the scale of studied structures.This configuration arises when a small vertical dipole is embedded in a vertical, uniform background field (Shibata 1998;Filippov et al. 2009;Pariat et al. 2009;Filippov et al. 2015).It is widely used in models of the jet formation.A small horizontal dipole embedded in an oppositely directed horizontal background field creates a null point with inclined separatrices.Previously horizontal field lines above the null point are sagging and form dips suitable for plasma storage.This configuration arises when a smaller horizontal dipole is imbedded in the field of an oppositely directed, horizontal, larger-scale dipole.Similar configurations were presented in several works (Su et al. 2013;Filippov 2018).
The appearance of the prominence at the limb on February 8 in the SDO/AIA 304 Å channel looks like a typical spider-type prominence with coronal rain flowing along widely spread coronal loops.The material drops down and there is no manifestation of it rising into the corona in the period of the prominence existence.There were several eruptions of different sizes before the prominence formation.The strongest and brightest event happened several hours before the prominence formation on February 7 starting from 13:20 UT behind the limb.It destructed an already-formed loop system similar to one shown in Figure 1(a).Figure 10 shows the developments of this eruption in running difference images in the SDO/AIA 211 Å channel.
At 13:39 UT, the erupting prominence was bright and looked like a twisted loop.The shape is then entangled with various stray threads, which form loops of a smaller scale (13:48-14:14 UT).After 14:09 UT, the legs of the large loop approached each other and formed an elongated vertical structure similar to the current sheet in the "standard flare model."It is possible that there is reconnection between oppositely directed fields in the legs, similar to the process described by Sun et al. (2015).This is revealed by the appearance of horizontal threads going up from the upper edge of the supposed current sheet (14:20-14:30 UT).Hot plasma ejected into the upper layers of the corona can condense into the spider prominence due to thermal instability.At 21:00 UT, the condensation of matter at the place where prominence appeared became noticeable.Brightness significantly increased at 22:00 UT in a small area at the bottom of sagged loops both in SDO/AIA 304 Å and 171 Å images (Figure 9 and its associated animation).Bright features appeared first in the 171 Å images then in the 304 Å images (with a lapse of about 5 minutes), which indicate the cooling of plasma in this region.Although the material is observed falling down in both SDO channels, denser matter lingers in the dips and forms the prominence visible in absorption in the 171 Å images.Figure 11 shows the light curves in three SDO/AIA channels at the point marked with a small green circle in Figure 9(a).Peaks appear earlier in hotter channels than in colder ones.The 211 Å channel is sensitive to plasma emission with a temperature of about 2 MK (Lemen et al. 2012).The brightness in this channel reaches its maximum at 21:45 UT.Almost at the same time, the light curve in the 171 Å channel, which shows a plasma with a temperature of ∼0.6 MK, reaches a rather broad peak lasting more than 40 minutes.The emission of the coldest plasma with a temperature of ∼0.5 MK in the 304 Å channel reaches its maximum values at 22:00 UT.Thus, the observations show the cooling of the hot plasma in the corona after energetic eruptive processes.
Similar process of coronal condensation and prominence formation after an earlier eruption was studied by Liu et al. (2012).They also pointed to the significant role of magnetic dips for the prominence formation.However, the dips were not as clearly visible in this event as on 2023 February 8, and their presence was not supported in this work by magnetic field calculations.However, the delay in brightening in different channels in the event studied by Liu et al. (2012) was much longer (2-5 hr).Liu et al. (2017) reported SDO/AIA observations that showed that the prominence material was formed and resided near magnetic null points.They suggested that a null-point environment is favorable for the radiative cooling process.
Coronal cloud prominences are rather elusive objects for observations.Studying their formation, mass storage, conditions for equilibrium and stability or metastability, and relationship with other coronal structures may shed light on physical processes in the corona and thermodynamic properties of the coronal plasma.

Figure 1 .
Figure 1.High-altitude spider-type prominence at the east limb observed on 2023 February 8 at 16:09 UT by SDO/AIA in the 304 Å channel (a) and 171 Å channel (b).White line shows a slit used for the construction of a time-distance diagram.An animation of this figure with slightly greater fields of view is available.The animations run from 10:00 UT on February 8 to 03:28 UT on February 9 and show the evolution of the prominence and surrounding loops.The real-time duration of the animations is 20 s. (Courtesy of the SDO/AIA science team).(An animation of this figure is available.)

Figure 2 .
Figure 2. The passage of the prominence through the solar disk from the east limb to the west limb observed in the SDO/AIA 193 Å channel.Green arrows show the position of the prominence at limbs and the corresponding filament on the disk.

Figure 3 .
Figure 3. Hα images of the prominence at the eastern limb (a), close to the central meridian (b), and at the western limb (c).(Courtesy of the Cerro Tololo Inter-American Observatory, Chile).

Figure 4 .
Figure 4. Changes of the prominence visibility during the day on 2023 February 15 observed in the SDO/AIA 193 Å channel.Green arrows show the position of the prominence; blue arrows show long coronal loops related to the prominence.

Figure 5 .
Figure 5. Fragment of the SDO/AIA image taken in the 211 Å channel on February 15 at 07:10 UT (a), SDO/HMI magnetogram of the same area (b), and the same image with superposed PILs at the height of 66 Mm (red lines).Green marks show the section of the PIL with the upward-directed curvature of field lines.(Courtesy of the SDO/AIA and SDO/HMI science teams).

Figure 6 .
Figure 6.PILs of the potential magnetic field at different heights.Green marks show the sections of PILs with the upward-directed curvature of field lines.

Figure 7 .
Figure 7. Distribution of the curvature radius of field lines along the dipped section of the PIL marked with small green circles in Figure 5(c).

Figure 8 .
Figure 8. Distance-time diagram along the slit AB shown in Figure 1(b).

Figure 9 .
Figure 9.Initial phase of the prominence condensation at the east limb observed on 2023 February 7 by SDO/AIA at 21:50 UT in the 304 Å channel (a) and at 21:45 UT in the 171 Å channel (b).The small green circle shows the location where light curves were constructed.An animation of this figure with slightly greater fields of view is available.The animations run from 20:30 to 23:51 UT on 2023 February 7 and show changes in brightness in the area surrounding the prominence.The realtime duration of the animations is 20 s. (An animation of this figure is available.)

Figure 10 .
Figure 10.Development of eruptive prominence on February 7 started after 13:20 UT, which preceded the formation of the spider prominence as it is seen in running difference images in the SDO/AIA 211 Å channel.The red dashed line shows the position of the solar limb.Blue arrows indicate the reconnection downflow below the hypothetical reconnection site.An animation of this figure with a slightly greater field of view is available.The animation runs from 13:23 to 14:55 UT on 2023 February 7 and shows the development of the eruptive prominence and formation of the structure similar to the current sheet in the "standard flare model."The realtime duration of the animations is 11 s.(An animation of this figure is available.)