Large-scale Coronal Dimming Foreshadowing a Solar Eruption on 2011 October 1

Understanding large-scale solar eruptions requires detailed investigation of the entire system’s evolution, including the magnetic environment enveloping the source region and searches for precursor activity prior to event onset. We combine stereoscopic observations from the Solar Dynamics Observatory (SDO) and STEREO-B spacecraft for several hours before a filament ejection, M1.2-class eruptive flare, and coronal mass ejection (CME) originating in NOAA active region (AR) 11305 on 2011 October 1. Two episodes of significant preeruption coronal dimming that occurred well to the southeast of the ejected filament are identified. The CME subsequently took off with a substantial component of velocity toward the dimming, which became very pronounced during eruption. We used SDO/Helioseismic and Magnetic Imager (HMI) data to reconstruct the magnetic environment of the system and found that it contains a null point near the dimming region. AR 11305 had quite complex connections to nearby ARs 11302 and 11306, as well as to other regions of decayed AR flux. The intensifying and spatially expanding precursor dimming was accompanied by southeastward rising motions of loops toward the null point and northeastward and southwestward motions of loops retracting away. These motions and the dimming are consistent with persistent magnetic reconnection occurring at the null point as it moved upward and southeastward, thereby removing a strapping magnetic field high above AR 11305. Eventually, the filament was ejected explosively toward the null point. We conclude that the breakout model for solar eruptions provides a compelling account of this event. Furthermore, we conjecture that preeruption dimmings may be much more frequent than currently recognized.


Introduction
Transient reductions in radiative emissions from the Sun's corona that are limited in spatial extent and, in many cases, temporally abrupt in onset have been known for at least a halfcentury.Initially they were called "coronal depletions" (Hansen et al. 1974), which implies a loss of matter from the corona.The less presumptive term "coronal dimmings" (Hudson et al. 1996;Sterling & Hudson 1997;Gopalswamy & Hanaoka 1998;Thompson et al. 1998) was adopted later and has been used ever since.It has been recognized that coronal dimmings can result from changes in temperature of the coronal material that reduce its emission within the range of detected wavelengths, especially when observed in the extreme-ultraviolet (EUV), as well as from the decreases in the plasma density that are true depletions.It is widely accepted that both types of dimmings occur routinely in the corona.
The higher spatial resolution and temporal cadence available due to improved instrumentation have revealed that intense dimmings concentrated in two localized regions are commonly produced in association with large-scale coronal mass ejections (CMEs).These so-called twin (Gibson & Low 2000;Webb et al. 2000) or double (Hudson & Cliver 2001) dimmings are signatures of the footpoints of an erupting magnetic flux rope that is ejected in the event.The flux rope is subject to a rapid, manyfold increase in its volume and, therefore, a similarly abrupt decrease in the density of its entrained (and conserved) material.In addition to these intense dimmings within the core of the eruptive event's source region, more subtle dimmings that are more remote from the source region also have been observed in association with CMEs (Thompson et al. 2000;Wang et al. 2002;Mandrini et al. 2007;Attrill et al. 2009;Dissauer et al. 2018;Vanninathan et al. 2018).The remote dimmings, also often referred to as "secondary dimmings" in contrast to the twin "core dimmings," are regarded as reflecting the expansion and/or opening of the overlying magnetic field that is rooted in regions adjacent to, or even rather far from, the source of the eruption.Analyses of the dimmings that occur in conjunction with CMEs have been used to quantitatively estimate the ejected masses and other properties of the eruptions (Harrison et al. 2003;Tian et al. 2012;Aschwanden 2016;Cheng & Qiu 2016).For a review of the current state of knowledge on dimmings from statistical studies during the Solar Dynamics Observatory (SDO) era, see Kazachenko et al. (2022), especially their Section 3.1.
Far less widely observed and reported are preeruption dimmings and other signatures that clearly precede the acceleration of the CME and the onset of the flare in some eruptive events, in certain cases by several hours.The earliest examples known to us were described by Gopalswamy et al. (1999) from EUV observations by the Solar and Heliospheric Observatory's EUV Imaging Telescope (SOHO/EIT) on 1998 April 27 and by Sterling et al. (2001) and Sterling & Moore (2004) in EUV from SOHO/EIT and in soft X-rays (SXRs) from Yohkoh's Soft X-ray Telescope on 1999 April 18.During the SDO era, a handful of preeruption dimming events observed by the Atmospheric Imaging Assembly (AIA) were reported and interpreted as signatures of quasi-equilibrium expansion, sometimes for more than a couple hours, of coronal structures prior to the catastrophic loss of equilibrium leading to subsequent CMEs (Qiu & Cheng 2017;Zhang et al. 2017;Wang et al. 2019Wang et al. , 2023)).The cause of the expansion, however, has been less discussed in these reports.These early signatures of imminent eruption are much more subtle and slowly developing than the intense, sudden dimmings associated with CME onset and flux-rope ejection.
The above-cited 1999 April 18 event occurred in a multipolar topology that is expected to host at least one overlying magnetic null point.Hence, the source region was susceptible to outward coronal expansion and the reconnection and removal of restraining magnetic flux.The progressive, accelerating weakening and removal of the restraining field are key to the eventual onset of explosive ejection featuring a CME and an eruptive flare, according to the magnetic breakout model for solar eruptions (Antiochos et al. 1999;Wyper et al. 2017).Expected signatures of the breakout mechanism include preeruption dimmings due to the coronal expansion.More recent observations from the SDO/AIA of coronal jets and CMEs from pseudostreamers have revealed similarly early preeruption EUV dimmings (Kumar et al. 2021).In addition, numerous small-scale plasma blobs have been observed to form within and stream away from the vicinity of the inferred coronal null points above other jets (Kumar et al. 2019).The latter observations provide even more compelling and more direct evidence for the coronal reconnection that is predicted by the breakout model (Wyper et al. 2016(Wyper et al. , 2017(Wyper et al. , 2018)).
Recently, Zhu et al. (2020b) investigated 60 solar eruptive events to assess timing relationships between the flare reconnection flux rate and the acceleration of the CME.One event included in that study was a filament ejection accompanied by a CME and an M1.2-class eruptive flare, which occurred on 2011 October 1 and originated in active region (AR) NOAA 11305.AR 11305 spawned three C-and three M-class flares with accompanying CMEs that produced recurring dimmings over the 4 days between September 29 and October 2 (Krista & Reinard 2013).The October 1 eruption also generated an EUV shock wave that was linked to energetic electron acceleration and radio emission from the corona (Long et al. 2021).Both groups of investigators pointed out the complex large-scale topology of AR 11305 and its surroundings, citing the role of coronal interchange reconnection in allowing rapid volumetric expansion of the magnetic field encircling the ejected filament to produce the dimming (Krista & Reinard 2013) and the escape of accelerated electrons along newly opened field lines to generate the radio emission (Long et al. 2021).Others have focused on the local-scale magnetic structure of the filament within AR 11305 and its role in providing the free energy needed to power the event (Temmer et al. 2017;Titov et al. 2018).In particular, Temmer et al. presented Hα images of the filament before and after its ejection (see their Figure 3), along with analyses of the CMEassociated coronal EUV dimming and the subsequently detected interplanetary magnetic cloud.
In this paper, we reexamine the eruption from AR 11305 on 2011 October 1 by focusing on its evolution during the several hours prior to the peak of the M1.2-class flare at about 10:00 UT.Two intervals of preeruption EUV dimmings are identified in the near vicinity of the coronal magnetic null point inferred from a potential-field extrapolation of the available magnetic data.In addition, loop motions detected in the dimming region are consistent with the southeasterly rise of loops toward the null point, where they reconnect and then recede to the northeast and southwest away from the null.Our new findings are consistent with the posteruption roles of interchange reconnection in this event that were suggested by Krista & Reinard (2013) and Long et al. (2021).In addition, our results provide compelling evidence for its role in the buildup to and initiation of the eruption.The weakening and removal of the overlying strapping field prior to the onset of an eruptive flare with CME is a key element in the breakout model for solar eruptions.Our results support the conclusion that the breakout model accounts very well for the observed evolution of the eruption observed in AR 11305.
The remainder of our paper is organized as follows.In Section 2, we present our analysis of the simultaneous observations of AR 11305 from SDO and the Solar-Terrestrial Relations Observatory (STEREO) on 2011 October 1.In Section 3, we interpret the observations of this event in terms of the breakout model.We summarize our findings in Section 4.

Observations
On 2011 October 1, AR 11305 was near disk center (see Figure 1) as viewed from Earth and the SDO (Pesnell et al. 2012).SDO/AIA (Lemen et al. 2012) takes full-disk images of the Sun in 10 EUV/UV channels ( [ ] T K log ∼ 3.7-7.3)at a cadence of 12-24 s and a pixel size of 0 6.SDO's Helioseismic and Magnetic Imager (SDO/HMI; Scherrer et al. 2012) takes full-disk magnetograms with 1″ spatial resolution at 45 s cadence.STEREO (Kaiser et al. 2008) is composed of twin spacecraft, STEREO-A (Ahead; STA) and STEREO-B (Behind; STB).Their separation angles relative to the Earth (and SDO) were 104°and 98°, respectively, on the event date (see Figure 2).Their distances to the Sun during the observations were about 0.97 and 1.08 au, respectively.The dimming region under investigation was located to the east of AR 11305 and appeared near the west limb as seen from STB, while it was mostly blocked by the east limb as seen from STA.Consequently, we focus on STB for the limb observations of this event.The 195 Å images from the Extreme-Ultraviolet Imager (STB/EUVI; Wuelser et al. 2004) are taken at 5 minutes cadence and 1 6 pixel size.We compare these spatially resolved data with disk-integrated SXR light curves from the Geostationary Operational Environmental Satellite (GOES) spacecraft.

Eruption Overview
An M1.2-class eruptive flare with filament ejection and CME occurred within AR 11305 near solar disk center on the morning of 2011 October 1.A snapshot of the event at 09:42 UT as seen by SDO/AIA at 171 Å is shown in Figure 1(a); an animation of the full eruption observed in this passband is provided with this article online.Although the ejected filament resided close to disk center, its motion was clearly directed southeastward from AR 11305 as viewed from SDO.Hence, we tracked the leading edge of the eruption by placing a virtual slit (red line in panel (a)) along the general direction of motion.We then generated a spacetime stack plot along this slit, shown in Figure 1(b).The red curve in panel (b) tracks the leading edge of the bright, rising flux-rope structure along the virtual slit.The flux rope rose quickly but very briefly prior to 09:22 UT, then ascended much more slowly until 09:37 UT, at which time it resumed its very fast upward motion, culminating in its ejection from the low corona.The corresponding acceleration is derived from time derivatives of the height-time profile and is shown in Figure 1(c).It briefly increased to 100 m s −2 at around 09:19 UT and then rose again at 09:34 UT until arriving at 320 m s −2 at 09:44 UT.Uncertainties in the fitting of Gaussian profiles to the intensity of the leading edge produce errors in the acceleration on the order of 100 m s −2 prior to the onset of the flux-rope ejection at about 09:37 UT.
The motion of the CME as observed from STA was analyzed by Zhu et al. (2020b) and is shown in Figure 1(d). 8Data points and error bars are displayed for the height (black), velocity (blue), and acceleration (pink); the smooth curves are functional fits to the data points.The onset of strong acceleration of the CME is essentially simultaneous with that of the flux rope (panel (c)), as indicated by the vertical dashed line.We measured the reconnection rate of magnetic flux in AR 11305 by summing up the photospheric magnetic fluxes covered by the spreading flare ribbons in SDO/AIA 1600 Å (see, e.g., Isobe et al. 2002;Qiu et al. 2002Qiu et al. , 2004;;Asai et al. 2004;Krucker et al. 2005;Miklenic et al. 2007).The resultant reconnection rate is displayed in Figure 1(e).Three lowamplitude, short-lived bursts of reconnection occur between 08:30 and 09:00 UT.These bursts are associated with localized, transient brightenings that can also be seen in the 171 Å animation and do not involve any obvious outward motions of the AR 11305 loop structures.A larger-amplitude, sustained interval of reconnection begins at about 09:12 UT and attains a first peak at about 09:22 UT and a second at about 09:33 UT before subsiding.This interval is centered on the time of upward motion of the flux-rope bright edge (09:22 UT; panel (b)).There follows a stronger but shorter interval of reconnection that lasts from about 09:37 UT until after 10:00 UT.Its onset coincides very closely with the start time of the sharp final rise of the flux rope leading edge (panel (b)) and the strong acceleration of the CME (panels (c) and (d)).The reconnection rate peaks at about 8 × 10 17 Mx s −1 near 09:45 UT, at nearly the same time as the maximum CME acceleration (panel (d)).GOES disk-integrated SXRs exhibit multiple peaks, as shown in Figure 1(f), with the SXR flare maximum occurring at around 10:00 UT.A smaller, C2.7 eruptive flare peaked much earlier, at 09:11 UT; it originated in AR 11302, an AR near the west limb that is not shown in Figure 1(a)).Krista & Reinard (2013) have suggested that this weaker event may have contributed to the destabilization of AR 11305 due to magnetic connections between the two ARs, even though the core polarities of ARs 11302 and 11305 were well separated from one another.

Preeruption Dimming
Examination of the EUV observations from STEREO and SDO during the several hours prior to the eruptive flare revealed clear signatures of preeruption dimming.The view from STB/EUVI shows that a dark void region formed above the western limb and to the south of AR 11305 (see the boxed regions in Figure 2 d1) and (d2).The dimming regions grow in extent and depth over time, as indicated by the contours outlining the regions in the four panels.The unique stereoscopic views reveal that the dimming region is extending upward and southward as seen from STB and eastward and southward as seen from SDO.As discussed below (see Section 2.3 and associated animations), the bright loops below the dimming region (top left in (b1) and (b2); top right in (d1) and (d2)) show clear evidence of rising and converging motions during the two dimming episodes.
The evolving intensities within the dimming region (dashed rectangles in Figures 2(a  swept through the dimming region, producing a brief intensity increase peaking at about 09:50 UT.Thereafter, the intensities dropped sharply, especially in the limb view from STB, during the eruption-driven dimming episode marked D3 in the figure (see also Krista & Reinard 2013;Temmer et al. 2017;Dissauer et al. 2019;Chikunova et al. 2020).
The evolving areas of the dimming regions from the two viewpoints (contours in Figures 2(b b1) and (d1)), the dimming area measured from STB increases rapidly, at a rate of 2.0 Mm 2 s −1 .During the same interval, it is only 0.7 Mm 2 s −1 as viewed from SDO.However, the SDO observations show that the dimming region broadened in the east-west direction over a much longer time interval, increasing in area until around 03:00 UT.The maximum dimming areas are 5.7 × 10 3 Mm 2 (STB) and 4.1 × 10 3 Mm 2 (SDO), respectively.These values are quite close in magnitude, despite being derived from measurements along essentially orthogonal viewpoints.The difference supports the possibility that the volumetric expansion may be stronger radially than horizontally.
During dimming episode D2 (panels (b2) and (d2)), the area increases approximately linearly from 07:00 UT to 09:10 UT at a rate of 0.9 (0.7) Mm 2 s −1 viewed from STB (SDO).The maximum areas occur at around 09:10 UT at 8.0 × 10 3 and 5.9 × 10 3 Mm 2 , respectively.The difference again favors a slightly stronger radial expansion.By way of comparison, the dimming areas from the base difference images during the CME eruption (episode D3) are, respectively, 1.1 × 10 5 and 4.2 × 10 4 Mm 2 from the two viewpoints.The maximum areas during preeruption episode D2 are about an order of magnitude smaller (7% and 14%, respectively) than those during CME dimming episode D3.A different thresholding method based on logarithmic base ratio images and a region-growing algorithm implemented by Chikunova et al. (2020) and Dissauer et al. (2019) produced similar results during interval D3 (correspondingly, 1.3 × 10 5 and 5.4 × 10 4 Mm 2 ).This indicates that measurements of the observed dimming areas during this eruption are not very sensitive to the details of the applied detection technique.

Coronal Loop Motions
In order to understand the origin and development of the preeruption dimming region, we examined in detail the highcadence, high-resolution observations from SDO/AIA at 171 and 193 Å.An expanded FOV of the corona surrounding AR 11305 at time 07:20 UT is shown in Figures 3(a) and (b).The dominant positive and negative magnetic polarities (P1, N1) of AR 11305 are marked here, as well as the negative polarity (N2) of AR 11306 to the east.Figure 3(c) shows the SDO/HMI magnetogram within the dashed box shown in panel (a).Numerous large-scale loops connect P1 to N1, while others connect P1 to N2.We placed three virtual slits directed roughly southeast beginning at S1 and roughly northeast beginning at S2 and S3 on the EUV images.We then generated time-distance stack plots from running different images along the virtual slits.Dimming episode D1 is highlighted in panels (d) and (e) along slits S1 and S2; episode D2 is highlighted in panels (f) and (g) along slits S1 and S3.In all of these panels, the center of slit S1 is marked with a red plus sign, while the During the dimming episodes, long coronal loops, which connect the two polarities in AR 11305, N1 and P1, and arch to the south in the EUV image (Figure 3(a)), expanded toward the southeast.Beginning at about 00:45 UT during episode D1, several moving features were identified in the stack plot along slit S1, shown in Figure 3(d).Linear fits to these features (red lines) yield projected velocities of 10.8 ± 2.4 km s −1 .These features fade from view in the different images (i.e., cease their motion) before they arrive at the position of slit S2, which is marked with a red plus sign along the vertical axis.In the stack plot along the transverse slit S2 shown in Figure 3(e), two features can be seen to separate in opposite directions from the center of the slit.The northern feature has a projected velocity of 5.8 km s −1 toward the northeast, and this loop joins the loop system connecting P1 and N2; the southern feature has a speed of 19.0 km s −1 toward the southwest, and this loop joins dimmer loops connecting N1 with dispersed positive magnetic polarity to the south.The timing of these loop motions from 00:45 UT to around 01:45 UT coincides with that of the dimming evolution shown in Figure 2(e).It is worth noting that the loop expansion along S1 is well identified in AIA 171 Å, which typically represents cooler material at 0.6 MK; the separation of loops along S2 actually is better observed in AIA 193 Å, which represents warmer material at 1 MK.This may reflect reconnection-associated heating of the plasma in the retracting loops.
After about 02:00 UT, the directed motions of the loops along S1 became much less noticeable and appear to have ceased completely by about 03:00 UT, when dimming episode D1 saturated.Thereafter, the dimming began to recover and the emission from the corona rose until a disadvantageous gap in the SDO data began at around 06:00 UT.During this interval of about 3 hr, the systematic upward motion of the loops paused, suggesting that the inferred coronal reconnection was halted for all that time.The reason for the cessation is not obvious from the observations; but that such a cessation occurred is strongly supported by the data, in particular the provided animation.
During dimming episode D2, after the data gap ended and SDO observations resumed, the loops started to expand as early as 07:00 UT, and the motion lasted for at least 45 minutes.The projected velocity at 07:10 is around 12.6 ± 2.7 km s −1 ; later it increased to 66.6 ± 20.7 km s −1 .This increase in inflow speed may indicate an increase in the reconnection rate, a decrease in the inflow field strength, a change in the spatial orientation of the loops, or some combination of these effects.It can be seen at 07:25 UT in Figure 3(f) that the tracks of two identified features extend beyond the position of slit S2 by roughly 6″, showing that the loops expanded a greater distance along S1 during episode D2.Therefore, we placed a third slit, S3, farther along S1 to track the loop motions during this time interval (Figure 3(g)).As before, several moving features (indicated by pink lines) are observed to separate in opposite directions from the center of the slit.The projected velocities of the features are 17.5 ± 1.6 km s −1 , comparable to those during dimming episode D1.

Magnetic Field Geometry
To investigate relationships between the dimming regions and the magnetic configuration underlying the eruption, we created a cylindrical equal area map (Sun 2013) of the SDO/ HMI data.A Green's function method (Aly 1989) was used to generate the current-free, minimum-energy potential magnetic field above the surface.A Cartesian representation was used to generate the magnetic field in order to ensure adequate spatial resolution of the multiple contributing source regions on the surface and the complex low-altitude structure including the null point in the overlying corona.The results are shown in Figure 4(a).A magnetic null point (marked by a cyan cross) exists well to the southeast of AR 11305.The field lines around this null point primarily connect four polarities-N1 and P1 in AR 11305, N2 in AR 11306, and P2 in AR 11302-as well as some dispersed positive polarity flux to the north and the south of ARs 11305 and 11306.The null point is positioned about 0.09 R e above the solar surface.The field geometry is highly asymmetric, with the null point positioned southward from and between the easternmost polarities, N2 and P1.
The field lines were then projected onto the helioprojective Cartesian coordinate system (Thompson 2006) in which SDO and STEREO data are taken.Figures 4(b b2) and (d2)).The inner spine line of the magnetic field's null point and fan structure is directed toward the southeast from its origin in the positive polarity region P1.A strongly nonpotential magnetic field associated with the filament channel in AR 11305 would be expected to displace the null point outward along the inner spine.Hence, the null point of the actual preeruption magnetic field on the Sun is likely to be positioned nearer the center of the dimming regions, i.e., higher in the corona and southeastward of the potential-field null-point location shown in the figure.

Interpretation
The observations described above reveal a persistent preeruption coronal-dimming feature that was seen along two orthogonal lines of sight by SDO and STB (Section 2.2) near the null point of the reconstructed coronal magnetic field (Section 2.4).A succession of long coronal loops migrating steadily toward the null point from the direction of AR 11305 to the southeast (as seen from SDO) was accompanied by fainter loops migrating away from the null along the orthogonal directions toward the northeast and southwest (Section 2.3).These loop motions are consistent with the occurrence of magnetic reconnection at the null point in the high corona.This process would remove strapping magnetic flux above AR 11305 (and below the null) by reconnecting it with external flux above the null, forming newly reconnected loops that then would retract to the sides away from the reconnection region at the null, as observed.Over time, this removal process is expected to monotonically weaken the magnetic tension forces restraining the strongly nonpotential, highly energized magnetic field of the filament in AR 11305 (Titov et al. 2018).After the dimming and the loop motions had persisted for several hours, the filament was ejected from the corona, accompanied by a strong flare and a CME.
The scenario just described, deduced directly from the observations presented, is precisely the evolution of the magnetic field predicted by the well-established breakout model for solar eruptions (Antiochos et al. 1999;Lynch et al. 2008;Karpen et al. 2012;Wyper et al. 2017;Dahlin et al. 2019).The ongoing buildup of magnetic free energy and pressure in the filament channel pushes the null point ever higher in the corona against the tension force holding down the channel and its filament.Eventually, reconnection sets in at the current sheet that forms at the null, and the restraining overlying flux begins to erode away.A catastrophe ensues when the balance between upward pressure and downward tension forces can no longer be maintained; the reconnection process then runs away, and the filament-channel field explosively erupts from the corona into the inner heliosphere.
Previous work on the breakout model, including the studies cited above and several others, has focused primarily on the progress of the magnetic evolution and the resulting dynamics of plasma motion.To acquire deeper insight into the observations shown in this paper, we have visualized the evolution of the coronal plasma density in a recent simulation of a breakout eruptive flare and CME by Dahlin et al. (2019), shown in Figure 5.We emphasize that the comparison between this simulation and the observations is illustrative, not definitive, for three important reasons.First, the magnetic geometry in the simulation obviously is much simpler; second, for computational efficiency, the simulated energy buildup is much faster than what occurs on the Sun; and third, the thermodynamic model employed, adiabatic evolution of the temperature-stratified initial atmosphere, is much simpler than the actual evolution of the coronal plasma.All of these caveats notwithstanding, however, the resulting time history of the mass density in the model bears a close qualitative resemblance to that seen in the EUV observations, as we now describe.
The initial magnetic configuration of the simulation is shown in Figures 5(a The simulation geometry is much simpler than that of the observations shown in Figure 4, but our goal is to highlight the evolution of the plasma density in the vicinity of the null point.We would not expect this local behavior of the simulated evolution to be substantially different in the more complex geometry of the observed eruptive event versus the simple geometry of the simulated event, all else being equal.The gray-scale shading against the plane of the sky in Figures 5(c) and (d) contours the logarithm of the plasma mass density.Beyond the gravitational stratification of the initial, spherically symmetric atmosphere, two principal types of structural feature are evident.One type is the transient, smallscale dimmings visible principally at low to middle heights within the central and northern closed arcades in the figure.These result from the specifics of the driver mechanism employed in the simulation and will be explained below.The other type, which is relevant to the observations presented, is the extended, persistent, large-scale dimmings near the apexes of the two arcades of loops.The dimming within the central arcade is particularly intense and extends along the fan surface, which is delineated by the red field line rooted on each side of the AR's polarity inversion line and passing near the null at its apex.Notable but less intense is the dimming within the northern arcade.Both dimmings reflect the volumetric expansion of the magnetic field as it expands upward, reducing the local density of the entrained plasma mass.This expansion induces slow downflows along the legs of the vertically expanding loops, which contribute further to the reduction in density.Once breakout reconnection has set in at the null, the downflows along the fan surface speed up to become Alfvénic reconnection outflows, further enhancing the density deficit below and to the sides of the null as is seen in the late panel (d).This dimming feature precedes the simulated eruption by many thousands of seconds, i.e., by hours; grows more intense as eruption onset approaches; and is localized to the null-point vicinity.All of these characteristics have been noted in the observations that we analyzed.
We believe that this explanation accounts correctly for the dimming observed in the 2011 October 1 eruption, but there are qualifications.First, although the surface driving imposed at the base of the corona in the numerical simulation was subsonic (peak speed = 25 km s −1 ), it is substantially faster than the observed photospheric motions (typical speeds are on the order of 1 km s −1 ).Consequently, the simulated energy buildup and attendant volumetric expansion are artificially fast compared to solar values.This may exaggerate the depth of the calculated mass depletion in the high corona due to the long transit time along those extended loops of slow upflows, which in principle could act to refill the loops with plasma.Second, the highly simplified coronal thermodynamic (adiabatic) model used could likewise exaggerate the dimming; the simulated atmosphere lacks the deep reservoir of chromospheric mass that could also assist the refilling of loops in the observed corona.Third, the energy injection was persistent and continuous in the simulation, whereas this is rarely true on the Sun.A segmented energy-injection profile could, in principle, explain the multiple episodes of preeruption dimming in the observed event, although other critical factors cannot be ruled out based on the observations that were analyzed.
All of these limitations could be alleviated by performing a more comprehensive simulation of a similar event but at much greater cost in computational resources and sophistication.Such an improved model for the observed event should also include a more complex surface magnetic flux distribution giving rise to the much more elaborate field geometry deduced from the observations (Figure 4).However, this detail is unlikely to be germane to understanding the preeruption nullpoint dimming that was observed.If the dimming turns out to be a durable feature of the simple simulation geometry (Figure 5) with improved driving and thermodynamics, we are confident that it would be found in the complex observed geometry for the same physical reasons.
As a final note, the transient, small-scale dimmings at low and intermediate altitudes in the arcade loops are due to the specific driving mechanism employed by Dahlin et al. (2019).Close-packed circular vortices were imposed at the simulated surface to emulate the injection of magnetic helicity and free energy into the corona as a test of the helicity condensation theory for solar filament-channel formation (Antiochos 2013).
The key implication of the theory and the key result demonstrated by the simulation are that a filament channel of a strongly sheared field containing substantial magnetic free energy forms at the polarity inversion line of the model AR.Eventually, the overlying field can no longer hold down the filament; hence, it erupts.For computational convenience, in the simulation, the prescribed vortices were large in size, fixed in position, and high in assumed flow speed (as noted previously).In a more realistic simulation with smaller vortices whose positions shift randomly and whose flow speeds are much smaller, the structured dimmings seen in our simulated images would be much less noticeable.We believe that only the persistent, large-scale dimming adjacent to the null point and perhaps that near the apex of the northern arcade of loops would be significant.Nevertheless, the magnetic shear and energy buildup would occur as before, albeit more slowly, and inexorably an explosive eruption would take place.Testing our intuition and the model on all of these points must be left to a different investigation to be performed on another occasion.

Summary
In this article, we have presented multiviewpoint observations of recurrent coronal dimming before a major solar eruption in AR 11305 on 2011 October 1.During each of two extended episodes of preeruption dimming, the projected areas of the dimming region increased approximately linearly for 1-2 hr.In conjunction with the dimming, low-lying coronal loops expanded toward the dimming region and stalled there, while high-lying loops retracted to both sides from the dimming region.This evolution is highly suggestive of persistent reconnection occurring in the high corona.The dimming region was found to be associated with a coronal null point in the complex coronal magnetic configuration, which was composed of magnetic polarities distributed among three neighboring ARs (11302, 11305, and 11306) and the background surface field.This correspondence further substantiates the hypothesis that reconnection was taking place within the dimming region.
To provide context and aid in interpretation, we also have shown images of the magnetic field and plasma density from a first-principles numerical simulation of a solar eruptive flare with CME from a null-point topology.Those results show that the rise in the null point and the expansion of the arcade below, which overlies the preeruptive filament, produce significant depletion of the coronal material.This process forms a dimming region at and around the null point.Although highly idealized, the simulation supports our interpretation of the observed event.We conclude that the 2011 October 1 eruption occurred due to the removal of the overlying field restraining the filament by null-point reconnection, leading to a catastrophic failure of equilibrium as described by the breakout model for solar eruptive flares with CMEs.
The multiviewpoint character of our observations of largescale, preeruption coronal dimmings is evidently a first, although similar phenomena were reported from single vantage points long ago (Gopalswamy et al. 1999;Sterling et al. 2001;Sterling & Moore 2004).In our case, the dimmings are low in intensity contrast, remote in spatial location from the source region, and very early in temporal occurrence relative to the eventual explosive eruption.Subtraction of the background EUV submission was required to enable these features to stand out in our processed data.Those three properties, individually but especially in combination, may well explain the paucity of prior observations of such preeruption dimmings.That is, the dimmings may not be especially rare in occurrence; instead, they may simply be rarely noticed and reported.Given the long-recognized magnetic complexity of the solar atmosphere, except during some epochs of minimum sunspot number, coronal null points can be expected to be plentiful and their generic evolution ubiquitous.Careful searches for additional examples of similar preeruption dimming, although challenging, might be found to succeed with rather surprising frequency.

Figure 1 .
Figure 1.Overview and measurements of the filament ejection, eruptive flare, and CME from AR 11305 on 2011 October 1 during 08:00-11:00 UT.(a) Observation from SDO/AIA at 171 Å at 09:42.The eruption is tracked along a virtual slit (red line); the reconnection rate of magnetic flux is measured in a region that encloses AR 11305 (white box).AR 11306 lies east of AR 11305 in the image.(b) Time-distance stack plot along the virtual slit in (a); the red line tracks the rise of the ejected bright flux rope.(c) Flux rope acceleration profile measured from the track in panel (b); red bars indicate the estimated errors.(d) CME height (black), velocity (blue), and acceleration (pink) measured from STA/COR1 and COR2 and reported previously by Zhu et al. (2020b); see the main text for details.(e) Measured magnetic flux reconnection rate within the boxed region in panel (a).(f) GOES SXR fluxes.The dotted and dashed lines mark the times of the early, brief rise and the later, sustained ejection of the SDO/AIA flux rope evident in panel (b), respectively.The tracking of the eruption along the chosen virtual slit in AIA 171 Å (panel (a)) is displayed as an animation.The animation runs from 2011 October 1 08:00 to the same day at 11:00.The real-time duration of the associated animation is 8 s. (An animation of this figure is available.) Figures 2(d1) and (d2).The dimming regions grow in extent and depth over time, as indicated by the contours outlining the regions in the four panels.The unique stereoscopic views reveal that the dimming region is extending upward and southward as seen from STB and eastward and southward as seen from SDO.As discussed below (see Section 2.3 and associated animations), the bright loops below the dimming region (top left in (b1) and (b2); top right in (d1) and (d2)) show clear evidence of rising and converging motions during the two dimming episodes.The evolving intensities within the dimming region (dashed rectangles in Figures2(a) and (c)) are displayed in Figure 2(e) as the red (STB/EUVI 195 Å) and green (SDO/AIA 193 Å) curves, respectively.The gradual preeruption dimming episodes are marked as D1 and D2 in panel (e).Episode D1 starts at roughly 01:00 UT and saturates at about 02:10 UT.The intensities then slowly recover, with new loops rising and filling in this region.Dimming episode D2 begins at about 07:00 and saturates at around 09:10 UT.Shortly after 09:30 UT, the CME front associated with the filament eruption Figures 2(d1) and (d2).The dimming regions grow in extent and depth over time, as indicated by the contours outlining the regions in the four panels.The unique stereoscopic views reveal that the dimming region is extending upward and southward as seen from STB and eastward and southward as seen from SDO.As discussed below (see Section 2.3 and associated animations), the bright loops below the dimming region (top left in (b1) and (b2); top right in (d1) and (d2)) show clear evidence of rising and converging motions during the two dimming episodes.The evolving intensities within the dimming region (dashed rectangles in Figures2(a) and (c)) are displayed in Figure 2(e) as the red (STB/EUVI 195 Å) and green (SDO/AIA 193 Å) curves, respectively.The gradual preeruption dimming episodes are marked as D1 and D2 in panel (e).Episode D1 starts at roughly 01:00 UT and saturates at about 02:10 UT.The intensities then slowly recover, with new loops rising and filling in this region.Dimming episode D2 begins at about 07:00 and saturates at around 09:10 UT.Shortly after 09:30 UT, the CME front associated with the filament eruption

Figure 2 .
Figure 2. Preeruption dimming observed by STB and SDO.(a) Large-scale view of the dimming region observed by STB/EUVI 195 Å. Close-up views within the solid rectangle are shown in panels (b1) and (b2); calculated emission intensities and dimming areas within the dashed rectangle are shown in panels (e) and (f), respectively.((b1) and (b2)) Base difference images from STB/EUVI show the dimming region, highlighted by contours.(c) The dimming region observed by SDO/ AIA in 193 Å with similarly restricted fields of view for panels (d1), (d2), (e), and (f).((d1) and (d2)) Base difference images from SDO/AIA 193 Å with the same timings as in (b1) and (b2).(e) Normalized intensities of the dimming regions (dashed rectangles in panels (a) and (c)), with three episodes of dimmings denoted as D1, D2, and D3 at the top.(f) Time evolution of the areas of the preeruption dimming regions (contours in panels (b1), (b2), (d1), and (d2)) viewed from STB (red) and SDO (green).Parameters of the linear fits (blue) are noted at the top.An animation is available that displays the evolution of the dimming during ∼10 hr before the eruption from the two viewpoints of STB and SDO.The animation starts on 2011 October 1 at 00:21 and ends the same day at 10:05.The real-time duration of the associated animation is 26 s.Note that panel (f) is not shown in the animation.(An animation of this figure is available.) ) and (d)) are displayed in Figure 2(f).The ranges for the contours are determined by eye, within around [−80, −3] DN pixel −1 for STB/EUVI 195 Å and [−250, −20] DN pixel −1 for SDO/AIA 193 Å.The lower limits here are chosen to exclude the darker region related to the rising, lower-lying loops from AR 11305.During dimming episode D1 (panels (

Figure 3 .
Figure 3. Motions of coronal loops in the vicinity of the preeruption dimming region.(a) and (b) Views from SDO/AIA 171 and 193 Å, respectively.Virtual slit S1 is placed along the direction of expansion to generate a spacetime stack plot.Similarly, two virtual slits, S2 and S3, are placed perpendicular to the direction of expansion.The symbols mark the start points of these slits in panels (d)-(g).The centers of the slits are marked with plus signs.(c) SDO/HMI magnetogram in the dashed box in panel (a).Three magnetic polarity regions related to the large-scale loops in (a) are denoted N1, P1, and N2.(d) and (e) During dimming episode D1 (see Figure 2(e)), a stack plot using the running difference images shows motions of coronal loops along S1 in (d) and S2 in (e).The trajectories of several moving features are tracked by the solid lines.The center of each slit is marked with a plus sign along the vertical axis.(f) and (g) Loop motions during episode D2 along S1 in panel (f) and S3 in panel (g).The loop motions observed in AIA 171 and 193 Å (panels (a) and (b)) are displayed as an animation.The animation begins on 2011 October 1 at 00:00 and ends the same day at 11:00.The real-time duration of the associated animation is 27 s.(An animation of this figure is available.) ) and (c) show the field lines superposed on images from STB/EUVI 195 Å and SDO/AIA 193 Å, respectively.The projected location of the null point at 09:01 UT is around [964″, 121″] as viewed from STB and [−194″, 12″] as viewed from SDO, corresponding to the northernmost and radially innermost parts of the identified dimming regions (contours are the same as shown in Figures 2( ) and (b).It is a single, isolated model AR embedded in the northern hemisphere of the background global dipole field of the Sun.The configuration has a fan/spine topology with a single null point in the corona above the AR, located where the white field lines intersect (seen most easily in panel (b)).Red field lines indicating the location of the filament-channel magnetic field within the AR are shown in panel (b).

Figure 4 .
Figure 4. Magnetic configuration showing the existence of a null point in the extrapolated potential field.(a) Magnetic field lines superposed on the SDO/HMI magnetogram.The field lines shown originate from a small region around the null point (cyan cross).Positive/negative polarities are denoted by white/black shading.(b) and (c) Extrapolated field lines projected onto STB/EUVI 195 Å (b) and SDO/AIA 193 Å (c) images.The yellow contours in these panels are the same as in Figures 2(b2) and (d2), indicating the locations of the dimming regions.

Figure 5 .
Figure 5. Mass depletion in the vicinity of the null point in an ARMS simulation of a breakout CME (Dahlin et al. 2019).(a) and (b) Initial embedded-bipole configuration, consisting of a strong AR in the northern hemisphere whose negative polarity (black) is surrounded by the positive polarity of the background global dipole field.The null point is located where the white field lines intersect.Red field lines within the AR represent the filament-channel field.(c) and (d) Longitudinal slice of the mass density (gray scale) in the central meridian reveals a density void near the null point (marked by the cyan cross) at two different simulation times prior to the eruption, which occurs at t ≈ 88,300 s.An animation is attached to show the development of the mass depletion near the null point in an ARMS simulation of a breakout CME (panels (c) and (d)).The real-time duration of the associated animation is 10 s. (An animation of this figure is available.)