# Expulsion of counter Evershed flows from sunspot penumbrae

J. S. Castellanos Durán Max Planck Institute for Solar System Research,
Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany  Georg-August-Universität
Göttingen, Friedrich-Hund-Platz 1, D-37077. Göttingen, Germany  A. Korpi-Lagg
Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3,
D-37077 Göttingen, Germany  Department of Computer Science, Aalto University,
PO Box 15400, FI-00076 Aalto, Finland  S. K. Solanki Max Planck Institute for
Solar System Research, Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany
School of Space Research, Kyung Hee University, Yongin, 446-101 Gyeonggi,
Republic of Korea

###### Abstract

In addition to the Evershed flow directed from the umbra towards the outer
boundary of the sunspot, under special circumstances, a counter Evershed flow
(CEF) in the opposite direction also occurs. We aim to characterize the proper
motions and evolution of three CEFs observed by the Solar Optical Telescope
onboard the Japanese Hinode spacecraft and the Helioseismic and Magnetic
Imager onboard the Solar Dynamics Observatory. We use state-of-the-art
inversions of the radiative transfer equation of polarized light applied to
spectropolarimetric observations of the Fe I line pair around 630 nm. The
three CEFs appeared within the penumbra. Two of the CEF structures, as part of
their decay process, were found to move radially outwards through the penumbra
parallel to the penumbral filaments with speeds, deduced from their proper
motions, ranging between 65 and 117 m s-1. In these two cases, a new spot
appeared in the moat of the main sunspot after the CEFs reached the outer part
of the penumbra. Meanwhile, the CEFs moved away from the umbra, and their
magnetic field strengths decreased. The expulsion of these two CEFs seems to
be related to the normal Evershed flow. The third CEF appeared to be dragged
by the rotation of a satellite spot. Chromospheric brightenings were found to
be associated with the CEFs, and those CEFs that reached the umbra-penumbra
boundary showed enhanced chromospheric activity. The two CEFs, for which line-
of-sight velocity maps were available during their formation phase, appear as
intrusions into the penumbra. They may be associated with magnetic flux
emergence.

Sunspot groups (1651); Solar photosphere (1518); Solar magnetic fields (1503);
Solar active region velocity fields (1976); Solar chromosphere (1479); Solar
flares (1496).

##  1 Introduction

Evershed flows are characteristic outflows observed in the penumbrae of
sunspots (Evershed, 1909) with typically subsonic velocities of $\sim$1-3 km
s-1 in the body of the filament (e.g., Schlichenmaier & Schmidt, 2000;
Strecker & Bello González, 2022) and 5-10 km s-1 at the endpoints (e.g. Tiwari
et al., 2013). The characteristic filamentary structure of penumbrae observed
in continuum images is the result of the interaction between buoyant
convective cells rising from the solar interior and inclined magnetic field
(see Solanki, 2003; Borrero & Ichimoto, 2011, for reviews). The normal
Evershed flows transport plasma radially111The term ‘radial’ is referring to
the direction along the solar surface away from the center of the sunspot.
outwards along the penumbral filaments (= intraspines; e.g., Lites et al.,
1993; Jurcák et al., 2007; Borrero & Solanki, 2008). In the last decade,
penumbral regions with the opposite direction of the flow at photospheric
layers, but otherwise indistinguishable in the continuum images, were observed
(Kleint, 2012; Kleint & Sainz Dalda, 2013; Louis et al., 2014; Siu-Tapia et
al., 2017; Castellanos Durán et al., 2021). The new type of penumbral flow was
named counter Evershed flow (CEF) to distinguish it from the distinct
chromospheric inverse Evershed flow (e.g., St. John, 1911a, b; Choudhary &
Beck, 2018; Beck & Choudhary, 2020). CEFs have also been observed in ideal
magnetohydrodynamic simulations (MHD; Siu-Tapia et al., 2018).

Louis et al. (2014) did one of the first specific analyses of a CEF. They
reported a maximum line-of-sight velocity of 1.6 km s-1, an area of 5.2
arcsec2 ($\sim$2.6 Mm 2), and a lifetime of 1 h for the single event they
studied. These authors associated these flows with the evolution of the
sunspot, which fragmented two days after the analyzed observations. Siu-Tapia
et al. (2017) found that the global properties inside a CEF, such as
temperature, magnetic field strength ($B$), and the line-of-sight velocity
($v_{{\rm LOS}}$) vary with height similarly to the properties in the parts of
the penumbra displaying the normal Evershed flow. Nonetheless, at the umbra-
penumbra boundary, magnetic fields with strengths of up to 8.2 kG and $v_{\rm
LOS}\gtrsim 15$ km s-1 at optical depth unity ($\tau=1$) were reported (Siu-
Tapia et al., 2019).

Recently, Castellanos Durán et al. (2021) reported that CEFs appear
ubiquitously in all types of sunspots. These authors found almost $\sim$400
CEFs in their survey and documented different types of CEFs. In particular,
they distinguished between those that appear in penumbrae bordering on regular
umbrae, and those CEFs that are linked to light bridges.

When analyzing the different contributions in the momentum equation inside a
simulated box from an MHD simulation, Siu-Tapia et al. (2018) confirmed that
the normal Evershed flow is a result of the overturning of the hot material
coming from the solar interior in the presence of an inclined magnetic field
(Rempel et al., 2009; Rempel, 2011). The CEFs in the simulations are,
according to Siu-Tapia et al. (2018), compatible with siphon flows, however.
Penumbral siphon flows result from asymmetric heating inside the flux tube
that produces the required difference in gas pressure to drive material along
the arched magnetic tubes (Thomas & Montesinos, 1993; Montesinos & Thomas,
1997), although, in CEFs, the siphon flows point in the opposite direction to
the normal Evershed flow.

Although the maintenance of CEFs during their steady phase, at least in the
MHD simulations, can be explained by the siphon flow mechanism, it remains
unclear, what process leads to the formation of the opposite direction to the
Evershed flow.Possible candidates identified by observers are flux emergence
(e.g., Louis et al., 2014, 2020), the adhesion of the penumbra from another
spot after two spots merge (Siu-Tapia et al., 2017), as well as the
association of granular and filamentary light bridges and CEFs (Castellanos
Durán et al., 2021).

The evolution over time of CEFs is still barely known (cf. Louis et al.,
2020). In contrast, the motion of another type of magnetic feature inside
sunspot penumbrae has been the topic of numerous studies. The expulsion of so-
called ‘sea-serpent’ magnetic fields lines was observed mainly in the plage
surrounding the sunspot, but also in the penumbra itself (Sainz Dalda & Bellot
Rubio, 2008). These small, bipolar features have a filamentary structure,
their length ranges between 2″and 5″and with a mean width of 1.5″. They
appeared in the mid-penumbra and are expelled radially outwards with
velocities ranging from 0.3–0.7 km s-1. Their lifetime ranges from 30 min up
to 7 h. After the expulsion, these structures continue to travel in the moat
up to 3–6″away from the penumbral boundary into the surrounding plage region.
The same authors suggested that these bipolar structures are moving U-loops
driven by the Evershed flow and are the precursors of moving magnetic features
(MMF; Harvey & Harvey, 1973; Zhang et al., 2003; Sainz Dalda & Martínez
Pillet, 2005; Zhang et al., 2007). Also, the so-called Evershed clouds
prominent in proper motion studies, have been related to MMFs (Cabrera Solana
et al., 2006).

The moat flow is a horizontal radially outward orientated flow starting from
the outer part of the penumbra and connecting the penumbral filaments with the
quiet Sun (e.g., Sheeley, 1969; Vargas Domínguez et al., 2007, 2008; Strecker
& Bello González, 2018). The typical velocity of the moat outflow ranges
between 0.8 and 1.4 km s-1 and it vanishes abruptly at a distance of similar
length as the penumbra away from the outer penumbral boundary (Sobotka &
Roudier, 2007; Löhner-Böttcher & Schlichenmaier, 2013).

In this work, we study the thermal and velocity conditions, magnetic field
structure, and the temporal evolution of three CEFs observed in AR 10930
(solar cycle 23) and AR 11967 (solar cycle 24). Two of these CEFs are seen to
be expelled radially outwards beyond the outer boundary into the moat of the
main sunspot within the Active Region (AR). The host sunspots of these CEFs
have been widely studied not only due to their peculiar flows, but also
because they belong to ARs that harbored superstrong magnetic fields (Siu-
Tapia et al., 2017; Okamoto & Sakurai, 2018; Siu-Tapia et al., 2019;
Castellanos Durán et al., 2020), and AR 10930 hosted four large X-class
flares. These solar flares are among the most studied and modeled X-class
flares of solar cycle 23 (e.g., Wang et al., 2008; Schrijver et al., 2008;
Gosain et al., 2009; Fan, 2011, 2016; Wang et al., 2022, and references
therein).

In this study, we aim to characterize the temporal evolution of three CEFs. In
particular, we analyze their appearance, evolution and expulsion, and describe
the new magnetic configuration after their expulsion. In addition, we discuss
the chromospheric response to the presence of CEFs.

This article is arranged as follows: Section 2 introduces the data and the
applied inversion method to retrieve the physical conditions within the CEFs
from spectropolarimetric data. Sections 3.1 and 3.2 describe the properties of
the three studied CEFs. The appearance and expulsion of CEFs are presented in
Sections 3.3 and 3.4. Section 3.5 illustrates the evolution of the magnetic
regions that are left after the expulsion of CEFs. In Section 3.6, we describe
the variation of $B$ and $v_{\rm LOS}$ within the CEFs. The chromospheric
response to the presence of CEFs is presented in Section 3.7. In Section 4, we
discuss our results and we conclude in Section 5.

Figure 1: Temporal evolution of AR 10930 as observed by Hinode/SOT-SP. Time
runs from top to bottom. Columns are the temperature, the magnetic field
strength $B$, $v_{{\rm LOS}}$ and the inclination of the magnetic field in the
line-of-sight. Contours show the inner and outer penumbra boundaries. The
black and green arrows mark CEF-1 and CEF-2, respectively. White circles shown
on the four bottom rows mark an intrusion into the umbra associated with
CEF-2. See Figure 3 for a zoom-in of this intrusion. See also Animation 1 part
of the online material.

##  2 Observations and methods

###  2.1 Data

We observed two sunspot groups from two different solar cycles. The sunspot
group AR 10930 was followed for 8 days starting on 2006 December 8, and the
sunspot group AR 11967 for 6 days starting from 2014 February 1. We analyzed
spectropolarimetric observations taken by the Japanese Hinode mission launched
in 2006 (Kosugi et al., 2007). The Spectro-Polarimeter (SP; Ichimoto et al.,
2008) aboard Hinode measures the four Stokes parameters $(I,Q,U,V)$ of the Fe
I line pair around 6302 Å, with a spectral sampling of 21.5 mÅ. We analyzed 42
scans of AR 10930 and 32 of AR 11967 (hereafter SCANS-A(00-41) and
SCANS-B(00-31), respectively). The spatial sampling along the slit and scan
direction can be either 0$\farcs$16 (normal mode) or 0$\farcs$32 (fast mode)
depending on the observing mode. Data were reduced using the nominal
Hinode/SOT-SP pipeline sp_prep (Lites & Ichimoto, 2013). We also analyzed all
the available photospheric $G$-band filtergrams and the chromospheric Ca II H
images taken by Hinode/SOT-BFI (Tsuneta et al., 2008), and the Stokes $V$ maps
from Hinode/SOT-NFI (Tsuneta et al., 2008) recorded in the intervals 2006
December 6 to 15 and 2014 February 1 to 6.

We use the following nomenclature throughout the paper: Letters A and B are
used to differentiate the Hinode/SOT-SP SCANS of AR 10930 and AR 11967,
respectively. Notice that for AR 10930, the Hinode/SOT-SP scans covered the
entire sunspot group; however, for AR 11967, many of the Hinode/SOT-SP scans
focused only on the eastern group of sunspots. We restrict our analysis to the
eastern group containing one of the CEFs, accounting for approximately
$\sim$1/3 of the total sunspot area within AR 11967. The left columns in
Figures 1 and 2 show a continuum image each of parts of AR 10930 and AR 11967
(see following sections for details). We use numbers 1 to 3 to mark the three
CEFs analyzed in detail in this study.

In addition, we used data from the Solar Dynamic Observatory (SDO; Pesnell et
al., 2012) taken by the Helioseismic and Magnetic Imager (HMI; Scherrer et
al., 2012; Schou et al., 2012). We analyzed the continuum intensity,
Dopplergrams ($v_{{\rm LOS}}$), and magnetograms ($B_{{\rm LOS}}$) obtained at
a spatial resolution of 1″. Two intervals were used with each of them having
different cadences and fields-of-view (FOV). The first interval covered the
entire passage of AR 11967 over the solar disk from 2014 January 28 at 20:00
UT to February 8 at 20:00 UT at a cadence of 12 minutes. The second interval
started on 2014 February 1 at 04:00 UT and lasted until February 2 at 12:00 UT
with the data taken at a cadence of 45 seconds. The FOV of the first dataset
was cropped to cover the entire AR 11967, whilst the second FOV was cropped to
cover the same region as observed by Hinode/SOT-SP, but extended to include
the eastern moat of the main sunspot of AR 11967 (see Animation 2). Continuum
maps were corrected for limb darkening following Castellanos Durán & Kleint
(2020).

###  2.2 Inversion scheme

To extract the physical information encoded in the Stokes profiles, we used
the Stokes Profiles Inversion-O-Routines (SPINOR) inversion code (Frutiger et
al., 2000). SPINOR builds on the STOkes PROfiles routines (STOPRO) that solve
the radiative transfer equations for polarized light (Solanki, 1987). In the
traditional scheme, SPINOR (as well as other inversion codes commonly used in
solar physics; e.g., the Stokes Inversion based on Response functions code
(SIR; Ruiz Cobo & del Toro Iniesta, 1992), the He-Line Information extractor+
code (HeLIx+; Lagg et al., 2004, 2009), the HAnle and ZEeman Light code
(HAZEL; Asensio Ramos et al., 2008), the Spectropolarimetic NLTE Analytically
Powered Inversion code (SNAPI; Milić & van Noort, 2018)), invert each pixel
$(x,y)[I(\lambda),Q(\lambda),U(\lambda),V(\lambda)]$ within the FOV
independently. However, these pixels are spatially coupled due to the action
of the point spread function (PSF) of the telescope. Recently, the spatially-
coupled concept has been extended into the STockholm inversion Code (STIC; de
la Cruz Rodríguez et al., 2019) to account for simultaneous observations taken
by different instruments with intrinsically different PSFs (de la Cruz
Rodríguez, 2019).

For the data analyzed here, the pupil of Hinode/SOT with its central
obscuration and the triangular spider produces a complex radially non-
symmetric PSF (Danilovic et al. (2008); cf. Figure 10 in van Noort, 2012).
This complex PSF couples the information of neighboring pixels and needs to be
taken into account when analyzing Hinode/SOT-SP observations. This was
achieved when van Noort (2012) developed the spatially coupled scheme for
inversions and implemented it into SPINOR (hereafter spatially coupled
inversion) that treated both, the spectropolarimetric information and the
inherent spatial degradation caused by the spatial PSF. This technique was
improved by showing that improved results are obtained by applying it to
finer, i.e. interpolated spatial pixels (van Noort et al., 2013).

Figure 2: Same layout as Figure 1 for AR 11967. Black arrows indicate the
location of CEF-3. See also Animation 2, which is part of the online material.
Figure 3: Zoom-in into the northern arrowhead-shaped region referred to as the
tip of CEF-2 in the main text (marked by the arrows). Time runs from top to
bottom. Columns are the temperature, the magnetic field strength $B$, $v_{{\rm
LOS}}$ and the inclination of the magnetic field relative to the line-of-
sight.

The spatially coupled inversions allowed to obtain excellent fits to the
observed Stokes profiles, while keeping a single depth-depended atmospheric
model when fitting different photospheric features (see e.g., van Noort et
al., 2013; Tiwari et al., 2015; Castellanos Durán, 2022). The spatially
coupled inversions of the Hinode/SOT-SP observations were carried out with a
depth-stratified atmosphere at three-node positions for the temperature,
magnetic field strength, inclination and azimuth, $v_{\rm LOS}$, and a
constant value for micro-turbulence that accounts for the broadening of the
spectral lines by unresolved turbulent motions. The spectral PSF is taken into
account by convolving the synthetic spectra with the instrumental profile
representing the spectral resolution of Hinode/SOT-SP (van Noort, 2012). The
node positions were placed at $\log\tau=(0,-0.8,-2.0)$ for AR 10930 following
Siu-Tapia et al. (2017), and at $\log\tau=(0,-0.8,-2.3)$ for AR 11967. Maps of
the retrieved atmospheric conditions for these two sunspot groups are
presented in Sections 3.1 and 3.2, as well as some examples of fits to the
observed Stokes profiles.

When the spatial PSF of the optical system is known, the spatially coupled
inversions can be used to estimate atmospheric conditions up to the
telescope’s diffraction limit. We upsampled the data by a factor of two before
running the spatially coupled inversions to fit substructures that are below
the spatial resolution of the telescope as recommended by van Noort et al.
(2013). After final convergence of the spatially coupled inversion, we
downsampled the retrieved atmospheric conditions and the best-fit profiles to
the original sampling. Data upsampling and downsampling were performed in
Fourier space.

Several Hinode/SOT-SP scans of all the CEFs analyzed in this work were taken
at $\mu-$values larger than 0.8, allowing us to determine their polarity with
reasonable accuracy without transforming the magnetic field into the local
reference frame. Examples of observed Stokes profiles and their fits obtained
with spatially coupled inversions are shown in Figure A1. These profiles were
chosen to display that even highly complex Stokes profiles are well modelled
with our inversion scheme.

Figure 4: Temporal evolution of the center of gravity of $v_{\rm LOS}$
($R_{v_{\rm LOS}}$; black line), magnetic field strength ($R_{B}$; dark gray
line), and brightness ($R_{I_{\rm c}}$; light gray line), as well as the area
(blue line; right axis) of CEF-1 (panel (a)) and CEF-3 (panel (b)). The
vertical line on the left panel represents the time when CEF-1 is totally
expelled from the penumbra of the main sunspot of AR 10930. After this time,
panel (a) shows the location of the centers of gravity and area of the spot
that formed at the location of where CEF-1 ended into the moat of AR 10930.
The vertical lines on panel (b) mark the times when CEF-3 started to grow
($t_{0}$, vertical solid line), when CEF-3 started to be expelled ($t_{1}$,
vertical gray dashed line), when the LOS magnetic field and velocity had their
maximum ($t_{2}$, vertical red dotted line), when the maximum area was reached
($t_{3}$, vertical blue dash-dotted line), and when CEF-3 was totally expelled
from the penumbra into the moat of AR 11967 ($t_{4}$, vertical grey dashed
line; see main text for details).

##  3 Results

###  3.1 CEFs in AR 10930

The $\delta$-sunspot group AR 10930 contains two large colliding sunspots of
opposite polarity, with the southern spot rotating rapidly counterclockwise.
This active region hosted two CEFs, both in the penumbra of the main sunspot
located in the north of AR 10930. The complexity and rotation of the sunspots
within AR 10930 influence the evolution of the CEFs that it harbored (see
below).

The first CEF (CEF-1) was observed on the north-west part of this sunspot and
remained within the penumbra for 17 Hinode/SOT-SP scans recorded between 2006
December 8 at 06:11 UT (SCANS-A00, $\mu=0.56$) and 2006 December 10 at 21:00
UT (SCANS-A16, $\mu=0.92$). CEF-1 appeared as a red-shifted region within the
center-side penumbra surrounded by the normal Evershed flow, which appeared
blue-shifted when AR 10930 was located on the eastern hemisphere.

The second CEF (CEF-2) emerged on 2006 December 9 at 07:00 UT (SCANS-A08,
$\mu=0.76$) and completely vanished on 2006 December 11 at 11:10 UT
(SCANS-A20, $\mu=0.98$) before AR 10930 crossed the central meridional. CEF-2
appeared as an elongated, blue-shifted penumbral region enclosed by normal
penumbra on the limb-side (i.e., the normal Evershed flow in that part of the
penumbra was red-shifted). CEF-2 was located on the south-side of AR 10930.
CEF-2 connected the main umbra of AR 10930 and a smaller umbra with opposite
magnetic polarity. CEF-2 appeared like a normal Evershed flow, but oriented
from the smaller umbra towards the bigger one, while on both sides of the
CEF-2 the Evershed flow was dominated by the main umbra (which would be CEFs
when viewed from the small umbra). This example shows the difficulty of
distinguishing between the normal Evershed flow and a CEF in more complex ARs.

Figure 1 displays the temporal evolution of both, CEF-1 and CEF-2. Columns
display from left to right the temperature, $B$, $v_{\rm LOS}$ and
$\gamma_{\rm LOS}$, all at the middle node.

The magnetic configurations of CEF-1 and -2 were very different. CEF-1 had the
same polarity as the main spot in AR 10930 close to the umbra-penumbra
boundary and opposite in outer penumbra. CEF-2 had opposite polarity to the
surrounding penumbrae. CEF-1 covered an area starting from the umbra-penumbra
boundary to the quiet Sun. CEF-2 appeared as a thin elongated filamentary
structure that grew until it formed a bridge between the main north positive
umbra and the growing south negative umbra. To better display the temporal
evolution of the CEF-1 and -2, we co-aligned the Hinode/SOT-SP scans with each
other and present them as Animation 1 among the online material.

###  3.2 CEF in AR 11967

Active region 11967 was one of the largest and most complex sunspot groups of
solar cycle 24. We tracked AR 11967 for 11.1 days. During this period 19 CEFs
were found at different parts of the sunspots belonging to this intricate
active region. In this work, we focus only on one of these CEFs, which was co-
observed by Hinode/SOT-SP. Hereafter we refer to this CEF as CEF-3 (Figure 2).
CEF-3 was observed when AR 11967 was on the eastern hemisphere and it emerged
as an intrusion in the penumbra with opposite polarity. CEF-3 was present in 9
out of 11 scans taken by Hinode/SOT-SP between 2014 February 1 at 10:42 UT
(SCANS-B00, $\mu=0.83$) and 2014 February 2 at 10:20 UT (SCANS-B10,
$\mu=0.96$). CEF-3 first appeared as two elongated penumbral filaments that
grew and later merged (Figure 2, SCANS-B00 to B02). It had opposite magnetic
polarity compared to the surrounding penumbra and the umbra in its vicinity.
CEF-3 expanded until it filled the entire length of the penumbra before it got
expelled. Animation 2 showing the temporal evolution of CEF-3 as seen by
SDO/HMI is available as online material.

In AR 11967 there is another elongated blue-shifted region in the south-west
of CEF-3 (see Figure 2, SCANS-B08 at (40, 20) Mm). This region is a widely
studied bipolar light bridge (Okamoto & Sakurai, 2018; Castellanos Durán et
al., 2020) that separates opposite polarity umbrae. Bipolar light bridges
usually harbor bi-directional flows, which can be identified by velocities of
alternating sign (Castellanos Durán, 2022). Consequently, the direction of
flows inside these regions cannot be classified as either normal or counter
Evershed flows.

###  3.3 Appearance of the CEFs

Unfortunately there are no Hinode/SOT data during the appearance phase of
CEF-1. For CEF-2 and CEF-3, we could follow their entire formation process.
These two CEFs appeared as intrusions inside a fully formed penumbra without
any merging with an external magnetic structure (see Figures 1 and 2),
resembling the emergence of new magnetic flux at the solar surface. This
appearance process of CEF-2 and CEF-3 is better seen in Animation 1 and
Animation 2.

In addition, during the appearance phase of CEF-2, the northern edge of the
penumbral filament that harbored CEF-2 showed a fairly distinctive behavior.
As time progresses, it developed into an arrowhead-shaped intrusion of the
penumbra towards the umbra. When the intrusion was fully formed, the umbra-
penumbra boundary shifted by $\sim$5 Mm towards the inner umbra. This region
is encircled in Figure 1, centered at (56, 56) Mm. Figure 3 shows a zoom-in
into this intrusion, revealing an enhanced $B$ at its edges. The flow at the
tip of the intrusion is of opposite direction to CEF-2 but has the same
direction of the normal Evershed flow at that location. Projection effects can
be excluded as a reason for the opposite flow direction and polarity, as
$\mu\\!\gtrsim\\!0.8$ and the tip of CEF-2 was located on the center side of
the main sunspot of the group. The continuum images exhibit a continuous
filamentary structure from the tip to the main body of CEF-2. The sign of the
flow and magnetic field in this region is consistent with a downflow at the
locality after being nearly vertical at the filament’s head. The filament that
harbored CEF-2 became more horizontal in the body and finally bent over to
return into the Sun at the tail. In that location within the tip, strong
fields were observed. When CEF-2 moved away from the umbra, the magnetic field
returned to nominal penumbral values.

###  3.4 Expulsion of the CEFs

After CEF-1 and CEF-3 grew to occupy almost the entire distance from umbral to
the outer penumbral boundary, the entire region containing the CEFs started to
move. The temporal evolution of these regions harboring CEFs shows a radially
outwards motion from the place they first appeared within the penumbra. They
moved towards the outer boundary of the main sunspot of the group parallel to
the penumbral filaments. We can trace the location of the CEFs at all times,
as the direction of $v_{\rm LOS}$ within them stayed opposite to the local
normal Evershed flow of the surrounding penumbra. Hereafter, we refer to the
outward motion of CEFs from the place they initially appear as their
expulsion.

Figure 5: Maps of the $v_{\rm LOS}$ (top) and continuum (bottom) during the
expulsion of CEF-1 and after it left the penumbra. $v_{\rm LOS}$ are clipped
at $\pm$4 km s-1. In the first two columns, AR 10930 was located on the
eastern solar hemisphere, while in the last four columns AR 10930 is on the
western hemisphere. This change in viewing geometry between hemispheres of AR
10930 causes the normal Evershed flow to appear in panels (a) to (b)
blueshifted and the CEF redshifted, while in panels (e) to (h) this pattern is
reversed. The time and heliocentric coordinates of each scan are marked on the
top part of each column. The full temporal evolution of CEF-1 is shown in the
middle row of Animation 1 part of the online material.

We used the available low-cadence Hinode/SOT-SP scans for CEF-1 and the
SDO/HMI data for CEF-3 to estimate the apparent velocity of the expulsion of
the CEFs through their proper motion. The restriction of SDO/HMI is the low
spectral resolution; however, SDO/HMI provides continuous 45 s-cadence LOS
velocity and magnetic field measurements, albeit at a single height (see
Animation 2). For the two data sets, we masked the CEFs and calculated the
location of the center of gravity $R$ of a quantity $F$ within the CEF as

$R_{F}=\frac{\sum_{\\{i,j\\}\in A_{\rm
CEF}}F_{ij}\sqrt{({r}_{0}-{r}_{ij})^{2}}}{\sum_{\\{i,j\\}\in A_{\rm
CEF}}F_{ij}},$ (1)

where $A_{\rm CEF}$ is the area covered by the CEF, $i,j$ identify pixels
inside the CEF (identified using the $v_{\rm LOS}$ maps) and ${r}_{0}$ is the
reference point chosen inside the closest umbra-penumbra boundary. By
replacing the placeholder $F$ by the parameters $I_{\rm c}$, $B$ or $v_{\rm
LOS}$, we obtained the centers of gravity of the brightness ($R_{I_{\rm c}}$),
of the magnetic field ($R_{B}$), and of the LOS velocity ($R_{v_{\rm LOS}}$).

In Figure 4 we present the temporal evolution of $R_{v_{\rm LOS}}$ (black
line), $R_{B}$ (dark gray), and $R_{I_{\rm c}}$ (light gray). The blue line
shows the temporal evolution of the area of the CEFs. Before CEF-1 and CEF-3
were expelled, $R_{B}$ was closer to the umbra, while $R_{I_{\rm c}}$ is
located in the mid-penumbra. This displacement between the centers of gravity
comes from the fact that the field strength increases towards the umbra, also
inside the CEFs. When these CEFs started moving the distance between the
centers of gravity reduced until they coincide.

The horizontal velocity of expulsion for CEF-1 is on average $65$ m s-1 (red
line in Figure 4(a)). This horizontal velocity traces the proper motion of the
entire CEF-1 on the surface of the Sun, and not the plasma flow velocities
within the penumbral filaments harbored inside CEF-1. The vertical dashed line
marks the time when the magnetic structure that forms CEF-1 leaves the
penumbra and a new spot starts forming. The maximum area of CEF-1 inside the
penumbra is 24.7 Mm2. In addition, the decay of CEF-1 reveals that it is
composed of individual strands harboring oppositely directed flows. While the
center-of-gravity of CEF-1 moves smoothly radially outwards, an individual
strand was observed moving with a speed ten times larger than the center-of-
gravity velocity (see the middle row of Animation 1).

We marked the expulsion of CEF-3 at five different moments (see vertical lines
in Figure 4(b)). The reference time is 2014 February 1 at 04:00 UT, which
corresponds to the first frame of Animation 2 provided as online material.
CEF-3 was sporadic (i.e., it appeared and disappeared) in the early phase
which lasted for 2 hours until it reached an area of $\sim$3 Mm2. Figure 4
starts at this time. At $t_{0}=\text{10:05\,UT}$ the size of CEF-3 started to
grow almost linearly in area at a rate of $130$ km2 s-1. Approximately five
hours later ($t_{1}=\text{14:40\,UT}$), CEF-3 started to be expelled with a
horizontal velocity of $117$ m s-1. Its maximum magnetic flux density and
maximum $v_{\rm LOS}$ were reached at $t_{2}=\text{18:50\,UT}$, well before it
reached its maximum area (13.1 Mm2) at $t_{3}=\text{20:58\,UT}$. This, again,
is because the strongest fields and $v_{\rm LOS}$ values are to be found at or
close to the umbral boundary. The innermost part of CEF-3 reached the outer
penumbral boundary at $t_{4}=\text{02:30\,UT}$ on February 2. After $t_{4}$, a
new spot started forming in the moat of the original host sunspot. The
opposite-directed flow with respect to the adjacent penumbra inside the new
spot suggests that this spot is formed from the same magnetic structure which
previously formed CEF-3. The further evolution plotted in Figure 4 follows
this spot.

Figure 6: Temporal evolution of the magnetic field strength (left column) and
$|v_{\rm LOS}|$ (right column) at $\tau_{5000\,\AA{}}=1$ inside the ROI in AR
10930 and AR 11967 and their CEFs. The black lines display the magnetic field
strength and $|v_{\rm LOS}|$ averaged over the entire ROI inside the sunspot
group. Colored lines show the mean values within CEF-1 (top), CEF-2 (middle)
and CEF-3 (bottom), while the colors indicate the Hinode/SOT-SP scan times,
starting from red and progressing to blue. The light-blue curve in each panel
(referring to the right axis) indicates the $\mu-$values of the scans.

CEF-2 also undergoes dynamical changes and moves away from the region where it
first appeared within AR 10930. However, a different mechanism seems to be at
work here. Recall that CEF-2 was located in between the north spot (main) and
the south spot (satellite). On 2006 December 10, the satellite spot started to
slowly rotate counterclockwise. The temporal evolution suggests that CEF-2
followed the counterclockwise rotation of the satellite spot, indicating that
it was anchored in the satellite umbra and was stretched by the satellite
spot’s rotation until CEF-2 disappeared (see e.g., Figure 1). This stretching
of CEF-2 can be seen in the bottom panels of Animation 1 provided as online
material.

###  3.5 What happens with the CEF magnetic structure after its expulsion?

During the expulsion of CEF-1, in the outer penumbra of the main spot of AR
10930, or just outside its boundary, a number of pores developed, which then
coalesced to form a small umbra with a penumbra attached to it (Figure 5).
Panel 5(i) shows the CEF-1 when it was located inside the penumbra of the main
spot. In panel 5(j) four small pore-like dark regions appear (black arrows).
These regions seem to merge and form a complex structure, as shown in panels
5(k) and 5(l). In panel 5(m) the new feature has coalesced into an umbra that
forms a penumbra on two sides including the one facing the penumbra of the
main spot. The flow inside the newly formed penumbra has the same flow
direction as the CEF-1 had when it was located inside the penumbra of the main
spot. This flow pattern can be seen in the change from a redshifted patch when
AR 10930 was on the eastern hemisphere (black arrows) to a blueshifted patch
of flow on the western hemisphere (green arrows). From the perspective of the
small umbra, the flow running along the newly formed penumbra has the
direction of the normal Evershed flow.

The newly formed region has the opposite magnetic polarity compared to the
main spot. The polarity of the new spot could be unambiguously determined from
the 19 Hinode/SOT-SP scans of AR 10930 that were taken close to disk center
($\mu\\!>0.9$). The newly formed region also showed a slow counter-clockwise
rotation in the moat of the main spot of AR 10930. The penumbra of the newly
formed spot reached its maximum area around 20 UT on December 11, before it
started to decay to a small pore on Dec 14. This pore was present for at least
six days, before disappearing behind the west limb. The full temporal
evolution can be seen in the middle row of Animation 1, which is part of the
online material. These observations suggest that the origin of the small spot
is closely related to the magnetic structure that harbored CEF-1.

Figure 7: Location of the strong magnetic field in CEF-1. The two rows show
the temperature (top) and magnetic field strength (bottom) at $\tau=1$.
Contours mark the umbra-penumbra boundary (yellow) and CEF-1 (blue).

CEF-3 was expelled into a region where the penumbra appeared to be extended in
a way that suggested a separate penumbra attached to the main penumbra of the
spot (in particular it suggests the same polarity and curvature of the field,
see Animation 2). Once outside the main penumbra of the sunspot, CEF-3
appeared to form small patches of penumbra, moving radially outward from the
host sunspot in the moat of AR 11967, increasingly resembling an orphan
penumbra (see Animation 2).

###  3.6 $B$ and $v_{\rm LOS}$ inside the CEFs

The magnetic field strength and $|v_{\rm LOS}|$ within the CEFs were taken
from the spatially coupled inversion of the Hinode/SOT-SP data. The left and
right columns of Figure 6 show the temporal evolution of the averaged $B$ and
$|v_{\rm LOS}|$, respectively. The black lines are the averaged values within
the region of interest (ROI) inside the sunspot group. We define the ROI as
the full map displayed in Figures 1 and 2, where we masked out the quiet Sun
(as the CEFs are present only in penumbrae), and the dark umbra (where the
inversion results are less reliable due to the blends with molecular lines
that form at low umbral temperatures). From top to bottom, the color-coded
lines are the averaged values of $B$ and $|v_{\rm LOS}|$ for CEF-1 to CEF-3.
Color-coded marks indicate the different time stamps of the scans. For CEF-1
and CEF-2 some scans overlap because CEF-1 and -2 are partly present at the
same time, hence some data points appear in both the top and middle panels.

The mean $B$ value within the ROIs was on average $\sim$2 kG, and showed
little variation over the course of the evolution of the active regions. In
the case of CEF-1, superstrong fields were observed in the early stages, when
the area of CEF-1 was largest and filled the entire penumbral sector. In this
phase, the CEF-1 reached the umbra-penumbra boundary (Figure 6(a)). In a later
stage, CEF-1 showed moderate field strengths, similar to the field strengths
observed in CEF-2 and -3 although CEF-2 also harbored individual pixels with
field strengths reaching 6 kG.

For CEF-2 the strongest magnetic fields occurred at the time of its
appearance, while the mean magnetic field of the spot was around $\sim$3.2 kG
(Figure 6(c)). Magnetic fields larger than 4 kG were seen inside CEF-2 during
its formation phase. The mean $B$ remained at a high value until about 20 hr
after its appearance. Thereafter it decreased.

The magnetic evolution of CEF-3 is different compared to the other two CEFs.
The mean value of $B$ inside CEF-3 oscillated around $\sim$1.9 kG (Figure
6(e)). The general trend of decreasing mean field strength with time, as seen
for CEF-1 and CEF-2, is not visible in CEF-3.

The $v_{\rm LOS}$ values strongly depend on the projection ($\mu$-value), and
therefore we do not compare their values one-to-one between different scans,
but rather provide a qualitative description of their evolution. For scans
observed close in time, the $\mu$-variation between scans is small, which
allows us to describe roughly the temporal evolution of the line-of-sight
velocity.

The temporal evolution of the line-of-sight velocity shows that CEF-1 harbored
considerably larger $|v_{\rm LOS}|$ values than the other two CEFs (Figure 6,
right column). Particularly during the early scans, CEF-1 was characterized by
supersonic $|v_{\rm LOS}|$. The photospheric sound speed lies typically in the
range $c_{s}\\!\sim\\!6\\!-\\!8$ km s-1. These fast $|v_{\rm LOS}|$ were co-
temporal and roughly co-spatial with the superstrong magnetic fields found in
CEF-1. In the late stages of CEF-1, the velocities returned to nominal
penumbral values. CEF-2 and CEF-3 showed mainly low $|v_{\rm LOS}|$ values,
with CEF-2 having a few points with clearly supersonic flows (roughly similar
in number to points having $B>4$ G).

The early superstrong fields in CEF-1 were located in the same pixels as those
first reported by Siu-Tapia et al. (2017, 2019). These strong magnetic fields
within CEF-1 stayed mostly close to the umbra-penumbra boundary at all times
(Figure 7). The number of pixels with strong fields decreased along with their
maximum field strength (Figure A1) at the time when CEF-1 lost contact with
the umbra. After the complete expulsion of CEF-1, the magnetic field strength,
as well as the other atmospheric parameters in the patch of penumbra that had
previously hosted it, returned to typical penumbral values (see e.g., Figure
1, SCANS-A14).

Figures 3.4 and 3.7 of Castellanos Durán (2022) show the distributions of $B$
and $|v_{\rm LOS}|$ inside these three CEFs and how they vary over time. As
discussed previously, those figures show a high number of pixels with strong
magnetic fields and fast LOS velocities when CEF-1 and CEF-2 were in contact
with the umbra-penumbra boundary. CEF-3 did not touch the umbra-penumbra
boundary and strong magnetic fields on the side of CEF-3 that was closer the
umbra-penumbra boundary were not present in CEF-3 at any time.

Figure 8: (a): Filtergram image of the chromospheric Ca II H lines. (b)-(g):
Examples of the chromospheric brightenings above CEF-1. (h), (i) and (k):
Light curves of the Ca II H mean intensity inside the three circular-sectors
enclosing CEF-1 (blue), CEF-2 (green) and a control region without CEF
(orange) marked in panel (a). See main text for how the circular sectors were
selected. (j): GOES light curve at 1-8 Å. GOES classes A to C represent the
X-ray flux integrated over the entire Sun in logarithmic scale ranging from
$10^{-8}$ to $10^{-6}$ W m-2, respectively. Images (b)-(g) and (l)-(q) show
examples of brightening events observed above CEF-1 ((b)-(g)) and CEF-2
((l)-(q)). Locations of CEFs are marked with yellow contours. The time is
marked with respect to the light curves in panels (h) and (k). Images are
normalized to the averaged quiet-Sun intensity and their dynamic ranges are
shown on the bottom left of each panel.

###  3.7 Chromospheric response above the CEFs

While the continuum images of the CEFs look very similar to the normal
penumbra, the chromosphere above these structures is much more dynamic. The
chromospheric images of the Ca II H line taken by Hinode/BFI show brightening
events that are co-spatial or appear at the boundaries of CEFs (cf. Louis et
al., 2014). These brightening events were observed repeatedly. To quantify
this chromospheric activity, we calculated the radiative flux in the Ca II H
line within three circular sectors for AR 10930 that hosted CEF-1 and CEF-2.
The aperture of these sectors is 90∘ with a radius of 36″. We selected the
areas to be of the same size for an unbiased comparison. The aperture and
radius of the sectors were chosen to fully contain the CEFs during all phases
of their evolution, covering also the strong elongation of CEF-2. In addition,
tests were performed by varying the aperture and radius of the circular
sectors (not shown). The similarity of the results obtained suggests that the
discussion below does not depend on the selection of the sectors.

Figure 8 displays the temporal evolution within the three sectors color-coded
blue for CEF-1, green for CEF-2, and orange for a control region containing
only a typical penumbra region without any CEF. The three-light curves (h),
(i), and (k) are normalized dividing by the area inside the circular sector
and the averaged quiet-Sun intensity. Since we are interested to quantify the
brightenings, i.e., short peaks in the light curve, rather than the long-term
evolution of the sunspot group, we fitted the background with a
10${}^{\mbox{th}}$-order polynomial and subtracted this fit from the light
curve. We also included the GOES 1-8 Å flux showing the soft X-ray activity
integrated over the entire solar disk. The light curves of the two CEF regions
indeed showed enhanced chromospheric emission. Examples of associated
brightenings appearing above or next to the location of CEFs range from small
events (Figure 8(b), (c), (l), (n)) to a large C-class flare seen in soft
X-rays (Figure 8(g)).

A similar analysis was carried out for CEF-3. Little brightening events are
also observed above CEF-3 (see Figure 9), however, their frequency and
intensity are lower compared to the high chromospheric activity above CEF-1
and CEF-2. The complex magnetic topology of AR 11967 and the continuous
chromospheric activity all over AR 11967 makes the chromospheric activity
above CEF-3 only a minor contributor.

Figure 9: Examples of chromospheric brightenings observed in the Ca II H line
above CEF-3. The dynamic range of the images, normalized to the averaged
quiet-Sun intensity, is given in the bottom part of each panel. Yellow
contours mark the location of CEF-3 in the underlying photosphere.

##  4 Discussion

We analyzed the photospheric properties inside three CEFs using spatially
coupled inversions. We also consider the influence of CEFs to the
chromosphere. We followed the temporal evolution of the CEFs by inverting all
the available spectropolarimetric maps taken by Hinode/SOT-SP of the sunspot
groups harboring them. The response at chromospheric heights above the CEFs
was characterized using the filtergraph images in the Ca II H line. Table 1
summarizes the properties of the three CEFs analyzed. We found that the CEFs
are expelled from the location in the main sunspot of the group at a velocity
of about $\sim$100 m s-1 where they emerged radially outwards into the moat of
the sunspot. To our knowledge there is just one report that showed the
expulsion of a CEF (Kleint & Sainz Dalda, 2013), however, that study focused
on the so-called umbral filaments and did not provide further information
about the CEF beyond the movement of the CEF.

The analyzed CEFs appear to be the result of two different processes. Although
there were no Hinode/SOT data available during the appearance phase of CEF-1,
Hinode/SOT-BFI and -NFI images of December 6 and early 7, when AR 10930
appeared on the east limb and before CEF-1 was formed, were available. Siu-
Tapia et al. (2017) suggested that CEF-1 resulted from the coalescence of a
satellite spot with the main spot, which inherited the penumbra of the
satellite spot. For CEF-2 and CEF-3 it was possible to follow their entire
formation process. These two CEFs appeared as intrusions within a fully
developed penumbra without the merging with any external magnetic structure
already visible on the solar surface. These intrusions mimic the appearance of
new magnetic flux at the surface of the Sun. Similar emergence-like CEFs were
observed in MHD simulations (Chen et al., 2017).

Using MHD simulations, Siu-Tapia et al. (2018) proposed that CEFs can be
driven by siphon flows. The gas pressure difference required to drive these
flows can originate from any process that leads to a field strength
enhancement at the endpoint of the flow. For a CEF, this is at the boundary
between the umbra and penumbra. Such field strength enhancements were indeed
observed for CEF-1 and CEF-2, making the siphon flow a possible driver of
these two flows. However, for CEF-3, no such field strength enhancement was
observed.

CEFs showed a slightly different inclination relative to the surrounding
penumbrae. This indicates that the reversed flow direction, which is the
signature of CEFs, is associated by and likely driven by a somewhat different
magnetic structure. Indeed, this is consistent with the finding of Siu-Tapia
et al. (2018) that CEFs are driven by a siphon flow, while the normal Evershed
flow is not.

ID | CEF-1 | CEF-2 | CEF-3
---|---|---|---
NOAA AR ID | 10930 | 10930 | 11967
Date first observed | 2006 Dec 8 | 2006 Dec 7 | 2014 Feb 01
SP/SCAN ID | A | A | B
Observed in SP/SCANS | 00-16 | 08-20 | 00-10
SDO/HMI | No | No | Yes
Lifetimea (hr) | 50 | 49 | 24
$\mu$ range | 0.56-0.92 | 0.76-0.98 | 0.83-0.96
Maximum areab (Mm2) | 24.7 | 12.3 | 17.7
Opposite polarityc? | No | Yes | Yes
Max $B(\log\tau=0)$ (kG) | 8.4 | 6.7 | 5
Max $v_{\rm LOS}(\log\tau=0)$ (km s-1) | 22.2 | 8.2 | 12.1
Location strongest $B$ | UPBd | UPBd | EPPFe
New spot formed? | Yes | No | Yes
Ejection mechanism | Radiale | Rotation AR | Radiale
Table 1: Properties of the three expelled CEFs. aLifetime inside the penumbra.
bMaximum area of the CEF. cOpposite polarity of the CEF with respect to the
main spot. dUPB: Umbra-penumbra boundary. eEPPF: End-point penumbra filament.
eRadially outward towards the moat of the AR.

CEF-1 (Animation 1) and CEF-3 (Animation 2) travelled radially outwards
through the penumbra. When these CEFs reached the outer boundary of the
penumbra of the main spot, a satellite spot started forming. The Evershed flow
of this newly formed spot was originally the CEF of the main spot and did not
change its flow direction (Figure 5) when detaching from the main sunspot.
This could suggest that the newly formed spot belonged to the same magnetic
structure that formed the CEFs inside the penumbra of the main spot. The newly
formed spot continued traveling into the moat of the main sunspot up to a
distance similar to the length of the adjacent penumbra of the main sunspot.
This distance coincides with the typical extension of the sunspot’s moat,
which often has the width of the penumbra in its vicinity (e.g., Brickhouse &
Labonte, 1988; Sobotka & Roudier, 2007). After the new spot travelled this
distance, it stopped its radially outward motion. During this process, the new
spot started decaying, losing its penumbra in the process (Figure 5l).

There is evidence that connects the Evershed flow and the moat flow as its
extension (Vargas Domínguez et al., 2007, 2008; Rempel, 2011). Also, there are
previous reports of magnetic structures moving radially outwards from the
penumbra into the moat, such as the expulsion of sea-serpent features and
Evershed clouds (Rimmele, 1994; Sainz Dalda & Bellot Rubio, 2008; Cabrera
Solana et al., 2006, 2007, 2008). Sea-serpent features and Evershed clouds
have (proper motion) expulsion speeds of $\sim$300–500 m s-1. These expulsion
speeds are faster than the expulsion speeds of CEF-1 ($\sim$65 m s-1) and
CEF-3 ($\sim$117 m s-1). The mean areas of sea-serpent features and Evershed
clouds ($\sim$1.2–2.5 Mm2) tend to be smaller than the areas covered by CEF-1
($\sim$10–25 Mm2) and CEF-3 ($\sim$2–13 Mm2). For all the features, the
direction of the expulsion is parallel to the Evershed flow direction at this
location. This suggests that the expulsion speed of a feature depends on its
area, although the statistics are rather poor. We speculate that this may
reflect a common mechanism responsible for the expulsion. This mechanism could
be related to the Evershed flow itself, accelerating smaller features to
higher velocities than larger ones. One possible test of this scenario would
be to use the large sample of CEFs presented by Castellanos Durán et al.
(2021). The sample covers a wide range of CEF areas. A common expulsion
mechanism may show up in a correlation of the areas of CEFs with their
expulsion speeds.

The process leading to the expulsion of CEF-2 appears to be different from
that affecting CEFs 1 and 3. The temporal evolution of CEF-2 suggests that its
disappearance is caused by the rotation of the satellite spot. CEF-2 was
anchored in the satellite umbra and subsequently stretched by the satellite
spot’s rotation until it disappeared (Figure 1). Two studies found that the
total rotation of the satellite spot in AR 10930 between 2006 December 10 and
2006 December 13 is $240^{\circ}-440^{\circ}$ (Zhang et al., 2007; Minoshima
et al., 2009). The rotation velocity of the spot increased almost linearly
from $\sim$0.25∘ hr-1 to $\sim$8∘ hr-1 (Figure 8(c) of Min & Chae, 2009) at
the time when CEF-2 vanished.

CEF-1 and CEF-2 showed downflows co-spatial with strong magnetic fields.
Strong $B$-values were always present at the umbra-penumbra boundary as long
as CEF-1 was in contact with it. The area covered by strong magnetic fields
and the maximum field strengths within these areas decreased when CEF-1 lost
contact with the umbra. After the complete expulsion of CEF-1, the magnetic
field strength and other atmospheric conditions in the same penumbral patch
returned to normal. In the case of CEF-2, the gas flowing towards the main
umbra was compressed by the strong field at the boundary of the umbra. The
compression subsequently amplified $B$ and $v_{\rm LOS}$ to the observed high
values in CEF-2. As with CEF-1, the magnetic field and $v_{\rm LOS}$ returned
to nominal penumbral values after the expulsion of CEF-2 (cf. Figures 3.5 and
3.7 of Castellanos Durán, 2022). The strong fields inside CEFs 1 and 2 could
be related to the so-called “magnetic barrier” (van Noort et al., 2013) as
proposed for CEF 1 by Siu-Tapia et al. (2019). This mechanism was first
proposed to explain the superstrong fields found at the endpoints of penumbral
filaments. In the case of CEFs 1 and 2, the material flowing in a penumbral
filament towards the umbra is forced to descend rapidly because of the
presence of the strong umbral field acting as the magnetic barrier and
hindering the flow from continuing. The magnetic barrier scenario also
explains why $B$ and $v_{\rm LOS}$ returned to nominal values after the CEFs
moved away from this barrier.

CEF-3 harbored strong fields of up to 5 kG located at the endpoints of the
penumbral filaments, similarly to the observations by van Noort et al. (2013).
Contrary to CEF-1 and CEF-2, CEF-3 emerged $\sim$1″ away from the umbra-
penumbra boundary. Therefore, no compression towards the umbra occurred there.

In concordance with previous works (e.g., Kleint, 2012; Kleint & Sainz Dalda,
2013; Louis et al., 2014, 2020), our data show many flares and brightenings
associated with CEFs (Figures 8 and 9). In addition, we also found increased
chromospheric activity that appears to depend on how far the inner part of the
CEF is located from the umbra-penumbra boundary. Thus, CEFs 1 and 2 that reach
this boundary show considerably higher activity than CEF-3.

The combination of the shear induced by the rotation of AR 10930 and the
complexity of the polarity inversion line (PIL) were proposed to be crucial to
triggering the X3.4 flare (SOL20061213T02:40; e.g., Kubo et al., 2007; Wang et
al., 2008; Schrijver et al., 2008; Jing et al., 2008; Lim et al., 2010; Gosain
& Venkatakrishnan, 2010; Fan, 2011; Ravindra et al., 2011; Inoue et al., 2011,
2012; He et al., 2014; Wang et al., 2022). However, to our knowledge, previous
studies neglected the opposite direction of the flow along the penumbral
filaments at the location where the major flare was triggered. CEF-2 appeared
in the middle of the penumbra and was then dragged/expelled with a rotation
rate of 4∘ hr-1 (Min & Chae, 2009) by the south satellite spot in AR 10930.
The remnants of CEF-2, visible in the $v_{\rm LOS}$ column of Animation 1,
coincide exactly with the location at the PIL which previous studies
recognized as the region where this major flare was triggered. The presence of
various opposite-directed flows, remnant from CEF-2 in this region, presents
an extra factor in the complexity of the PIL and might therefore be another
ingredient in triggering this X-class flare.

##  5 Summary and conclusions

In this study, we analyzed three CEFs observed in two sunspots groups. We
investigate their temporal evolution, and their chromospheric impact. In the
following, we summarize the main results of our study:

  * –

CEFs first appear close to or at the umbra-penumbra boundary and they grow
until they reach the outer penumbral boundary.

  * –

Two different processes can explain the formation of the three CEFs part of
this study. For CEF-1, Siu-Tapia et al. (2017) suggested that it could have
resulted from the coalescence of a satellite spot and the main umbra.
Differently, CEF-2 and CEF-3 appeared as intrusions within a fully formed
penumbra, independent of visible external magnetic structures (cf. Louis et
al., 2014, 2020; Guglielmino et al., 2017). This behavior is compatible with
the emergence of sub-surface magnetic flux within the penumbra. This was
discussed for a simulated spot that is forming (Chen et al., 2017). In these
circumstances, CEFs are related to new flux (either emerging directly in the
penumbra or just outside it). However, the CEFs studied here are within mature
spots.

  * –

After a growth phase, CEFs 1 and 3 are seen to start moving parallel to the
penumbral filaments. When they reach the outer part of the penumbra, a new
spot starts forming in the moat of the main sunspot. The direction of the flow
inside the penumbra of the newly formed spot is the same as in the CEFs and
opposite to the adjacent penumbra of the main spot. This provides strong
circumstantial evidence for a linkage between the CEFs and the newly formed
spots.

  * –

In the moat, the newly formed spot reached a maximum distance to the penumbra
at the outer boundary of the moat flow.

  * –

The expulsion speeds observed of CEF-1 and -3 in the penumbra are lower than
the ones of Evershed clouds (Cabrera Solana et al., 2006) and sea-serpent
magnetic features (Sainz Dalda & Bellot Rubio, 2008). Considering CEFs are
typically larger features (covering a larger area), one possible explanation
is that these speeds depend on the size of the features. These photospheric
features are often seen moving parallel to the penumbral filaments similar to
CEF-1 and CEF-3. Common to all (CEFs, Evershed clouds, and sea-serpent
features) is the presence of the normal Evershed flow surrounding these
features and parallel to the direction of the expulsion.

  * –

Siu-Tapia et al. (2017, 2019) showed for one Hinode/SOT-SP scan that
superstrong $B$ observed in CEF-1 were associated with these flows directed
towards the umbra, and that they were located mainly at the umbra-penumbra
boundary. We confirm the presence of the superstrong fields in several
Hinode/SOT-SP scans at different $\mu$-values. This makes a possible
interpretation of a strongly Doppler shifted component as a magnetic component
of strongly Zeeman splitted spectral lines less likely (cf. Castellanos Durán
et al., 2020). The temporal evolution of these superstrong $B$ showed that as
soon as the expulsion of CEF-1 begins, and the contact to the umbra is lost,
the maximum field strength drops. This supports the interpretation of Siu-
Tapia et al. (2019) that the origin of the superstrong fields in AR 10930 is
related to compression at the magnetic barrier formed by the umbral field (van
Noort et al., 2013).

  * –

The expulsion mechanism of CEF-2 is influenced by the complex evolution of AR
10930, and it is completely different from that of CEFs 1 and 3. CEF-2 was
apparently dragged and subsequently stretched by the rotation of the satellite
spot with a rotation rate of $\sim$4∘ hr-1.

Observers identify three physical processes that can lead to CEF formation:
flux emergence (e.g., Louis et al., 2014, 2020), adhesion of the penumbra from
another spot after merging (Siu-Tapia et al., 2017), and the association of
granular and filamentary light bridges and CEFs (Castellanos Durán et al.,
2021). Further observations of CEFs and analyses of the deeper layers using
simulated CEFs are needed to gain insight into the physical mechanisms
responsible for their formation and maintenance.

A total of 19 CEFs were identified in AR 11967, however, in this study we
focused on only two of them, for which multiple Hinode/SOT-SP observations
were available. These 19 CEFs come on top of the 387 CEFs already reported by
Castellanos Durán et al. (2021). An analysis of the known $\sim$400 CEFs could
form the basis of an in-depth statistical study of CEF properties and
evolution, to enhance not only our understanding of the nature of CEFs
themselves, but also their impact on the sunspot dynamics and on the layers
above CEFs.

In addition, the combination with new observations, in particular,
stereoscopic observations between Hinode or SDO/HMI, combined with SO/PHI
(Solanki et al., 2020) onboard Solar Orbiter (Müller et al., 2020), will allow
determining the two components of the velocity vector and not only the line-
of-sight component. This will provide us with the necessary additional
information to better understand CEFs.

We would like to thank the anonymous referee for careful reading and
suggestions that improved the quality of the manuscript. J. S. Castellanos
Durán was funded by the Deutscher Akademischer Austauschdienst (DAAD) and the
International Max Planck Research School (IMPRS) for Solar System Science at
the University of Göttingen. This project has received funding from the
European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation program (grant agreement No. 695075). Hinode is a
Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic
partner and NASA and UKSA as international partners. It is operated by these
agencies in cooperation with ESA and NSC (Norway). SDO is a mission of the
NASA’s Living With a Star program.

## Appendix

#### Figure A1

Examples of observed Stokes profiles and the location of the strong fields
within CEF-1 as a function of time. Highly complex Stokes profiles were chosen
to display the quality of the fits. The first two columns display the $v_{\rm
LOS}$ and continuum maps of CEF-1, where CEF-1 can be identified as a red
patch in the first column. Time runs from the top row to the bottom. Green,
blue, and yellow contours on columns 1 and 2 mark the locations harboring
fields stronger than 3.5 kG, 4 kG, and 5 kG, respectively. The number of
pixels inside the green contours (Nc) are displayed in the second column.
Columns 3 to 6 in Figure A1 show examples of observed Stokes profiles (gray
open circles) and the fits using the spatially coupled inversions (blue
lines). Notice that despite the high complexity of the observed Stokes
profiles at these locations, the spatially coupled inversions obtained
remarkably good fits (e.g., Castellanos Durán et al., 2020).

#### Animation 1

Temporal evolution of CEF-1 and CEF-2 as seen by Hinode/SOT-SP. This animation
is composed of nine panels that mainly show the expulsion of CEF-1 and CEF-2.
The columns display the continuum intensity, the magnetic field strength
(clipped below 1 kG and above 5 kG), the LOS velocity (clipped between $\pm$3
km s-1), and the LOS inclination of the magnetic field. The top row shows the
full AR 10930, while the second and third rows present close-ups of CEF-1 and
CEF-2 (black arrows). The cadence of the animation varies depending on the
availability of the Hinode/SOT-SP maps. The first frame starts on 2006
December 08 at 6:11 UT when AR 10930 was located in the solar western
hemisphere at (–697″, –83″). The last frame was taken on 2006 December 15 at
13:02 UT when AR 10930 was located in the eastern hemisphere at (711″, –86″).
The duration of the animation is 5 seconds.

#### Animation 2

Temporal evolution of CEF-3 as seen by SDO/HMI. The animation consists of four
panels that show the expulsion of CEF-3. Panels display the continuum
intensity (a), LOS magnetic field (b), LOS velocity (c), and the location of
CEF-3 (d; enclosed by black contours). The field of view covers an area of
$\sim 50\times 50$ Mm. Thin contours in all panels mark the locations of the
penumbra and umbra boundaries. The first frame starts on 2014 February 2 at
00:00 UT when the sunspot group was at (540″, –130″). The last frame was taken
on 2014 February 2 at 13:30 UT when AR 11967 was at (–220″, –125″). The
cadence between images is 45 seconds. The duration of the animation is 27
seconds. For better visibility of the processes in the penumbra, we masked out
umbral pixels in panels (b) and (c).

Figure A1: The full Stokes vector for seven different times in places where
CEF-1 harbored superstrong fields. Time runs from top to bottom. The locations
from where the profiles were extracted are marked on the $v_{\rm LOS}$ maps
and continuum images displayed in the first two columns, respectively. The
green, blue, and yellow contours on the same columns mark the
$B(\log\tau=-0.8)$ at 3.5 kG, 4 kG, and 5 kG levels, respectively. Nc is the
number of pixels within the green contours. The observed Stokes profiles
$I/I_{\rm c}$, $Q/I_{\rm c}$, $U/I_{\rm c}$, and $V/I_{\rm c}$ are displayed
in columns 3–6 by the black circles, and the best fit to the data using the
spatially coupled inversion is presented by the blue lines. The
$B(\log\tau=-0.8)$ values at each location retrieved by the spatially coupled
inversion are given in the panels in the third column (showing Stokes
$I/I_{\rm c})$.

## References

  * Asensio Ramos et al. (2008) Asensio Ramos, A., Trujillo Bueno, J., & Landi Degl’Innocenti, E. 2008, ApJ, 683, 542
  * Beck & Choudhary (2020) Beck, C. & Choudhary, D. P. 2020, ApJ, 891, 119
  * Borrero & Ichimoto (2011) Borrero, J. M. & Ichimoto, K. 2011, Living Reviews in Solar Physics, 8, 4
  * Borrero & Solanki (2008) Borrero, J. M. & Solanki, S. K. 2008, ApJ, 687, 668
  * Brickhouse & Labonte (1988) Brickhouse, N. S. & Labonte, B. J. 1988, Sol. Phys., 115, 43
  * Cabrera Solana et al. (2006) Cabrera Solana, D., Bellot Rubio, L. R., Beck, C., & del Toro Iniesta, J. C. 2006, ApJ, 649, L41
  * Cabrera Solana et al. (2007) Cabrera Solana, D., Bellot Rubio, L. R., Beck, C., & Del Toro Iniesta, J. C. 2007, A&A, 475, 1067
  * Cabrera Solana et al. (2008) Cabrera Solana, D., Bellot Rubio, L. R., Borrero, J. M., & Del Toro Iniesta, J. C. 2008, A&A, 477, 273
  * Castellanos Durán (2022) Castellanos Durán, J. S. 2022, PhD thesis, University of Göttingen
  * Castellanos Durán & Kleint (2020) Castellanos Durán, J. S. & Kleint, L. 2020, ApJ, 904, 96
  * Castellanos Durán et al. (2021) Castellanos Durán, J. S., Lagg, A., & Solanki, S. K. 2021, A&A, 651, L1
  * Castellanos Durán et al. (2020) Castellanos Durán, J. S., Lagg, A., Solanki, S. K., & Noort, M. v. 2020, ApJ, 895, 129
  * Chen et al. (2017) Chen, F., Rempel, M., & Fan, Y. 2017, ApJ, 846, 149
  * Choudhary & Beck (2018) Choudhary, D. P. & Beck, C. 2018, ApJ, 859, 139
  * Danilovic et al. (2008) Danilovic, S., Gandorfer, A., Lagg, A., et al. 2008, A&A, 484, L17
  * de la Cruz Rodríguez (2019) de la Cruz Rodríguez, J. 2019, A&A, 631, A153
  * de la Cruz Rodríguez et al. (2019) de la Cruz Rodríguez, J., Leenaarts, J., Danilovic, S., & Uitenbroek, H. 2019, A&A, 623, A74
  * Evershed (1909) Evershed, J. 1909, MNRAS, 69, 454
  * Fan (2011) Fan, Y. 2011, ApJ, 740, 68
  * Fan (2016) Fan, Y. 2016, ApJ, 824, 93
  * Frutiger et al. (2000) Frutiger, C., Solanki, S. K., Fligge, M., & Bruls, J. H. M. J. 2000, A&A, 358, 1109
  * Gosain & Venkatakrishnan (2010) Gosain, S. & Venkatakrishnan, P. 2010, ApJ, 720, L137
  * Gosain et al. (2009) Gosain, S., Venkatakrishnan, P., & Tiwari, S. K. 2009, ApJ, 706, L240
  * Guglielmino et al. (2017) Guglielmino, S. L., Romano, P., & Zuccarello, F. 2017, ApJ, 846, L16
  * Harvey & Harvey (1973) Harvey, K. & Harvey, J. 1973, Sol. Phys., 28, 61
  * He et al. (2014) He, H., Wang, H., Yan, Y., Chen, P. F., & Fang, C. 2014, Journal of Geophysical Research (Space Physics), 119, 3286
  * Ichimoto et al. (2008) Ichimoto, K., Lites, B., Elmore, D., et al. 2008, Sol. Phys., 249, 233
  * Inoue et al. (2011) Inoue, S., Kusano, K., Magara, T., Shiota, D., & Yamamoto, T. T. 2011, ApJ, 738, 161
  * Inoue et al. (2012) Inoue, S., Shiota, D., Yamamoto, T. T., et al. 2012, ApJ, 760, 17
  * Jing et al. (2008) Jing, J., Wiegelmann, T., Suematsu, Y., Kubo, M., & Wang, H. 2008, ApJ, 676, L81
  * Jurcák et al. (2007) Jurcák, J., Bellot Rubio, L., Ichimoto, K., et al. 2007, PASJ, 59, S601
  * Kleint (2012) Kleint, L. 2012, ApJ, 748, 138
  * Kleint & Sainz Dalda (2013) Kleint, L. & Sainz Dalda, A. 2013, ApJ, 770, 74
  * Kosugi et al. (2007) Kosugi, T., Matsuzaki, K., Sakao, T., et al. 2007, Sol. Phys., 243, 3
  * Kubo et al. (2007) Kubo, M., Yokoyama, T., Katsukawa, Y., et al. 2007, PASJ, 59, S779
  * Lagg et al. (2009) Lagg, A., Ishikawa, R., Merenda, L., et al. 2009, in Astronomical Society of the Pacific Conference Series, Vol. 415, The Second Hinode Science Meeting: Beyond Discovery-Toward Understanding, ed. B. Lites, M. Cheung, T. Magara, J. Mariska, & K. Reeves, 327
  * Lagg et al. (2004) Lagg, A., Woch, J., Krupp, N., & Solanki, S. K. 2004, A&A, 414, 1109
  * Lim et al. (2010) Lim, E.-K., Chae, J., Jing, J., Wang, H., & Wiegelmann, T. 2010, ApJ, 719, 403
  * Lites et al. (1993) Lites, B. W., Elmore, D. F., Seagraves, P., & Skumanich, A. P. 1993, ApJ, 418, 928
  * Lites & Ichimoto (2013) Lites, B. W. & Ichimoto, K. 2013, Sol. Phys., 283, 601
  * Löhner-Böttcher & Schlichenmaier (2013) Löhner-Böttcher, J. & Schlichenmaier, R. 2013, A&A, 551, A105
  * Louis et al. (2020) Louis, R. E., Beck, C., & Choudhary, D. P. 2020, ApJ, 905, 153
  * Louis et al. (2014) Louis, R. E., Beck, C., Mathew, S. K., & Venkatakrishnan, P. 2014, A&A, 570, A92
  * Milić & van Noort (2018) Milić, I. & van Noort, M. 2018, A&A, 617, A24
  * Min & Chae (2009) Min, S. & Chae, J. 2009, Sol. Phys., 258, 203
  * Minoshima et al. (2009) Minoshima, T., Imada, S., Morimoto, T., et al. 2009, ApJ, 697, 843
  * Montesinos & Thomas (1997) Montesinos, B. & Thomas, J. H. 1997, Nature, 390, 485
  * Müller et al. (2020) Müller, D., St. Cyr, O. C., Zouganelis, I., et al. 2020, A&A, 642, A1
  * Okamoto & Sakurai (2018) Okamoto, T. J. & Sakurai, T. 2018, ApJ, 852, L16
  * Pesnell et al. (2012) Pesnell, W. D., Thompson, B. J., & Chamberlin, P. C. 2012, Sol. Phys., 275, 3
  * Ravindra et al. (2011) Ravindra, B., Venkatakrishnan, P., Tiwari, S. K., & Bhattacharyya, R. 2011, ApJ, 740, 19
  * Rempel (2011) Rempel, M. 2011, ApJ, 729, 5
  * Rempel et al. (2009) Rempel, M., Schüssler, M., Cameron, R. H., & Knölker, M. 2009, Science, 325, 171
  * Rimmele (1994) Rimmele, T. R. 1994, A&A, 290, 972
  * Ruiz Cobo & del Toro Iniesta (1992) Ruiz Cobo, B. & del Toro Iniesta, J. C. 1992, ApJ, 398, 375
  * Sainz Dalda & Bellot Rubio (2008) Sainz Dalda, A. & Bellot Rubio, L. R. 2008, A&A, 481, L21
  * Sainz Dalda & Martínez Pillet (2005) Sainz Dalda, A. & Martínez Pillet, V. 2005, ApJ, 632, 1176
  * Scherrer et al. (2012) Scherrer, P. H., Schou, J., Bush, R. I., et al. 2012, Sol. Phys., 275, 207
  * Schlichenmaier & Schmidt (2000) Schlichenmaier, R. & Schmidt, W. 2000, A&A, 358, 1122
  * Schou et al. (2012) Schou, J., Scherrer, P. H., Bush, R. I., et al. 2012, Sol. Phys., 275, 229
  * Schrijver et al. (2008) Schrijver, C. J., DeRosa, M. L., Metcalf, T., et al. 2008, ApJ, 675, 1637
  * Sheeley (1969) Sheeley, N. R., J. 1969, Sol. Phys., 9, 347
  * Siu-Tapia et al. (2017) Siu-Tapia, A., Lagg, A., Solanki, S. K., van Noort, M., & Jurčák, J. 2017, A&A, 607, A36
  * Siu-Tapia et al. (2019) Siu-Tapia, A., Lagg, A., van Noort, M., Rempel, M., & Solanki, S. K. 2019, A&A, 631, A99
  * Siu-Tapia et al. (2018) Siu-Tapia, A. L., Rempel, M., Lagg, A., & Solanki, S. K. 2018, ApJ, 852, 66
  * Sobotka & Roudier (2007) Sobotka, M. & Roudier, T. 2007, A&A, 472, 277
  * Solanki (1987) Solanki, S. K. 1987, PhD thesis, ETH, Zürich
  * Solanki (2003) Solanki, S. K. 2003, A&A Rev., 11, 153
  * Solanki et al. (2020) Solanki, S. K., del Toro Iniesta, J. C., Woch, J., et al. 2020, A&A, 642, A11
  * St. John (1911a) St. John, C. E. 1911a, ApJ, 34, 57
  * St. John (1911b) St. John, C. E. 1911b, ApJ, 34, 131
  * Strecker & Bello González (2018) Strecker, H. & Bello González, N. 2018, A&A, 620, A122
  * Strecker & Bello González (2022) Strecker, H. & Bello González, N. 2022, A&A, 664, A195
  * Thomas & Montesinos (1993) Thomas, J. H. & Montesinos, B. 1993, ApJ, 407, 398
  * Tiwari et al. (2013) Tiwari, S. K., van Noort, M., Lagg, A., & Solanki, S. K. 2013, A&A, 557, A25
  * Tiwari et al. (2015) Tiwari, S. K., van Noort, M., Solanki, S. K., & Lagg, A. 2015, A&A, 583, A119
  * Tsuneta et al. (2008) Tsuneta, S., Ichimoto, K., Katsukawa, Y., et al. 2008, Sol. Phys., 249, 167
  * van Noort (2012) van Noort, M. 2012, A&A, 548, A5
  * van Noort et al. (2013) van Noort, M., Lagg, A., Tiwari, S. K., & Solanki, S. K. 2013, A&A, 557, A24
  * Vargas Domínguez et al. (2007) Vargas Domínguez, S., Bonet, J. A., Martínez Pillet, V., et al. 2007, ApJ, 660, L165
  * Vargas Domínguez et al. (2008) Vargas Domínguez, S., Rouppe van der Voort, L., Bonet, J. A., et al. 2008, ApJ, 679, 900
  * Wang et al. (2008) Wang, H., Jing, J., Tan, C., Wiegelmann, T., & Kubo, M. 2008, ApJ, 687, 658
  * Wang et al. (2022) Wang, X., Jiang, C., Feng, X., Duan, A., & Bian, X. 2022, ApJ, 938, 61
  * Zhang et al. (2007) Zhang, J., Li, L., & Song, Q. 2007, ApJ, 662, L35
  * Zhang et al. (2003) Zhang, J., Solanki, S. K., & Wang, J. 2003, A&A, 399, 755