11institutetext: Institute of Theoretical Astrophysics, University of Oslo,
P.O. Box 1029 Blindern, N-0315 Oslo, Norway 22institutetext: Rosseland Centre
for Solar Physics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo,
Norway

# Signatures of ubiquitous magnetic reconnection in the deep atmosphere of
sunspot penumbrae

Luc H. M. Rouppe van der Voort 1122 Jayant Joshi 1122 Vasco M. J. Henriques
1122 Souvik Bose 1122

( - submitted to A&A December 18, 2020 / accepted January 26, 2021.)

###### Abstract

Context. Ellerman bombs are regions with enhanced Balmer line wing emission
and mark magnetic reconnection in the deep solar atmosphere in active regions
and quiet Sun. They are often found in regions where opposite magnetic
polarities are in close proximity. Recent high resolution observations suggest
that Ellerman bombs are more prevalent than thought before.

Aims. We aim to determine the occurrence of Ellerman bombs in the penumbra of
sunspots.

Methods. We analyze high spatial resolution observations of sunspots in the
Balmer H $\alpha$ and H $\beta$ lines as well as auxiliary continuum channels
obtained with the Swedish 1-m Solar Telescope and apply the $k$-means
clustering technique to systematically detect and characterize Ellerman Bombs.

Results. Features with all the defining characteristics of Ellerman bombs are
found in large numbers over the entire penumbra. The true prevalence of these
events is only fully appreciated in the H $\beta$ line due to highest spatial
resolution and lower chromospheric opacity. We find that the penumbra hosts
some of the highest Ellerman bomb densities, only surpassed by the moat in the
immediate surroundings of the sunspot. Some penumbral Ellerman bombs show
flame morphology and rapid dynamical evolution. Many penumbral Ellerman bombs
are fast moving with typical speed of 3.7 km s-1 and sometimes more than 10 km
s-1. Many penumbral Ellerman bombs migrate from the inner to the outer
penumbra over hundreds of km and some continue moving beyond the outer
penumbral boundary into the moat. Many penumbral Ellerman bombs are found in
the vicinity of regions with opposite magnetic polarity.

Conclusions. We conclude that reconnection is a near continuous process in the
low atmosphere of the penumbra of sunspots as manifest in the form of
penumbral Ellerman bombs. These are so prevalent that they may be a major sink
of sunspot magnetic energy.

###### Key Words.:

Sun: activity – Sun: atmosphere – Sun: magnetic fields – sunspots – Magnetic
reconnection

##  1 Introduction

Magnetic reconnection is a fundamental process in magnetized astrophysical
plasmas for which magnetic energy is dissipated and converted into heat. In
the lower solar atmosphere, the hydrogen Balmer lines provide effective
tracers of reconnection sites as they exhibit remarkable enhanced emission in
their extended line wings as result of localised heating. This phenomenon of
enhanced wing emission, referred to as Ellerman “bombs” (EBs, Ellerman, 1917),
is particularly pronounced in emerging active regions with vigorous magnetic
flux emergence. At locations where opposite polarities are in close proximity
(i.e., at the polarity inversion line), EBs appear as subarcsecond sized
brightenings in H $\alpha$ line wing (see, e.g., Georgoulis et al., 2002;
Pariat et al., 2004; Fang et al., 2006; Pariat et al., 2007; Matsumoto et al.,
2008; Watanabe et al., 2008) and H $\beta$ line wing (Libbrecht et al., 2017;
Joshi et al., 2020) images. The fact that the enhancement is only in the wings
and that the EBs are invisible in the H $\alpha$ line-core locate the height
of the reconnection below the chromospheric canopy of fibrils (Watanabe et
al., 2011; Vissers et al., 2013; Nelson et al., 2013b). When observed from an
inclined observing angle, sufficiently away from the center of the solar disk,
and at sufficient spatial resolution, H $\alpha$ wing images show EBs as tiny
(1–2 Mm), bright, upright flames that flicker rapidly on a time scale of
seconds (Watanabe et al., 2011; Rutten et al., 2013; Nelson et al., 2015).
There is considerable spread in EB lifetimes but they rarely live longer than
a few minutes. We refer to Rutten et al. (2013) and Vissers et al. (2019) for
recent reviews of observational EB properties and their visibility in
different spectral diagnostics.

Traditionally, EBs have been associated with strong magnetic field
environments and therefore regarded as a typical active region phenomenon.
This view changed when Rouppe van der Voort et al. (2016) and later Shetye et
al. (2018) reported the existence of tiny ($\lesssim
0\aas@@fstack{\prime\prime}5$) Ellerman-like brightenings in quiet Sun when
observed at extremely high spatial resolution. Nelson et al. (2017) found
cases of quiet Sun EBs (QSEB) that were also visible in UV channels,
suggesting that at least some QSEBs are energetic enough to become detectable
in higher energy diagnostics. New high spatial resolution quiet Sun H $\beta$
observations presented by Joshi et al. (2020) show that QSEBs are much more
ubiquitous than the lower spatial resolution H $\alpha$ observations
suggested. The shorter wavelength H $\beta$ line allows for higher spatial
resolution and higher temperature sensitivity and the observations suggest
that about half a million QSEBs are present in the solar atmosphere at any
time.

The interpretation of EBs as markers of small-scale magnetic reconnection in
the lower solar atmosphere has been reinforced by the advanced numerical
simulations of Hansteen et al. (2017, 2019) and Danilovic (2017). In these
simulations, heating occurs along current sheets that extend over several
scale heights from the photosphere into the chromosphere. In synthetic H
$\alpha$ wing images, these current sheets are at the core of flame like
structures that resemble the characteristic EB flames in observations.

The sunspot penumbra is another environment in the lower solar atmosphere
where magnetic reconnection is likely to occur. In the penumbra, harboring an
“uncombed” magnetic field topology with strong magnetic fields at highly
variable inclination angles and considerable dynamic forcing from convective
flows, one may arguably expect ample occurrences of magnetic fields with
differing angles at sufficient close proximity to effectively interact and
reconnect (for reviews on the sunspot magnetic structure with strong-field
vertical spines and and weaker-field horizontal inter-spines, see e.g.,
Borrero & Ichimoto, 2011; Tiwari, 2017). Scharmer et al. (2013) detected small
regions of opposite polarity in a sunspot penumbra (also see Ruiz Cobo &
Asensio Ramos, 2013; Franz & Schlichenmaier, 2013), and that these regions
harbor convective downflows. Tiwari et al. (2015) found ample regions with
polarity opposite to the dominant sunspot polarity in a high quality Hinode
SOT/SP map.

Based on the experience that EBs are often found at the interface between
photospheric opposite polarity patches, we searched for EB signatures in high
quality H $\alpha$ and H $\beta$ sunspot observations. In particular, we
concentrated on the presence of flames in limbward observations as the
telltale EB signature. After close inspection of 13 datasets acquired over
more than a decade of observation campaigns, we conclude that EBs are
prevalent in sunspot penumbrae. The signature of penumbral EBs (PEBs) however
is often subtle and requires excellent observing quality. The H $\beta$ line
offers more clear detection in comparison to H $\alpha$, where the EB spectral
signature is often hidden by dense superpenumbral filaments. In this paper, we
present results from analysis of the best datasets.

##  2 Observations

The observations were obtained with the Swedish 1-m Solar Telescope (SST,
Scharmer et al., 2003a) on the island of La Palma, Spain. We used the CRisp
Imaging SpectroPolarimeter (CRISP, Scharmer et al., 2008) and the
CHROMospheric Imaging Spectrometer (CHROMIS) to perform imaging spectrometry
in the H $\alpha$ and H $\beta$ spectral lines. We used the standard SST data
reduction pipelines (de la Cruz Rodríguez et al., 2015; Löfdahl et al., 2018)
to process the data. This includes image restoration with the multi-object
multi-frame blind deconvolution (MOMFBD, van Noort et al., 2005) method and
the procedure for consistency across narrowband channels of Henriques (2012).
High image quality was further aided with the SST adaptive optics system
(Scharmer et al., 2003b) which has a 85-electrode deformable mirror operating
at 2 kHz.

The data recorded during the best seeing conditions was observed on 22
September 2017. During the best periods, the Fried’s parameter $r_{0}$ was
above 50 cm, with a maximum of 79 cm (for a discussion of measurements of
$r_{0}$ by the SST adaptive optics system, see Scharmer et al., 2019).
Unfortunately, the seeing was not consistently of high quality and the data
set is not optimal for temporal evolution studies. Most of the analysis and
data presented in Figs. 1–5 is based on the CHROMIS and CRISP spectral scans
recorded at 10:00:48 UT. The target area was the main sunspot in AR12681 at
$(X,Y)=(-749\arcsec,-296\arcsec)$, $\mu=\cos\theta=0.54$ with $\theta$ the
observing angle. With CHROMIS, we sampled the H $\beta$ line at 32 positions
between $\pm$1.37 Å with equidistant steps of 0.074 Å around the line core and
sparser in the wings to avoid line blends. The time to complete a full H
$\beta$ scan was 11.1 s. The CHROMIS data has a pixel scale of
0$\aas@@fstack{\prime\prime}$038 and the telescope diffraction limit
($\lambda/D$) is 0$\aas@@fstack{\prime\prime}$1 at $\lambda=4861$ Å. The
CHROMIS instrument has an auxiliary wide-band (WB) channel that is equipped
with a continuum filter which is centered at 4846 Å and has a full-width at
half-maximum (FWHM) of the transmission profile of 6.5 Å. This filter covers a
spectral region that is dominated by continuum and has relatively weak
spectral lines (see Löfdahl et al., 2018, for a plot of the transmission
profile in comparison with an atlas spectrum).

With CRISP, we sampled the H $\alpha$ line at 32 positions between $\pm$1.85 Å
from the line core with equidistant steps of 0.1 Å between $-1.6$ and $+1.3$
Å. In addition, CRISP was sampling the Fe i 6301 and 6302 Å line pair in
spectropolarimetric mode, with 9 positions in Fe i 6301 and 6 positions in Fe
i 6302, avoiding the telluric blend in the red wing. Furthermore, a continuum
position was sampled between the two lines. The time to complete full scans of
the H $\alpha$ and Fe i spectral lines was 19.1 s. The pixel scale of the
CRISP data is 0$\aas@@fstack{\prime\prime}$058.

The other dataset that we analyzed in detail was observed on 29 April 2016 and
was centered on the main sunspot in AR12533 at $(X,Y)=(623\arcsec,8\arcsec)$,
$\mu=0.75$. The seeing conditions were very good for the whole 1 h 30 m
duration of the time series which started at 09:43:09 UT. The $r_{0}$ values
were averaging at about 20 cm with peaks up to 30 cm. The online material
includes movies of the temporal evolution of the sunspot. For these movies we
have applied frame selection by rejecting 32 low quality images, this
corresponds to 12% of the total of 267 time steps. The CRISP instrument was
running a program with Ca ii 8542 Å spectropolarimetry and H $\alpha$ imaging
spectrometry at a cadence of 20 s. The H $\alpha$ line was sampled at 15
positions between $\pm$1.5 Å with 0.2 Å steps between $\pm$1.2 Å. We compare H
$\alpha$ wing images with images from the CRISP 8542 Å WB channel. For CRISP,
the WB channel branches off after the prefilter so that contrary to CHROMIS,
one cannot have imaging in a clean continuum band. The prefilter has a FWHM of
9.3 Å and is centered on the Ca ii 8542 Å line. The Ca ii 8542 Å spectra were
not included in our analysis. This data was earlier analyzed by Drews & Rouppe
van der Voort (2020) to study penumbral micro jets and the co-aligned SST and
IRIS data were publicly released as described by Rouppe van der Voort et al.
(2020).

For the exploration of all data, verification of detected events, and the
study and measurement of the dynamical evolution of PEBs in the 29 April 2016
data, we made use of CRISPEX (Vissers & Rouppe van der Voort, 2012), a widget-
based graphical user interface for exploration of multi-dimensional data sets
written in the Interactive Data Language (IDL).

##  3 Methods

#### Inversions.

We have performed Milne-Eddington (ME) inversions of the Fe i line pair
observed on 22 September 2017 to infer the magnetic field vector utilizing a
parallel C++/Python implementation111https://github.com/jaimedelacruz/pyMilne
(de la Cruz Rodríguez, 2019). The magnetic field vector retrieved from the ME
inversions are an average over the formation height of the Fe i line pair. For
these lines, the response of Stokes profiles to magnetic field is maximum
around optical depth 0.1 at 5000 Å in sunspot penumbrae (e.g., see Fig. 9 of
Joshi et al., 2017).

We resolved the 180° ambiguity in our magnetic field vector measurements using
the acute angle method (Sakurai et al., 1985; Cuperman et al., 1992). The
inferred magnetic field vector in the line-of-sight frame of reference is
projected to the disk center coordinates where $B_{z}$ represents the magnetic
field component normal to the solar surface and $B_{x}$ and $B_{y}$ are the
two orthogonal components projected onto the solar surface.

To better resolve opposite polarity patches in the penumbra, we corrected for
stray light prior to the inversions. We assumed a Gaussian point spread
function (PSF) with FWHM of 1$\aas@@fstack{\prime\prime}$2 and 45% stray
light, following similar stray light corrections that were considered for
CRISP/SST observations in earlier studies. For example, Scharmer et al. (2011)
and Scharmer & Henriques (2012) compensated for stray light using a PSF with
FWHM of 1$\aas@@fstack{\prime\prime}$2 and 56% stray light contribution. Joshi
et al. (2011) assumed 35% stray light and a Gaussian PSF with FWHM of
1$\aas@@fstack{\prime\prime}$6\. Moreover, from a detailed analysis of solar
granulation contrast, Scharmer et al. (2019) concluded that stray light at the
SST comes mainly from small-angle scattering and that the wings of the
uncorrected PSF do not extend beyond 2″.

####  k-means clustering.

We used the $k$-means clustering technique (Everitt, 1972) to identify EB
spectra in the H $\beta$ spectral line observed on 22 September 2017. The
$k$-means method is widely used for the characterization of a variety of solar
phenomena and observations. Examples include the classification of Mg ii h and
k line profiles observed with IRIS (Sainz Dalda et al., 2019), the
identification of Mg ii h and k spectra in flares (Panos et al., 2018), and Ca
ii K observations of on-disk spicules (Bose et al., 2019, 2021). Our approach
for clustering the H $\beta$ spectra is very similar to that employed by Joshi
et al. (2020) and Joshi & Rouppe van der Voort (2020) to identify QSEBs in
their H $\beta$ observations. With the $k$-means method we divided H $\beta$
spectra into 100 clusters and each cluster is represented by the mean of all
profiles in that cluster. This mean profile is referred to as representative
profile (RP). Out of 100 RPs we found that 29 RPs show line wing enhancement
that is characteristic of EBs. Of these 29 selected RPs with enhanced wings,
25 RPs have essentially an unaffected line core, while the rest show an
intensity enhancement in the line core. Inclusion of the four RPs, that have
an enhanced line core as EB profiles, is motivated by Joshi et al. (2020) who
found that unlike typical H $\alpha$ EB profiles, some EBs can show raised
intensity level even in the H $\beta$ line core. A detailed description of
selected RPs with EB-like H $\beta$ spectral profiles is provided in Sect. 4.

Based on spatial locations of selected RPs, we created a binary mask which was
then used to perform two dimensional (2D) connected component labeling (Fiorio
& Gustedt, 1996) that assigns a unique label for each isolated patch in the
binary mask. We then used the labels to estimate their area, brightness
enhancement and radial distance from the geometric center of the sunspot for
each individual EB. A detailed statistical analysis of these parameters is
presented in Sect. 4.

##  4 Results

###  4.1 PEB morphology and general appearance

Figure 1: Limb-side part of the sunspot in AR12681 observed on 22 September
2017 in H $\beta$ and H $\alpha$ blue wing and CHROMIS WB 4846 Å. PEBs are
visible as small bright features all over the penumbra, some with clear flame
morphology sticking straight up between filaments. These PEBs are invisible in
the continuum WB image. The direction to the nearest limb is approximately
upward along the $y$-axis. The top image includes six squares labelled A–F
that mark ROIs that are shown in detail in Fig. 2. An animation of this figure
is available as online material at
https://www.mn.uio.no/astro/english/people/aca/rouppe/movies/. This animation
shows a spectral scan through the H $\beta$ and H $\alpha$ lines.

Figure 2: Details of EBs in and outside the penumbra of the sunspot shown in
Fig. 1 in 6 ROIs. The spatial $X,Y$ coordinates are at the same scale as Fig.
1. The top row of panels for each ROI shows H $\beta$ and H $\alpha$ blue wing
and CHROMIS WB 4846 Å images. The bottom left panels show $\lambda x$-diagrams
of the spectral profiles along the red dotted line in the panels above. The
bottom right panel shows spectral profiles for H $\beta$ (solid black line)
and H $\alpha$ (dashed line) from the position of the red cross in the top
left panels. The thin gray profiles are reference spectral profiles averaged
over an area outside the sunspot. The intensity scaling is normalized to the
level of the far red wing of the reference profile. The red tickmark in the
bottom row panels indicates the line position of the wing images in the top
left. ROI A is centered on a strong EB outside the sunspot. ROI B is centered
on an EB at the outer edge of the penumbra. All other examples are PEBs inside
the penumbra.

Figure 1 shows the limb-side part of the 22 September 2017 sunspot in the blue
wings of H $\beta$ and H $\alpha$ as well as in CHROMIS WB 4846 Å. The offset
from line core was chosen to be close to the maximum of the typical EB profile
as to show EBs at highest contrast. Some prominent EBs are visible as
pronounced flames in the moat around the sunspot outside the penumbra. As
expected, the EBs are not visible in the continuum dominated WB image. Inside
the penumbra, there are a large number of small bright features present in the
Balmer wing images but clearest in the H $\beta$ wing image and not visible in
the WB image. Some of these appear as small linear features sticking straight
up from between the penumbral filaments, resembling the larger EB flames in
the surrounding sunspot moat.

The animation associated with Fig. 1 shows a spectral line scan through the H
$\beta$ and H $\alpha$ lines for comparison. From the animation it is evident
that in the penumbra the EB-like brightenings in the H $\beta$ wings also
persist in and close to the line core wavelength positions. However, these
compact brightenings in the H $\beta$ line core are absent in the H $\alpha$
line core which predominantly show chromospheric superpenumbral fibril
structures.

Figure 2 zooms in on 6 regions of interest (ROI). In the upper left, ROI A is
centered on the most prominent EB in the FOV, with the telltale flame towering
about 600 km above the intergranular lane from where it appears to emanate.
The CHROMIS WB image shows no trace of the EB, only some striations in the
background faculae, which are unrelated to the EB phenomenon. The $\lambda
x$-diagrams and spectral panel show the well-known characteristic EB Balmer
profile with enhanced wings and unaffected line core. The peak wing
enhancement is more than 2 times the level of the reference profile which is
averaged over a quiet region. The higher contrast and higher spatial
resolution in the H $\beta$ data compared to H $\alpha$ is clear, for example
from the fine structure and spatial variation in the $\lambda x$-diagram. The
EB in ROI A serves as reference for the EBs presented in the other ROIs.

In ROI B, a clear EB flame is located at the outer edge of the penumbra. The
vertical extension of this flame has a length of about 450 km. The other four
ROIs are all inside the penumbra and are centered on PEBs. Of these, ROI F is
centered on the tallest flame which has a length of about 350 km. The H
$\beta$ wing image shows clear substructure in the PEB while it is more an
extended fuzzy feature in the H $\alpha$ wing image. For this case, the wing
enhancement in the H $\beta$ profile is only slightly larger than in H
$\alpha$. For the PEB examples in ROIs C and D, the differences in wing
enhancement is larger, in particular in ROI C where the peak in wing
enhancement is almost as high as for the large EB in ROI A. Flame morphology
in ROI C might be difficult to discern because the PEB is aligned along the
penumbral filaments that, in this part of the penumbra, are aligned in the
direction of the nearest limb (i.e. along the line-of-sight). ROI E is
centered on a PEB that has hardly enhanced wings in the profile plot but
clearly shows a little flame in the H $\beta$ wing image and is unmistakably
present in the $\lambda x$-diagram. While this PEB might be weak, its absence
in the WB image is striking. This weak event is detected as a PEB with the
$k$-means method.

In all of these ROIs the penumbra in WB appears smoother than in the Balmer
wing images. Particularly in the H $\beta$ wing there are many small bright
features, like bright “crumbs”, scattered over the penumbra. Some of these are
very bright and show the characteristic EB wing enhancement and are clear
PEBs. Many others show only subtle wing enhancement but are notably absent in
the WB image. To the left of the PEB, in ROI F, the red dashed line crosses
some of these “crumbs” and the $\lambda x$-diagram shows wing enhancement when
compared to their surroundings, but clearly not so much as the central PEB.

Figure 3 shows all H $\beta$ RPs that have been identified as showing EB
spectral signatures. Representative profiles 0–24 have profiles similar to
typical H $\alpha$ EB profiles with enhanced wings and essentially unaffected
line core whereas RPs 25–28 display intensity enhancement in the line core
along with enhancement in the wings. Each detected EB in our dataset displays
a combination of RPs plotted in Fig. 3. For example, the PEB shown in the ROI
E of Fig. 2 is identified as a line core brightening and represented by a
combination of RPs 27 and 28. Similarly, a part of the PEB in ROI C is
identified as a line core brightening by RP 25. The rest of the EBs and PEBs
in Fig. 2 predominantly exhibit wing intensity enhancement in combination with
unaffected line cores and are clustered following RP 0–24.

Besides the RPs, Fig. 3 shows a density distribution of all H $\beta$ profiles
that are included in each cluster. The density distributions are narrow and
centered around the RPs. However, in some clusters the farthest profile shows
some significant deviation from the corresponding RP. For example, in clusters
represented by RP 7 and 23, the farthest profiles have quite different shape
as compared to their respective RPs. Nevertheless, these farthest profiles
also show characteristic EB-like spectral profiles.

Figure 3: Twenty nine representative profiles (RPs) from the $k$-means
clustering of the H $\beta$ line that are identified as signature of EB. The
black lines show RPs whereas shaded colored areas represent density
distribution of H $\beta$ spectra within a cluster; darker shades indicate
higher density. Within a particular cluster, the H $\beta$ profile that is
farthest (measured in euclidean distance) from the corresponding RPs is shown
by the black dotted line. As reference, the average quiet Sun profile (gray
line) is plotted in each panel. RPs 0–24 show the typical EB-like H $\beta$
profiles, i.e., enhanced wings and unaffected line core, while RPs 25–28
display both an enhancement in the wings as well as in the line core. The
parameter $n$ represents the number of pixels in a cluster as percentage of
the total of $\sim 1.73\times 10^{6}$ pixels.

###  4.2 Magnetic field environment

Figure 4: The location of PEBs compared to the vertical magnetic field
$B_{z}$. The top left panel shows a split image of the sunspot observed on 22
September 2017 with the left part in the H $\beta$ blue wing at $-0.2$ Å
offset and the right part at $-0.6$ Å. The blue contours indicate the radial
distance $r/\mathrm{R_{spot}}$ to the umbral center that is marked with the
blue cross. The contour for $r/\mathrm{R_{spot}}=1.00$ is the outer penumbra
boundary, defined from the associated WB image. The top right panel shows the
$B_{z}$ map, derived from ME inversions of the Fe i lines, scaled between
$-400$ and $+1600$ G. Regions with artifacts due to the de-projection method
are marked in green. The sets of panels at the bottom show four ROIs in H
$\beta$ $-0.2$ Å, $-0.6$ Å, and $B_{z}$ respectively. Red contours outline
PEBs detected through the $k$-means method.  Figure 5: Distribution of EBs and
their properties with respect to radial distance from the sunspot center
(observed on 22 September 2017). The outer sunspot boundary is at
$r/\mathrm{R}_{\mathrm{spot}}=1$ and is marked with the yellow vertical line,
also see the contours in Fig. 4. The statistics are based on $k$-means
detections, the total number of EB detections is 372, of which 108 are PEBs.
The top panel shows the EB occurrence. The red curve shows the ratio of
negative magnetic polarity flux relative to total absolute flux (the sunspot
is dominated by positive polarity). The blue curve shows the fraction of
pixels with negative polarity relative to all pixels with significant magnetic
signal ($|B_{z}|>50$ G). The middle panels show the area of the EB detections.
The bottom panels show the H $\beta$ wing brightness enhancement of the
brightest pixel in the EB detection relative to the local background in a
100$\times$100 pixel area and excluding EB detection pixels. The brightness
enhancement is relative to the outer most wavelength positions on both sides
of the line center of the background H $\beta$ profile and on a scaling set by
the normalized quiet Sun reference profile. For the two bottom rows, the right
panels show occurrence histograms with the black line outlining the histograms
for PEBs. The histogram bin size is 0.003 Mm2 in area and 0.12 in brightness
enhancement. The grey lines in the left panels mark the average values for
each radial distance $r/\mathrm{R}_{\mathrm{spot}}$.

In order to study the occurrence of PEBs with respect to the magnetic field in
the vicinity, we compare EB detections from the $k$-means method with the
$B_{z}$ map derived from the Fe i lines. This is illustrated in Fig. 4. The
sunspot is dominated by positive magnetic polarity but the $B_{z}$ map also
shows many small isolated patches with significant opposite (negative)
polarity within the outer penumbra boundary. We find that many PEBs are
located in the vicinity of these opposite polarity patches. This can be seen
at close look in the four ROIs in the bottom of Fig. 4. Red contours outline
EB detections and there are some clear examples of PEBs that are located at or
close to the interface where opposite polarities meet. We note however, that
we also find PEBs located in unipolar regions, for example the PEB in the
center of the lower left ROI.

As mentioned before, PEB brightenings can also be visible in and close to the
H $\beta$ line core, see the left H $\beta$ $-0.2$ Å part of Fig. 4 (top
left), that displays numerous compact brightenings in the penumbra. A number
of PEBs that can be seen in the H $\beta$ line core are shown in more detail
in the ROIs presented in the bottom of Fig. 4. For example, in the upper-left
ROI, two big PEBs at the sunspot boundary are visible in the wing as well as
close to the line core. The PEBs at
$(X,Y)=(41\aas@@fstack{\prime\prime}5,23\aas@@fstack{\prime\prime}6)$ and
$(X,Y)=(41\aas@@fstack{\prime\prime}0,22\aas@@fstack{\prime\prime}8)$ in the
upper-right ROI are predominantly visible at $-0.2$ Å while they have only
subtle brightenings in the outer H $\beta$ line wing.

The statistics shown in Fig. 5 provide a quantified context of the observation
that PEBs are often found in the vicinity of opposite polarities: the top
diagram shows that both the number of PEBs and the contribution from opposite
polarity patches increase towards the outer penumbra. Both the relative area
(blue curve) and opposite polarity flux (red curve) increase to more than 10%
at the outer penumbra boundary.

With the $k$-means clustering method, we detected a total of 372 EBs of which
108 are in the penumbra. We found no EBs in the umbra. In the inner penumbra,
$0.5\leq r/\mathrm{R}_{\mathrm{spot}}\leq 0.75$, the number density of
detected PEBs is 0.29 Mm-2, and the fraction of the total area covered by PEBs
is 0.007 (i.e., the area filling factor). In the outer penumbra,
$0.75<r/\mathrm{R}_{\mathrm{spot}}\leq 1$, the number density is 0.76 Mm-2,
and the area filling factor 0.032. In the immediate surroundings of the
sunspot, in the moat, $1<r/\mathrm{R}_{\mathrm{spot}}\leq 1.25$, the EB number
density is 1.72 Mm-2, and the area filling factor 0.037. The number density of
all 372 EBs detected over the full CHROMIS FOV is 0.27 Mm-2. For two other H
$\beta$ spectral scans of this sunspot, recorded under less optimal seeing
conditions, we find fewer but comparable numbers of EB detections: for a scan
with quiet Sun granulation contrast 15.0%, there are 304 EB detections of
which 90 PEBs, and for a scan with 14.6% contrast, there are 252 EBs of which
75 PEB (the contrast for the best scan is 15.7%). So about 30% of the EBs
detected in the FOV are inside the penumbra.

Figure 5 further provides statistics on the area and brightness enhancement of
the EB detections. The largest PEBs are found towards the outer penumbra and
PEBs do not stand out as being smaller or larger than EBs outside the sunspot.
The mean area for PEBs is 0.039 Mm2 (standard deviation $\sigma=0.055$ Mm2)
and for EBs outside the sunspot 0.022 Mm2 ($\sigma=0.041$ Mm2). The trend in
the area distribution has a sharp cut off at 0.0037 Mm2 (five pixels) which is
set by the spatial resolution. This suggests that there exist smaller EBs that
are not resolved. Many small bright features in the H $\beta$ wings described
as “crumbs” in Sect. 4.1 were not detected by the $k$-means method. In some
cases where these features were detected, only a few of the brightest pixels
were identified as PEBs and not the whole morphological structure. Thus, these
detections also contribute to the population of PEBs with smallest areas. We
excluded all EB events with area less than five pixels in our statistical
analysis.

Also in terms of wing brightness enhancement, as shown in the bottom of Fig.
5, PEBs do not stand out as compared to EBs. The average wing brightness
enhancement for PEBs is 0.72 ($\sigma=0.33$) and for EBs outside the sunspot
0.78 ($\sigma=0.35$). Here, the H $\beta$ wing enhancement was measured
against the average intensity of the outermost wavelength positions in the
local background (over an area of $100\times 100$ pixels). The majority of the
EBs, within the penumbra as well as in the surroundings of the sunspot, have a
brightness enhancement between 0.5 and 1. However, some PEBs in the outer
penumbra and some EBs in close proximity of the sunspot are brighter, and for
some, the intensity enhancement relative to the local surroundings is larger
than 2. The brightest EBs were classified as RP 0–2 (see Fig. 3) for which the
blue wing is raised more than three times the level of the reference quiet
Sun.

###  4.3 Temporal evolution

Figure 6: Temporal evolution of PEBs in the sunspot in AR12533 observed on 29
April 2016. The top left image shows an H $\alpha$ blue wing image at $-0.8$ Å
with three regions of interest (ROI) marked with labels A, B, and C. The
temporal evolution for these ROIs is shown in the rows with smaller H $\alpha$
wing images where the time is marked in the top left. The bottom row of images
shows the temporal evolution in ROI C in WB 8542 Å for comparison. The spacing
between large tick marks in the ROI images is 1″. The contrast in the top left
overview image is enhanced by applying a gamma correction with $\Gamma$=2, all
other images have linear scaling on a common scale for each ROI. Three
animations associated to this figure are available as online material: a movie
of the sunspot in the H $\alpha$ blue wing as in the upper left panel, the
corresponding movie in WB 8542 Å, and a combined movie showing the left part
of the sunspot. See
https://www.mn.uio.no/astro/english/people/aca/rouppe/movies/.

The temporal evolution of PEBs was studied in the 29 April 2016 observations
of the sunspot in AR12533, see Fig. 6. The online material includes a movie of
the full 90 min sequence of the entire sunspot at $-0.8$ Å offset from H
$\alpha$ line center, equivalent to the FOV shown in the upper left panel. The
movie shows many small bright PEBs in the penumbra that generally move
radially outward, away from the umbra. These are not visible in the reference
WB 8542 Å movie. This difference in visibility is best seen in the 3rd movie
that zooms in on the left part of the penumbra and combines the H $\alpha$
blue wing and WB 8542 Å, as well as a panel that blinks between these
diagnostics. There are numerous examples of PEBs that originate in the
penumbra, migrate outwards and eventually cross the outer penumbra boundary
where they continue their outward migration in the sunspot moat flow. From
inspection of the H $\alpha$ blue wing movie, it is clear that most of the
PEBs are found in the outer regions of the penumbra. This is similar to what
is described above for the 22 September 2017 sunspot and what was found from
the $k$-means detections.

We tracked 32 events to measure lifetimes, trajectories and velocities. These
PEBs were selected on the basis of clear visibility throughout their lifetime
and regarded as a representative sample. We measured PEB lifetimes ranging
between 1 and 9 min, and an average lifetime of about 3 min. During their
lifetime, these PEBs traveled distances ranging between 100 and 1640 km, with
an average of about 650 km. They traveled at an average speed of 3.7 km s-1
and the maximum speed measured is almost 13 km s-1. These velocities are
apparent motions and from these observations we cannot determine whether these
are real plasma flows or result from a moving front of for example
reconnection moving along a magnetic interface.

Figure 6 shows the evolution of selected PEBs in sequences of small images for
three ROIs. The three images for ROI A cover 2:43 min during which the PEB
migrates over a distance of 340 km with an average speed of 2 km s-1. The PEB
flares up for a duration of 102 s, with its brightest moment at 10:13:16 UT in
the middle panel. The PEB in ROI B migrates over 365 km with an average speed
of 1.4 km s-1. During its lifetime, the PEB splits into a number of bright
substructures, this is visible in the 3rd panel. The sequence for ROI C covers
1:41 min of a total lifetime of the PEB of 5:04 min. This PEB shows a clear
flame structure which is strikingly absent in the reference row of WB 8542 Å
images. This flame appears to eject a small bright blob that is visible in the
three last panels. This ejection can be followed for 2:22 min during which it
moves at a maximum speed of almost 11 km s-1. The PEB itself appears to move
at a maximum speed of almost 4 km s-1 while it moves at an average speed of 2
km s-1 during a migration over 650 km.

The rapid variability we see for these selected examples and other PEBs in the
time series is clearly limited by the temporal resolution. There often are
significant variations in brightness and morphology (e.g., in the form of
splitting, merging, and ejections) between subsequent time steps. This
suggests that PEBs are changing on a shorter time scale than 20 s.

##  5 Discussion and conclusion

Using high spatial resolution observations in the Balmer H $\alpha$ and H
$\beta$ lines, we find large numbers of EBs in the penumbrae of sunspots. The
EB nature of these penumbral events is established by 1: characteristic
spectral profiles with often strongly enhanced wings, 2: flame morphology
under slanted viewing angle, 3: rapid temporal variability in brightness and
morphology, and 4: absence in concurrent continuum passbands.

We find many small patches in the penumbra with characteristic EB wing
enhancement and note that there is considerable spread in the level of
enhancement: some reach the level of strong EBs traditionally found in active
region flux emergence regions with wing enhancement well above twice that of
quiet Sun, others have weak wing enhancement that is only discernible in
contrast to weak background penumbral profiles. In the H $\beta$ line, we find
that PEBs do not stand out in terms of area or wing brightness as compared to
EBs in the surroundings of the sunspot. We do note however, that PEBs are
easier to discern in H $\beta$ than in H $\alpha$. The shorter wavelength of H
$\beta$ offers the advantage of higher spatial resolution and higher contrast.
Furthermore, we observe that the sunspot in the H $\alpha$ line is much more
dominated by dense chromospheric fibrils. It appears that the sunspot
chromosphere has much less opacity in H $\beta$. Recently, from non-LTE
radiative transfer calculations, Zhang (2020) concluded that H $\beta$ Stokes
signals originate from the sunspot umbra photosphere. The difference between
the H $\alpha$ and H $\beta$ lines is well illustrated by the line scan
animation associated with Fig. 1 in the online material. At wing offsets that
have highest EB contrast, the H $\alpha$ line is much more dominated by the
chromospheric superpenumbra fibrils than the H $\beta$ line. These combined
reasons make it more difficult to detect PEBs in H $\alpha$ and appreciate the
ubiquity of PEBs. Here we present detailed analysis of two different sunspots,
but we note that we observe large numbers of PEBs in at least 11 other sunspot
datasets that we have acquired over the past ten years. In the 22 September
2017 dataset, we find more than 100 PEBs in the highest quality H $\beta$ line
scan which corresponds to almost 30% of all detected EBs. The number density
of PEBs is higher than the average number density of EBs over the whole FOV.
It is only in the sunspot moat, just outside the penumbra, that the number
density of EBs is higher than in the outer penumbra. In the moat we detect on
average about 3 EBs per typical granule, considering an average area of a
granule of 1.75 Mm2 (see Rincon & Rieutord, 2018). For the outer penumbra, we
detect about 1.3 PEBs per typical granule area. In the quiet Sun, Joshi et al.
(2020) found a QSEB number density of 0.09 Mm-2, which is more than 8 times
lower than the number densities of PEBs (0.76 Mm-2) and 19 times lower than
EBs in the moat (1.72 Mm-2).

Many events show clear flame morphology under inclined viewing angle which
underlines the similarity with EBs in active regions and quiet Sun. The rapid
variability and dynamics we see in the 29 April 2016 time series remind of the
rapid variability found in EB flames in active regions (Watanabe et al., 2011)
and quiet Sun (Rouppe van der Voort et al., 2016). We note however, that the
temporal cadence of these studies ($\sim 1$ s) is much faster than for the
time series presented here (20 s).

Establishing the ubiquity of EBs in the penumbra is aided by the concurrent
continuum observations that are available through the CHROMIS WB channel.
Absence of a bright feature in the associated continuum image confirms the
Balmer line wing enhancement. The EB features are as absent in the penumbra as
they are outside the sunspot and this further confirms the EB nature of PEBs.
The H $\beta$ wing images show many small bright features that are absent in
the WB image but have too weak wing enhancement to be (fully) detected by the
$k$-means method (in Sect. 4.1 described as “crumbs”). This suggests that PEBs
are more prevalent than the detection numbers from the $k$-means method
suggest.

For CRISP H $\alpha$ observations, a clean continuum channel is not as readily
available as the CRISP WB channel shares the same prefilter as the CRISP
narrow band images. CRISP WB 6563 Å images show EBs because the CRISP
prefilter transmission profile has relatively wide passband (FWHM=4.9 Å) and
is centered on the H $\alpha$ line. For the 29 April 2016 time series (see
Fig. 6) we compare H $\alpha$ blue wing images with concurrent CRISP WB 8542 Å
images since EB signature in this channel is weaker due to wider passband and
generally weaker EB emission in Ca ii 8542 Å.

The presence of EBs in the sunspot penumbra has been reported before. For
example, a number of small EBs inside the penumbra of a small sunspot can be
seen in the H $\alpha$ wing detection maps of Nelson et al. (2013a), and
Reardon et al. (2013) report the observation of EB profiles in the Ca ii 8542
Å line for two events in a study of penumbral transients. However, this is the
first time that the presence of large numbers of EBs in the penumbra is
reported.

The significance of EBs lies in their capacity of being markers of magnetic
reconnection in the low solar atmosphere. Numerical simulations demonstrated
that enhanced Balmer wing emission and flame morphology stems from heating
along current sheets at reconnection sites (Hansteen et al., 2017, 2019;
Danilovic, 2017). The flames we observe for PEBs appear to be rooted deep down
in the penumbra photosphere, in similar fashion as for EB flames in active
regions and quiet Sun. Further support for PEBs being markers of magnetic
reconnection in the deep penumbra photosphere comes from PEB detections being
located in areas where opposite polarities are in close proximity. The sunspot
of 22 September 2017 is of positive magnetic polarity. The $B_{z}$ map (Fig.
4) reveals the presence of many isolated patches of opposite (negative)
polarity within the penumbra. Many PEBs are located in the vicinity of these
opposite polarity patches and some are located right at the interface where
the two magnetic polarities meet. We also observe that the number density of
PEBs increases toward the outer penumbra, following the same trend of
increasing opposite polarity flux with increasing distance from the sunspot
umbra. We note however, that there are a few limitations that need to be kept
in mind when combining the $B_{z}$ and EB detection maps for inferring that
magnetic reconnection is taking place: spectral line inversions are sensitive
to a limited range in height and simplifications assumed for the ME inversion
method imply uncertainties. We estimate that our ME inversions of the Fe i
lines are valid as $\@vec{B}$ field measurements over a height range over a
few 100 km in the upper photosphere (see Grec et al., 2010). Joshi et al.
(2017) have shown that opposite polarity magnetic flux found in the deeper
penumbra could be more than four times larger than that in the the middle and
upper photosphere. Therefore, there is solid ground to believe that our ME
inversions which provide height-independent magnetic field vectors are not
able to resolve all opposite polarity patches in the penumbra. Furthermore,
stray light makes it difficult to detect weak signals and adds to the
uncertainty in the interpretation. We have applied a correction for stray
light that is consistent with previous studies but the full impact of stray
light on our measurements remains unknown. Further uncertainties come from
line-of-sight obscuration due to corrugation of the penumbral optical surface
and it may be possible that regions with opposite polarity are hidden behind
elevated foreground structures. Apart from these observational limitations
that mitigate the detection of opposite polarity patches, it should be
stressed that the condition of diametrically opposite direction fields is not
strictly required for reconnection to take place. Even in areas that appear
unipolar in observations, the complex magnetic topology of the penumbra can be
expected to host gradients in the magnetic field that allow for small-angle
magnetic reconnection.

The large number of PEBs we observe suggests that magnetic reconnection is a
very frequently occurring process in the low penumbra atmosphere. A
significant amount of magnetic energy may be dissipated through reconnection
in the highly abundant PEBs and as such PEBs may play an important role in
sunspot decay. Outward moving magnetic elements that leave the penumbra and
migrate through the sunspot moat, commonly referred to as moving magnetic
features (MMF), carry net flux away from the sunspot and are traditionally
regarded as main actors in sunspot decay (see, e.g. Solanki, 2003). The
ubiquity of PEBs we find here may implicate that some fraction of magnetic
energy is already dissipated and lost from the sunspot before MMFs cross the
sunspot boundary. Moreover, high density of EBs in the immediate vicinity of
the sunspot suggest that significant fraction of magnetic field in the moat
flow regions might also dissipate through magnetic field reconnection
occurring in the photosphere.

What impact do PEBs have on the upper atmosphere? There exist several
transient phenomena in sunspots that may be related to energy release in PEBs.
Penumbral micro-jets (PMJ) are short-lived elongated brightenings that can be
observed in the core of Ca ii lines (Katsukawa et al., 2007; Reardon et al.,
2013). Magnetic reconnection has been suggested as their driver but the idea
that they carry high-speed plasma flows as their name suggests has been
contested (Esteban Pozuelo et al., 2019; Rouppe van der Voort & Drews, 2019).
They can be observed in transition region diagnostics (Vissers et al., 2015;
Drews & Rouppe van der Voort, 2020) and Tiwari et al. (2016) reported the
existence of large PMJs originating from the outer penumbra in the regions
with abundant mixed polarities. These large PMJs leave signatures in some of
the transition region/coronal channels of the AIA instrument of NASA’s Solar
Dynamics Observatory Drews & Rouppe van der Voort (2017) found that there
exist on average 21 PMJs per time step in a time series of Ca ii 8542 Å
observations. This is significantly fewer than the number of PEBs that we
detect. Furthermore, clear PMJ detections are mostly found in the inner
penumbra where we find fewer PEBs as compared to the outer penumbra. Recently,
Buehler et al. (2019) and Drews & Rouppe van der Voort (2020) connected Ca ii
8542 Å PMJs with dark fibrilar structures close to the line core in H
$\alpha$. The connection between PEBs and PMJs warrants further study and
requires simultaneous observation of multiple spectral lines and extreme high
temporal evolution to resolve the onset of PMJs (Rouppe van der Voort & Drews,
2019). Possibly there is also a connection with transition region bright dots
observed above sunspots with IRIS (Tian et al., 2014; Samanta et al., 2017)
and Hi-C (Alpert et al., 2016). Furthermore, magnetic reconnection in the deep
atmosphere as marked by PEBs may play a role in the heating of bright coronal
loops that are rooted in penumbrae (see, e.g., Tiwari et al., 2017)

Finally, we conclude that EBs in the penumbra of sunspots are an excellent
target for new telescopes such as the 4-m DKIST (Rimmele et al., 2020) and the
planned EST (Schlichenmaier et al., 2019) since PEBs offer opportunities to
study magnetic reconnection in kG magnetic field environments at the smallest
resolvable scales in astrophysical plasmas.

###### Acknowledgements.

The Swedish 1-m Solar Telescope is operated on the island of La Palma by the
Institute for Solar Physics of Stockholm University in the Spanish
Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de
Canarias. The Institute for Solar Physics is supported by a grant for research
infrastructures of national importance from the Swedish Research Council
(registration number 2017-00625). This research is supported by the Research
Council of Norway, project number 250810, and through its Centres of
Excellence scheme, project number 262622. VMJH is supported by the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (SolarALMA, grant agreement No. 682462). We thank Shahin
Jafarzadeh, Ainar Drews, Tiago Pereira and Ada Ortiz for their help with the
observations. We made much use of NASA’s Astrophysics Data System
Bibliographic Services.

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