# Insight into the solar plage chromosphere with DKIST

David Kuridze National Solar Observatory, 3665 Discovery Drive, Boulder, CO
80303, USA  Han Uitenbroek National Solar Observatory, 3665 Discovery Drive,
Boulder, CO 80303, USA  Friedrich Wöger National Solar Observatory, 3665
Discovery Drive, Boulder, CO 80303, USA  Mihalis Mathioudakis Astrophysics
Research Centre, School of Mathematics and Physics, Queen’s University
Belfast, Belfast BT7 1NN, UK  Huw Morgan Department of Physics, Aberystwyth
University, Ceredigion, SY23 3BZ, UK  Ryan Campbell Astrophysics Research
Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast
BT7 1NN, UK  Catherine Fischer National Solar Observatory, 3665 Discovery
Drive, Boulder, CO 80303, USA  Gianna Cauzzi National Solar Observatory, 3665
Discovery Drive, Boulder, CO 80303, USA  Thomas Schad National Solar
Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA  Kevin Reardon
National Solar Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA  João
M. da Silva Santos National Solar Observatory, 3665 Discovery Drive, Boulder,
CO 80303, USA  Christian Beck National Solar Observatory, 3665 Discovery
Drive, Boulder, CO 80303, USA  Alexandra Tritschler National Solar
Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA  Thomas Rimmele
National Solar Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA

###### Abstract

The strongly coupled hydrodynamic, magnetic, and radiation properties of the
plasma in the solar chromosphere makes it a region of the Sun’s atmosphere
that is poorly understood. We use data obtained with the high-resolution
Visible Broadband Imager (VBI) equipped with an H$\beta$ filter and the
Visible Spectro-Polarimeter (ViSP) at the Daniel K. Inouye Solar Telescope to
investigate the fine-scale structure of the plage chromosphere. To aid the
interpretation of the VBI imaging data, we also analyze spectra from the
CHROMospheric Imaging Spectrometer on the Swedish Solar Telescope. The
analysis of spectral properties, such as enhanced line widths and line depths
explains the high contrast of the fibrils relative to the background
atmosphere demonstrating that H$\beta$ is an excellent diagnostic for the
enigmatic fine-scale structure of the chromosphere. A correlation between the
parameters of the H$\beta$ line indicates that opacity broadening created by
overdense fibrils could be the main reason for the spectral line broadening
observed frequently in chromospheric fine-scale structures.
Spectropolarimetric inversions of the ViSP data in the Ca II 8542 Å and Fe i
6301/6302 Å lines are used to construct semiempirical models of the plage
atmosphere. Inversion outputs indicate the existence of dense fibrils in the
Ca II 8542 Å line. The analyses of the ViSP data show that the morphological
characteristics, such as orientation, inclination and length of fibrils are
defined by the topology of the magnetic field in the photosphere.
Chromospheric maps reveal a prominent magnetic canopy in the area where
fibrils are directed towards the observer.

Solar chromosphere (1479); Spectroscopy (1558); Plages (1240)

††software: DeSIRe (Ruiz Cobo et al., 2022), adhoc_xtalk (Jaeggli et al.,
2022)

Accepted in ApJ — draft version

##  1 Introduction

Figure 1: Overview of the DKIST observations of the plage. Top row: Mosaics of
high-resolution H$\beta$ (left panel) and G-band (right panel) filtergrams
obtained with the VBI instrument on 2022 June 3 between 17:10 and 19:20 UT.
Bottom left: A context AIA 1600 Å passband full-disk image taken on 2022 June
3 at 16:40 UT. The black box indicates the plage region observed with DKIST.
Bottom right: A cut out of the 1600 Å image coaligned with the DKIST/VBI FoV.

The highly inhomogeneous nature of the solar chromosphere was discovered
already in the second half of the 19th century by Father Angelo Secchi, who
reported the existence of ‘vertical flames’ seen at the solar limb (Secchi,
1877), which are now called spicules (Roberts, 1945). This makes chromospheric
fine-scale structures one of the oldest scientific topics in solar physics.

Some major breakthroughs in our understanding of spicules, and their on-disk
counterparts, mottles, were delivered with the commissioning of half-meter
class solar telescopes equipped with narrow-band filters and spectrographs
able to perform simultaneous imaging and spectroscopic observations (see the
reviews by Beckers, 1968, 1972). Such data made possible to perform first
high-resolution measurements of spicules characteristics such as morphology,
thermodynamical properties, spectral characteristics etc. The seeing-free
broadband imaging provided by the Solar Optical Telescope (SOT) onboard Hinode
and the adaptive optic systems installed on 1-m class solar telescopes
equipped with Fabry-Pérot interferometers such as the Swedish Solar Telescope
(SST), the Dunn Solar Telescope (DST), and the Goode Solar Telescope (GST)
have further advanced our understanding of the chromosphere at fine scales.
For example, the data obtained from these telescopes have identified more
energetic, and short-lived features such as type II spicules (de Pontieu et
al., 2007) and their on-disk counterparts, Rapid Excursions (RE) (Langangen et
al., 2008; Rouppe van der Voort et al., 2009; Kuridze et al., 2015).

Still, many aspects of the fine-scale chromospheric structures, including
their magnetic field strength and topology, thermodynamical properties and
formation mechanisms remain poorly understood (Sterling, 2000; Tsiropoula et
al., 2012). The reasons for this are manifold, and include: i) the very
dynamic nature of spicular structures, with spatial and temporal scales close
to the resolution of present day solar telescopes; ii) the large number of
structures that appear to overlap; iii) the inherently low signal to noise
(S/N) ratios of polarimetric datasets in the chromosphere (Trujillo Bueno &
del Pino Alemán, 2022); iv) the challenges associated with the modeling and
interpretation of chromospheric spectral lines that rely on solving the
complex non-LTE (i.e., departures from local thermodynamic equilibrium)
radiative transfer problem (de la Cruz Rodríguez & van Noort, 2017; Beck et
al., 2019; Carlsson et al., 2019; Kuridze et al., 2021; Kriginsky et al.,
2023).

Figure 2: Left column: Composite ViSP net linear (top panel) and circular
(bottom panel) polarization images compiled from four different scans in
adjacent positions. The Stokes Q & U and V parameters are integrated over
$\Delta\lambda=\pm 0.17$ Å from the line core rest wavelength of the Fe I 6302
Å line. Top right: A context LoS magnetogram of the full Sun in the Fe i 6173
Å passband obtained with HMI. The black box indicates the plage region
observed by DKIST. Bottom right: A cut out of the HMI image coaligned with the
DKIST FoV. Table 1: Summary of the DKIST instruments and data used in this
work. Values refer to a single telescope pointing.

Start time | Instrument | filter/ | Wavelength | Spatial | Instantaneous | Time | Sampled | Full map | Number
---|---|---|---|---|---|---|---|---|---
UT |  | arm | range (Å) | sampling | FoV | step | FoV | time | of maps
17:10:50 | VBI | Blue | H$\beta$ at 4861.13 | 0.011″ | 45″$\times$45″ | 3 s | 115″$\times$115″ | 27 s | 20
17:10:22 | VBI | Blue | G-band at 4305 | 0.011″ | 45″$\times$45″ | 3 s | 115″$\times$115″ | 27 s | 20
17:09:55 | ViSP | arm 1 | 6295.2 - 6307.8 | 0.0298″aafootnotemark:  | 0.2142″bbfootnotemark: $\times$75″ | 3.3 s | 107″$\times$75″ | 27 min | 1
arm 3 | 8535.4 - 8544.9 | 0.0194″aafootnotemark:  | 0.2142″bbfootnotemark: $\times$48″ | 3.3 s | 107″$\times$48″ | 27 min | 1

††footnotetext: a pixel scale along slit, b width of the slit.

Chromospheric fine-scale fibrilar structures are intricately connected to the
local magnetic field distribution and are thought to act as tracers for the
local magnetic field topology, much like apparent coronal loops are used as
proxies for the magnetic field in the lower corona (Prasad et al., 2022). In
the quiet Sun (QS) network, chromospheric fine structures create rosettes
(“bushes”), which are clusters of elongated mottles expanding radially around
a common center over internetwork regions. Active regions (ARs) are
characterized by an increased number of magnetic elements producing a large
number of fine scale, elongated features, referred to as fibrils when on the
disk. Some of the most interesting fibril-dominated ARs are plages. These are
regions created by mostly unipolar, almost radial kG fields in the photosphere
that appear as bright areas, called faculae, in photospheric lines (see, e.g.,
Spruit, 1976; Keller et al., 2004; Rezaei et al., 2007). Resemblance has been
reported between QS mottles and plage fibrils (see the reviews by Tsiropoula
et al., 2012). Foukal (1971a) investigated the morphological relation between
chromospheric fine structures observed in regions with different magnetic
activity. By comparing the observed parameters of fine-scale chromospheric
structures they concluded that there is a continuous morphological progression
between QS spicules/mottles and AR/plage fibrils. Foukal (1971a) found that
spicules/mottles in QS bushes are less inclined with respect to the normal to
the surface, while AR/plage fibrils are mostly horizontal. The reason for this
is that the larger deflection of the magnetic field in plage creates a
relatively lower-lying horizontal canopy in the chromosphere. In a follow up
study, Foukal (1971b) concluded that fibrils are longer than mottles, with
stronger magnetic field strengths, but similar temperatures and densities.
Similar morphological properties of plage fibrils have been reported by
Pietarila et al. (2009) who analyzed a high-resolution Ca II K filtergram of
an AR plage recorded by the SST at disk centre. Anan et al. (2010) analyzed
broadband Ca II H filtergrams of a plage region close to the limb obtained by
Hinode/SOT and found that spicular jets are shorter in the plage than the QS
limb spicules, and are characterized by ballistic motions under constant
deceleration.

The strength and local inclination angle of the magnetic field in plage
magnetic flux concentrations (MFCs) has long been studied using
spectropolarimetric observations. Inversions of photospheric spectral lines
infer kG field strengths in the plage oriented mostly parallel to the solar
normal. Inclinations from the local vertical by up to 10∘-20∘ have also been
reported (Martínez Pillet et al., 1997; Topka et al., 1992; Bernasconi et al.,
1995; Buehler et al., 2015, 2019). By inverting the chromospheric He I 10830 Å
line together with the adjacent photospheric Si I 10827 Å line, Anan et al.
(2021) found vertically oriented MFCs in the plage photosphere that changed
direction, becoming nearly horizontal in the chromosphere. Using Ca II 8542 Å
observations, Pietrow et al. (2020) inferred the magnetic field strength of a
MFC in plage chromosphere as 450 G, with an inclination of $\sim$16∘. Using
full-Stokes observations in the Mg i 5173 Å, Na i 5896 Å and Ca II 8542 Å
lines, Morosin et al. (2020) found that the photospheric magnetic field in the
plage region were expanding horizontally toward the chromosphere and forming a
volume-filling canopy. They derived a value of $\sim$658 G for the mean total
magnetic field strength of the plage canopy in the chromosphere using the WFA
techniques. From the analysis of some of the chromospheric data used in this
paper, and using the Weak Field Approximation, da Silva Santos et al. (2023)
derive an average magnitude of the LOS chromospheric magnetic field in the
plage of approximately $-$210 G, with clear variations among the fibrils
surrounding the plage patches.

One of the main spectral characteristics of chromospheric fine-scale fibrillar
structures in strong chromospheric spectral lines is their broader line width
relative to the background atmosphere. The causes of this line broadening
still constitute a challenge. The combination of multi-instrument, multi-
wavelength optical and UV observations has provided evidence that there are
transition region (TR) and coronal signatures occurring co-spatially and co-
temporally with chromospheric fine structures (De Pontieu et al., 2011;
Madjarska et al., 2011; Henriques et al., 2016), suggesting that thermal
broadening could be a dominant mechanism of the increased line width in
spicular structures. However, this remains a controversial subject (cf., e.g.,
Beck et al., 2016). Non-thermal broadening mechanisms have also been
investigated to explain the enhanced line width of spicular jets (Erdélyi &
Fedun, 2007; Jess et al., 2009; Zaqarashvili & Erdélyi, 2009; Kuridze et al.,
2012, 2016).

In this paper we use data obtained with the high-resolution Visible Broadband
Imager (VBI; Wöger et al., 2021) and Visible Spectro-Polarimeter (ViSP; de
Wijn et al., 2022) on the recently commissioned Daniel K. Inouye Solar
Telescope (DKIST; Rimmele et al., 2020) to investigate the fine-scale
structure of a plage chromosphere. We were able to observe a large field of
view and resolve fine-scale structures of the chromosphere in broadband
H$\beta$ filtergrams. To aid the interpretation of the VBI/H$\beta$ data, we
also analyze H$\beta$ scans obtained with the CHROMospheric Imaging
Spectrometer (CHROMIS) on the Swedish Solar Telescope. Furthermore, we
inverted Stokes profiles obtained with the ViSP instrument in the Fe i
6301/6302 Å and Ca II 8542 Å lines with the Departure coefficient aided Stokes
Inversion based on Response functions (DeSIRe; Ruiz Cobo et al., 2022) code
and investigate the connection between the plage magnetic field and the
fibrils’ characteristics.

##  2 Observations and data reduction

###  2.1 DKIST observational setup

The observations used in this paper were obtained between 17:09 and 19:20 UT
on 2022 June 3 with the Visible Broadband Imager (VBI; Wöger et al., 2021) and
Visible Spectropolarimeter (ViSP; de Wijn et al., 2022) deployed at the Daniel
K. Inouye Solar Telescope (DKIST; Rimmele et al., 2020) under good seeing
conditions. The telescope was sequentially pointed at four adjacent positions
to cover a large plage region located at the south-east part of the solar
disk. The heliocentric coordinates of the center of the full field-of-view
(FoV) covered by the observations were (x, y) = ($-362$″, $-406$″), with
heliocentric angle $\mu\approx 0.843$ (see Figure 1). Details about the data
and instrumentation are given in the next subsections, and in Table 1.

Figure 3: Overview of the SST data. Monochromatic H$\beta$ line wing (top row)
and core (bottom left) images obtained with the CHROMIS instrument at 10:47 UT
on 2019 August 3 at disk center. The bottom right panel displays the
experimental transmission profile of the VBI filter (red line, right axis) and
the CHROMIS H$\beta$ average line profile (dashed blue line) calculated for a
QS region marked with the white box in the bottom left panel. Circles show the
spectral positions selected for the CHROMIS line scan. The dashed black line
is the double-gaussian fit of the average profile. The brown line is the FTS
atlas profile convolved with the CHROMIS instrumental profile.

####  2.1.1 ViSP data

At each telescope pointing, the ViSP spectropolarimeter performed a large
raster scan with the 0$\farcs$2142 wide slit oriented along the solar N-S
direction. Each scan consisted of 490 slit positions separated by a slit step
of 0$\farcs$219, with a time step of 3.3 s, for a total observing time of
about 27 minutes per scan. Arms 1 and 3 of the spectrograph were used to
observe the spectral ranges 6295.2 - 6307.8 Å and 8535.4 - 8544.9 Å,
respectively (arm 2 was not used for these observations). The spatial
samplings along the slit for arm 1 and arm 3 are 0$\farcs$0298 pixel-1 and
0$\farcs$0194 pixel-1, with a slit length of $\sim$ 75″ and 48″, respectively.
Hence, the FoV of each raster scan covered 107″$\times$75″ for arm 1 and
107″$\times$48″ for arm 3 (Table 1). The spectral sampling for arms 1 and 3
were 0.0128 and 0.0188 Å per pixel.

The polarimetric modulation consisted of 10 modulation states that were
repeatedly observed 12 times each, at a camera frame rate of 41 Hz and with
the exposure time of 4 ms for both cameras. The data were processed to level 1
using version 2 of the ViSP data reduction pipeline, that includes
polarimetric calibration to obtain the full Stokes vector. Additional cross-
talk corrections were applied based on the method developed by Jaeggli et al.
(2022). More details on the data post-processing can be found in da Silva
Santos et al. (2023).

The raster scans at the four different telescope pointings are then stitched
together to produce large mosaics (Figure 2) of the observed plage region.
Figure 2 shows full maps of Fe I 6302 Å net (wavelenght-integrated) Stokes Q &
U and V coaligned with a cutout of the HMI line-of-sight (LoS) magnetogram.
Polarization maps indicate that the observed region is a highly unipolar plage
without a sunspot. However, Stokes V map shows many small-scale parasitic
polarity elements that are not resolved in the HMI magnetogram (bottom panels
of Figure 2).

####  2.1.2 VBI data

During each ViSP raster scan, we used the VBI blue branch to obtain
filtergrams in G-band, Ca II K and H$\beta$. The wavelengths are selected
sequentially using interference filters mounted on a rotating filterwheel, and
the full width half maximum (FWHM) of the filters are approximately
4.37$\pm$0.048, 1.01$\pm$0.02 and 0.464$\pm$0.01 Å for the G-band, Ca II K and
H$\beta$, respectively (Wöger, 2014). Single exposure times were $\sim$0.7, 25
and 4 ms for the G-band, Ca II K and H$\beta$ with a frame rate of up to 30
Hz. In the following, we limit our analysis to G-band and H$\beta$ data.

The instantaneous FoV of VBI-blue is 45″$\times$45″ with a spatial sampling of
0$\farcs$011 pixel-1. For these observations, we employed the so-called
“field-sampling mode” to cover the full DKIST FoV of $2^{\prime}\times
2^{\prime}$ with a mosaic of 3$\times$3 tiles. This fully covers the field
sampled by ViSP during the raster (cf. Fig. 1 in da Silva Santos et al.,
2023). All VBI images were reconstructed using the speckle code of Wöger et
al. (2008) to remove residual atmospheric distortion from the data, bringing
the effective time step to 3 s per tile. Hence, at any given wavelength
(filter), the full DKIST FoV was sampled in 27 s, and the overall cadence for
the three filters’ sequence was 81 s. For each telescope pointing, the
sequence was repeated 20 times, for a duration of $\sim$27 minutes, i.e. the
duration of the ViSP raster scan. Adjacent tiles in the VBI field-sampling
mode have overlaps of about 7″, and were stitched with sub-pixel accuracy
using the World Coordinate System (WCS) header information and cross-
correlation techniques. The intensity in overlapping areas is taken as the
average at each location.

Finally, these 3$\times$3 mosaics obtained at each of the four different
telescope pointings were stitched together to produce a large mosaic covering
the plage region. Adjacent meta-tiles have overlaps of about 20″ resulting in
an overall FoV of about 175″$\times$205″ (Figure 1). The Figure 1 is produced
using the tiles with the best spatial resolution.

As mentioned above, seeing conditions were good throughout the observations.
After reconstruction, we estimate that multiple frames achieved a spatial
resolution close to the diffraction limit (0.022″at 430 nm), as determined by
the size of the smallest resolved structures seen in the data.

Figure 4: A qualitative comparison of the DKIST VBI image (left panel) and the
wavelength integrated SST CHROMIS (right panel) H$\beta$ image. Before
integrating over wavelength, the CHROMIS spectral scan is multiplied by the
VBI transmission filter. The DKIST FoV covered by the presented tile is
located at around (x, y) = (-340″, $-370$″) in the context image presented in
Figure 1 whereas the CHROMIS FoV is located at disk center; they are thus
neither co-spatial nor co-temporal

.

Figure 5: Top left: CHROMIS H$\beta$ line core image overlaid with a mask
where $I^{mean}_{\lambda_{0}}-I_{\lambda_{0}}\geqslant 2\sigma$ (see text for
explanation). Top right: Superimposition of the extracted line profiles of
detections shown in the top left panel. The average H$\beta$ profile is
overplotted as a blue solid line. Middle left: Map of pEWs of H$\beta$ line
profiles measured from the double Gaussian model. Middle right: Scatter plot
of the line core depths vs. pEWs for all identified fibrils. Bottom left: Map
of the width of H$\beta$ line profiles (see text for details in section
3.2.3). Bottom right: Scatter plot of the line widths vs. pEWs for all
identified fibrils. The Pearson correlation coefficients are displayed in the
top left corners.

###  2.2 SDO data

We also analyse observations of the same region obtained with NASA’s Solar
Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA; Lemen et al.,
2012) in its 1600 Å channel and the Helioseismic and Magnetic Imager (HMI;
Scherrer et al., 2012) magnetograms in Fe I 6173 Å. The SDO observations
provide full Sun context imaging and allow a comparison with the DKIST data.
SDO images are coaligned with the DKIST/VBI/ViSP dataset using the SolarSoft
auto_align_images function via cross-correlation.

###  2.3 SST/CHROMIS data

Since the VBI data lack fine spectral resolution, we use data obtained with
the CHROMIS dual Fabry-Pérot interferometer installed at the SST (Scharmer et
al., 2003; Scharmer, 2017) to further investigate the spectral characteristics
of chromospheric fine-scale structures in H$\beta$. Observations were
undertaken between 10:47 and 11:04 UT on 2019 August 3 in a quiet area at disk
center. The dataset includes narrow-band spectral imaging in H$\beta$ with a
spatial sampling of 0$\farcs$0378 pixel-1 and a FoV of about 62″$\times$41″.
Many images in the time series were observed under extremely good seeing
conditions, with spatial resolution close to the diffraction limit of the
telescope which is $\sim$0$\farcs$13 at this wavelength. The H$\beta$ line
scan consists of 25 profile samples ranging from $-1.2$ Å to $+1.2$ Å (Figure
3) from line center. CHROMIS spectral resolution (transmission profile full-
width at half-maximum) is 0.1 Å at 4860 Å. A full spectral scan had an
acquisition time of 7 s. The data were processed using the CHROMISRED
reduction pipeline which includes MOMFBD image restoration (Van Noort et al.,
2005; Löfdahl et al., 2021).

The pipeline also applied spectral intensity calibration to remove the effect
of the prefilter transmission profiles and scale intensity counts to SI units.
However, the position angle of the science data is not taken into account
during the calibration (Löfdahl et al., 2021).

For recalibrating CHROMIS H$\beta$ data we used a spatially averaged profile
over the disk center, quiet-Sun area marked with a white rectangle in Figure 3
($I_{av}(\lambda)$). The FTS atlas H$\beta$ profile ($I_{FTS}(\lambda)$)
(Neckel, 1999) convolved with the CHROMIS instrumental profile was used as the
calibration reference. The ratio of the reference and observed intensities
($I_{FTS}(\lambda)/I_{av}(\lambda)$) was used for calibration and applied to
the data (Figure 3).

##  3 Analysis and results

###  3.1 DKIST filtergrams

Figure 1 displays co-aligned images of the plage region in H$\beta$ and G-band
obtained between 17:10 - 19:20 UT. Context imaging of the full Sun is provided
by the AIA 1600 Å filtergram at 17:36 UT. It shows that the plage region
extends toward the east limb outside the DKIST FoV. The west, north and south
borders of the DKIST FoV are surrounded by QS. The bottom right panel shows a
cutout of the AIA 1600 Å image which is co-aligned with the H$\beta$/G-band
images.

The H$\beta$ image displays multiple features including granulation, small-
scale bright points, larger scale brightenings and dark fine-scale fibrils.
Larger scale brightenings coincide with G-band and 1600 Å bright regions
suggesting that they are associated with strong magnetic flux concentrations
(MFCs) known as faculae (e.g., Beck et al., 2007; Rezaei et al., 2007).
Faculae are hot granules seen as a result of opacity reduction and appear
brighter towards the limb (Keller et al., 2004; Berger et al., 2007). These
brightenings are footpoints of plage fibrils appearing as densely-packed, and
mostly parallel fine-scale strands (Figure 1). The existence of both
photospheric and chromospheric features in the H$\beta$ images is expected as
the VBI/H$\beta$ filter has a Lorentzian transmission profile centered at the
line core and covers a significant part of the line wings, with a FWHM of
$\sim$0.46 Å (bottom right panel of Figure 3).

###  3.2 SST/CHROMIS H$\beta$ images and spectra

####  3.2.1 Overview

To investigate why and how fine-scale chromospheric features appear as high-
contrast dark structures relative to the background in H$\beta$, we study the
line profiles of fibrillar structures using high-resolution H$\beta$ spectral
imaging obtained with CHROMIS. The top and bottom right panels in Figure 3
display CHROMIS H$\beta$ images in the line wings and core obtained at disk
center. The FoV is mostly QS with some network elements and the rosette region
centered around ($x,y$) = (43″, 15″) which is dominated by fine-scale
chromospheric structures. The bottom right panel of Figure 3 shows an average
QS H$\beta$ profile calculated over the relatively “fibril free” region marked
with the white box in the bottom left panel of Figure 3 with the spectral
positions selected for the line scan.

####  3.2.2 Integration with VBI transmission profile

To more closely replicate the DKIST H$\beta$ filtergrams, the CHROMIS data
were multiplied by the VBI transmission profile (bottom right panel of Figure
3) and integrated over the whole wavelength range covered by the spectral
scan. Figure 4 shows the comparison of the resulting wavelength-integrated
CHROMIS and DKIST H$\beta$ images. For a fair comparison we have selected a
region of the DKIST FoV covering a significant area of QS. Figure 4 confirms
that the wavelength-integrated CHROMIS H$\beta$ (called integrated H$\beta$
from now on) shows similar scenes including magnetic bright points, granular
patterns and fine-scale dark fibrillar structures as found in the VBI/H$\beta$
filtergrams. We note that the granulation in the VBI H$\beta$ image appears
more defined. This is most likely due to the fact that the CHROMIS data do not
extend into the continuum proper, but rather only sample up to wavelengths in
the wing of the line, formed in the middle photosphere.

####  3.2.3 Spectral line parameters

To study the line profiles of fibrillar structures in the CHROMIS data we
first identified them in the monochromatic line core images using simple
thresholding. In particular, we calculated the mean line profile,
$(I_{\lambda_{0}}^{mean})$ over the “fibril free” area marked with the white
box in Figure 3. For line core intensities $(I_{\lambda_{0}})$ we applied a
threshold as the mean line core intensity ($I^{mean}_{\lambda_{0}}$) minus 2
standard deviations ($\sigma$). Resulting detections are presented as red
contours plotted over the H$\beta$ line core image in the top left panel of
Figure 5.

A density diagram of the line profiles has been produced with the
superimposition of individual profiles from the detections (top right panel of
Figure 5). It shows that features with increased line depth also show an
enhanced spectral width, with respect to the average QS profile (top right
panel of Figure 5).

Figure 6: A typical set of Fe i 6301/6302 Å Stokes profiles with corresponding
well-fitting synthetic profiles obtained from the inversion. The selected
pixel have successfully fitted Stokes profiles with the realistic atmospheric
model. The two O2 telluric lines have been remove from the observed Fe i 6302
Å spectra.

We applied a double Gaussian fit to all spectral profiles to take into account
the blend due to the Cr I and Th II near 4861.5 Å (at $\Delta\lambda\approx
0.4$ Å in the bottom right panel of Figure 3). We calculated the line depth
$(I_{\rm{w}}-I_{\lambda_{0}})/I_{\rm{w}}$ where $I_{\lambda_{0}}$ is the
intensity of the line core and and $I_{\rm{w}}$ is the intensity of the line
wing located at $\Delta\lambda=-1.2$ Å from the line core. Due to the absence
of a clear continuum reference point in the data, the line depth is calculated
relative to a position in the far line wing. From the double-Gaussian model we
also calculated a parameter which we call the pseudo-equivalent width (pEW),
which is a good proxy for the line equivalent width. The pEW is the
wavelength-integrated depression of the line profiles for each pixel over the
FoV,

$pEW=\int_{\lambda_{\rm{bw}}}^{\lambda_{\rm{rw}}}\frac{I_{\rm{w}}-I_{\lambda}}{I_{\rm{w}}}\,d\lambda,$
(1)

where $\lambda_{\rm{rw}}$ and $\lambda_{\rm{bw}}$ correspond to the far red
and blue line wing wavelengths located at $\Delta\lambda=\pm 1.2$ Å from the
line core. The middle left panel of Figure 5 presents the map of the pEW
showing that the detected structures have increased pEWs. The middle right
panel of Figure 5 shows a scatter plot of the pEWs vs line depths for the
detected fine-structures revealing a correlation between these two parameters
with a Pearson correlation coefficient of $\sim$0.63.

Figure 7: Results of the spectral inversions for the Fe i 6301 and 6302 Å
lines, showing the LoS magnetic field, the field strength, inclination,
azimuth, temperature and LoS velocity maps at $\log\tau$= $-$1\. The bottom
panels depict histograms of the LoS magnetic field and magnetic field strength
for all pixels with negative $B_{LoS}$

inside the areas marked with the red and blue boxes in the top row. Median
values are displayed in the top corners.

The double-Gaussian models represent well the observed line profiles. However,
due to the relatively coarse spectral sampling of the data we are not able to
resolve and separate Gaussian components representing H$\beta$ and line blends
at the red wing, reliably. To quantify the width of the H$\beta$ line profiles
from the SST data we followed the method used in Leenaarts et al. (2012). For
each pixel in the data we define the width of the line as the intersections of
the profile and the line $I=I_{min}+(I_{max}-I_{min})/2)$, where $I_{min}$ and
$I_{max}$ are profile minimum and maximum. The bottom left panel of Figure 5
presents the map of the line width showing that the detected structures have
increased line width. The bottom right panel of Figure 5 shows scatter plot of
the pEWs calculated with the double-Gaussian model vs line width. There is a
clear correlation between these parameters suggesting that the pEW and line
width are increased with the same line broadening mechanism(s) and pEW is a
good proxy for the line width.

###  3.3 Spectropolarimetric inversions

In this section we provide some basic information on the inversions performed
on the ViSP spectropolarimetric data. A complete description will be presented
in a forthcoming paper (Uitenbroek et al., in preparation).

####  3.3.1 Code setup

To interpret the ViSP observations, we use the recently developed DeSire
inversion code (Ruiz Cobo et al., 2022). DeSire uses the LTE inversion code
SIR (Ruiz Cobo & del Toro Iniesta, 1994) with the forward modeling non-LTE
radiative transfer solver RH (Uitenbroek, 2001). The code solves the
multilevel non-LTE radiative transfer problem using analytical response
functions derived in LTE to invert or synthesize photospheric and
chromospheric spectral lines in 1D by assuming a plane-parallel geometry.

Prior to the inversion the observed Stokes profiles were averaged over 7 and
11 pixels along the slit $(\sim$0.208″ and 0.213″ for arm 1 and arm 3,
respectively) to equalize vertical and horizontal scales of the pixels. The
noise level of the averaged Stokes Q, U, & V profiles for Fe I and Ca II are
4.4$\times$10${}^{-4}I_{c}$ and 3.7$\times$10${}^{-4}I_{c}$, respectively.
Inversions were performed in four cycles, and Table 2 summarizes the number of
nodes used in the cycles. The magnetic filling factor, or the fraction of a
pixel occupied by the magnetic element, is taken as $f=1$. The stratification
of the atmospheric parameters obtained by the inversions is given as a
function of the logarithm of the optical depth scale at 5000 Å (hereafter
$\log\tau$).

####  3.3.2 Fe i 6301 and 6302 Å Lines

We inverted the full Stokes profiles of the Fe i 6301 and 6302 Å lines over
the entire ViSP FoV. A sample plage profile with signal in all of the
polarization parameters is presented in Figure 6 together with the best-fit
synthetic profiles obtained from the inversion.

Table 2: Number of cycles and nodes employed in the inversions of Ca II and Fe i lines. Physical parameters | nodes used in
---|---
| different cycles
Temperature, $T$ | 2, 5, 7, 9
Microturbulence, $v_{\rm{mic}}$ | 1, 3, 3, 3
LoS velocity, $V_{\rm LoS}$ | 2, 5, 7, 7
Magnetic field, $B$ | 2, 5, 7, 7
Inclination, $\gamma$ | 1, 2, 5, 5
Azimuth, $\phi$ | 1, 2, 2, 2

The inversion output showing maps of the LoS field ($B_{LoS}$), field strength
($B$), inclination ($\gamma$), azimuth ($\phi$), temperature ($T$) and LoS
velocity ($v_{LoS}$) at $\log\tau=-1$ (low photosphere) are presented in
Figure 7. Azimuth disambiguation has not been performed for the magnetic
field, and the inclination angle ($\gamma$) and azimuthal angle both describe
the direction of the magnetic vector with respect to the LoS, with $\gamma=0$
defined as the direction away from the observer. In the map of $B_{LoS}$ and
$B$, we only consider pixels that have at least one polarization profile
(Stokes Q, U and V) with maximum absolute amplitude greater than 4 standard
deviations ($\sigma_{s}$) (Lagg et al., 2016; Campbell et al., 2021). The
inversion reveals a large inclination angle, $\gamma$, in MFCs. This is due to
the large viewing angle (i.e., small $\mu$) of the FoV, where the magnetic
flux tubes that are oriented mostly along the surface normal are inclined with
respect to the observer. As a result, plage MFCs have a strong magnetic field
with maximum values of $B$ greater than 2 kG, with a LoS component of only a
few hundred Gauss (Figure 7). Furthermore, the maps reveal that the magnetic
field of the MFCs inside the plage (see e.g., the area within the red box in
the top panels of Figure 7) is stronger than the field at the edge of the
plage (area within the blue box in the top panels of Figure 7).

The map of the azimuth shows that there are dominant azimuthal directions
(dark blue patches in the right panel of the second row of Figure 7) with some
variations at the locations of almost all MFCs, confirming the presence of
field lines aligned along the same direction. The azimuth of the magnetic
field outside MFCs are not well defined as there are very weak Q and U
signals. A temperature map of the inverted region shows temperature
enhancements for MFCs at $\log\tau=-1$ (Figure 7). The plage elements exhibit
enhanced temperatures, similar to their appearance in G-band images. The LoS
velocity map indicates that there is a suppressed granular convection
(abnormal granulation) in the plage MFCs (Figure 7).

####  3.3.3 Inclination map

Figure 8 shows a co-aligned H$\beta$ image and an inclination map at
$\log\tau=-1.8$, corresponding to the middle photosphere.

Figure 8: Coaligned VBI H$\beta$ image and inclination map produced with the
inversion of ViSP Fe i 6301/6302 Å lines. Q1$-$Q3 mark areas where fibrils are
oriented preferably toward the QS. P1-P3 boxes mark the fibrils that are
directed away from the observer (blue boxes) and toward the observer (red
boxes) inside the plage. Inclination angle histograms of the areas marked with
blue and red boxes for the P1$-$P3 regions are presented in the bottom panels
with blue and red bars. Median values are also displayed in the top left
corners. The inclination map and histograms only include pixels with a maximum
absolute amplitude of the Stokes parameter more than $4\sigma_{s}$ (see text
for explanation). The vertical lines mark the inclination angles between LoS
and local vertical ($\gamma\approx 144^{\circ}$).

The P1$-$P3 boxes in Figure 8 mark selected regions of the MFCs within the
plage. The boxes are split into red and blue boxes that mark roughly the
fibrils directed toward the observer (red boxes) and away from the observer
(blue boxes). The disc center (DC) direction is indicated by the blue arrows.
Histograms of the field inclination within these boxes indicate that magnetic
flux tubes associated with the lower parts of away-directed fibrils (towards
the limb) are less inclined than flux tubes of fibrils directed toward the
observer (towards the DC; see bottom panels of Figure 8). We’ll discuss these
findings in Sect. 4.

###  3.4 Ca II 8542 Å line

We invert the Ca II 8542 Å (hereafter Ca II) together with the photospheric Si
I 8536 Å and Fe i 8538 Å lines located in the blue wing of the Ca II line. A
five bound level-plus-continuum Ca II model atom with complete angle and
frequency redistribution is used. The Stokes Q and U signals in the
chromosphere are inherently weak and the noise level in these data prevent
their reliable inversions.

The top row of Figure 9 presents maps of the Ca II Stokes I at line core and
Stokes V at $\Delta\lambda=-0.2$ Å, for the full FoV covered by ViSP scans at
four adjacent pointings. Due to the shorter length of the ViSP slit in this
spectral arm (Table 1) there is a gap between the upper and lower merged
raster scans. These maps show that the enhancement of circular polarization
signals (Stokes V) is cospatial with the MFCs and fibrils directed toward the
LoS in the intensity maps (Stokes I) (Figure 9).

Representative examples of Stokes profiles with the best-fit synthetic
profiles obtained from the inversion for the pixels located in a strong MFC
and a fibril outside MFCs are presented in Figure 10. The inversion output
showing the maps of temperature, LoS magnetic field, mass density and LoS
velocity, integrated between $\log\tau=-2.8$ and $-4.3$, are presented in the
middle and bottom rows of Figure 9. The temperature map derived from the
inversions (middle row, left column in the Figure) shows clear temperature
enhancements in correspondence of the MFCs, but over larger, more diffuse
areas than for the photospheric case (Fig. 7). The LoS velocity map of the
same region reveals weak downflows along the area where chromospheric
fibrillar features are located (Figure 9).

##  4 Discussion

We investigated the fine scale structure of the plage chromosphere by
analyzing broadband imaging and full Stokes spectropolarimetric observations
in the H$\beta$, Ca II 8542 Å, and Fe i 6301/6302 Å lines obtained with the
largest solar optical telescope, DKIST. Plages are unipolar magnetic regions
appearing either in the vicinity of strong active regions with sunspots or
smaller remnants of a decayed unipolar active regions without sunspots (e.g.,
Rutten, 2021). We observed a non-sunspot-associated plage located at around
(x, y) = (-362″, $-406$″). The large FoV of DKIST covered most of the plage
including its boundaries with the QS (Figures 1 & 2).

###  4.1 The appearance of H$\beta$ fibrils

The VBI H$\beta$ images are dominated by very prominent, fine-scale, densely
packed fibrils that are mostly parallel to each other (Figure 1) and are
anchored at the unipolar, extended photospheric MFCs (Figure 2). To understand
their appearance, we employed high-resolution spectral imaging data obtained
with SST/CHROMIS on a comparable target, and studied their spectral properties
(Figure 3). By multiplying the CHROMIS spectral imaging data with the VBI
transmission profile and averaging over the sampled wavelengths, we are able
to reproduce the H$\beta$ scene found in the VBI data (Figure 4). The analysis
shows that the dark, fibrillar structures seen in the composite CHROMIS data
have both increased line width and line depth with respect to the average QS
profile (Figure 5), explaining why these features appear as high-contrast dark
structures relative to the background in the VBI H$\beta$ image.

Figure 9: The top panels show the ViSP images in the Ca II 8542 Å Stokes I
line core and Stokes V at $\Delta\lambda=-0.2$ Å. The DeSIRe output showing
the temperature, LoS magnetic field, mass density and LoS velocity maps
averaged over the interval between $\log\tau=-2.8~{}\rm{and}-4.3$ are
presented in the middle and bottom panels. The white boxes mark an area where
fibrils are oriented toward the LoS direction.

Figure 10: Typical set of Stokes profiles with corresponding well-fitting
synthetic profiles obtained from the inversion of a pixel located in a strong
MFC (left panels) and a pixel in a fibril outside of MFCs (right panels).
These selected pixels have Stokes V successfully fitted with the realistic
atmospheric model. The two $\mathrm{H_{2}O}$ telluric lines have been remove
from the observed Ca II 8542 Å spectra.

###  4.2 Opacity broadening of the fibrils H$\beta$ line width

The line broadening of chromospheric fine structures is a well-known
phenomenon that has been reported in many observations (see the reviews by
Beckers, 1972; Tsiropoula et al., 2012). However, establishing the exact
reasons for the line broadening remains a central problem of chromospheric
research. The increased line width can be caused by increased local
temperatures produced by thermal and nonthermal heating processes, nonthermal
motions, turbulence and MHD waves. These mechanisms have been investigated in
recent decades using both advanced theoretical modeling and high-resolution,
multi-instrument observations but a definitive explanation still eludes us.

Another broadening mechanism relevant to chromospheric spectral lines is
opacity broadening. Increased opacity could enhance the absorption in the line
core/inner wing and hence broaden the line width. This could also cause larger
line core depth if the line core intensity is not saturated. The latter
scenario is encountered when the observed layer/structure in the chromosphere
is optically thin (Rutten, 2003). In this regime, there is a strong
correlation between line core optical depth and equivalent width (EW) through
the curve-of-growth.

Due to the absence of a clear continuum in our data, we are not able to
calculate EWs for the H$\beta$ line. Instead we measured the line depression
integrated over the wavelength range of the CHROMIS spectral scan. This
parameter (called pEW) can be taken as a good proxy of the EW and line width
(Figure 5). The maps of the pEWs and line width show that the detected
fibrillar structures have increased pEWs, line widths and variable line core
depths (Figure 5). Furthermore, the scatter plot of the pEW vs line depth
reveals a clear correlation between these two parameters (middle right panel
of Figure 5). This suggests that the optical thickness of fibrils in the
H$\beta$ line center is less than 1 which classifies the fibril plasma as
optically thin in this line, and not much larger than 1 $(\tau\gtrsim 1$). In
such conditions, the fibril’s line width and depth are very sensitive to the
optical depth and hence opacity broadening can make a significant contribution
to the observed line broadening. Opacity broadening of plage fibrils in the
H$\alpha$ line has been discussed in Molnar et al. (2019) where they proposed
that the broadening could be due to an increased population number of the
first excited level of hydrogen, due to an enhanced downward Ly$\alpha$ wing
flux. They concluded that this population number can be affected significantly
by the downward Ly$\alpha$ wing flux.

Leenaarts et al. (2012) showed that the H$\alpha$ opacity in the upper
chromosphere calculated using radiation-MHD simulations and three-dimensional
non-LTE radiative transfer computations is mainly sensitive to the mass
density and only weakly sensitive to the temperature. They showed that
enhanced chromospheric mass density in fibrils pushes the line formation
height upward where the source function is set by the horizontal average of
the angle-averaged radiation field. On the other hand, the radiation field is
independent of the local temperature and decreases as a function of height. As
a result fibrils appear dark in H$\alpha$ against their deeper-formed
background (Leenaarts et al., 2012). Increased opacity in the H$\beta$ line,
manifest as increased line depth and width, could be related to the increased
density in fibrils, with respect to their background atmosphere.

In contrast to H$\beta$, no correlation between line core intensity and line
width of H$\alpha$ has been reported by Cauzzi et al. (2009) (see Figure 6
therein). This difference is not surprising as the H$\alpha$ is more optically
thick. The oscillator strength of the H$\alpha$ transition is around seven
times larger than the oscillator strength of the H$\beta$ transition.
Therefore, the H$\alpha$ line core intensity for fibrils should saturate
faster with increased opacity. In our data, we note that despite a clear
linear tendency, the scattered data points (middle right panel of Figure 5)
indicate that the spectra of some H$\beta$ structures can be in the saturation
(optically thick) regime and/or other broadening mechanisms that are dominant
in some fibrils.

###  4.3 Morphology of fibrils and Magnetic canopy

It is widely accepted that fibrils are preferentially formed along continuous
lines of magnetic force with their footpoints rooted into the photospheric
MFCs. Our observations show that H$\beta$ fibrils within the plage appear
shorter compared to fibrils at the edge of the plage, parallel to each other,
and directed to both sides of the extended MFCs (see e.g., regions marked with
P1, P2, P3 in Figure 8). However, they appear longer and directed preferably
toward the QS regions near the edge of the plage (see regions marked with Q1,
Q2, Q3 in Figure 8). Similar results for plage fibrils observed in H$\alpha$
and Ca II K filtergrams have been reported by Foukal (1971a, b) and Pietarila
et al. (2009). Some limitations related to our inversions, such as large
viewing angle, lack of knowledge of exact geometrical heights, limited FoV,
and low S/N for linear polarizations in the chromosphere, hinder the
determination of the 3D geometry of the flux tubes and the height where the
magnetic canopy is merging in different part of the plage.

The maps of total magnetic field strength and LoS magnetic field in the
photosphere at $\log\tau=-1$ obtained from the inversion of the Fe i 6301/6302
Å lines show that there are larger MFCs located close to each other inside the
plage (Figure 7), hence a smaller separation between MFCs inside the plage
than at its edges. Following Durrant (1988) and Martínez Pillet et al. (1997)
we can define a “magnetic filling factor”, $f_{l}$111We note the filling
factor introduced here is not the same as the filling factor used in the
inversions. Here $f_{l}$ is the large-scale filling factor defined by the
separation of MFCs whereas in the inversions the filling factor is defined
within a resolution element., at a reference photospheric height. The canopies
of neighboring MFCs merge at a distance above the reference level given by the
analytical formula, $z_{m}\approx-2H\ln f_{l}$, where $z_{m}$ is the height at
which the canopy merges, $H$ is the pressure scale height of the isothermal
atmosphere. Assuming that the scale height of the plage MFCs is approximately
the same everywhere, $z_{m}$ has to be lower inside the plage. A low-lying
canopy with funnel-like cross-section can explain why fibrils are shorter
inside the plage (Figure 11).

At the edges of plage regions the magnetic field strength of MFCs are weaker
than the field strength of neighboring MFCs inside the plage (Figure 7). As a
result the funnel-like magnetic field configuration can be bent away from the
plage toward the edge of the plage and QS to compensate for the lateral
magnetic pressure imbalance (Figure 11). This could explain why observed
fibrils at the edges of the plage have a preferred orientation toward the QS
(see regions marked with Q1$-$Q3 in Figure 8).

Maps of the inclination angle reveal that flux tubes at the lower parts of
fibrils directed toward the observer (toward the DC) have larger inclination
angle ($\gamma$) than flux tubes of fibrils directed away from the observer
(toward the limb) (Figure 8). This is manifested in the histograms comparing
the distribution of inclination angle for blue and red boxes marking lower
parts of fibrils directed towards the DC and limb, respectively (Figure 8).
The average heliocentric angle of the regions marked with P1$-$P3 is 36∘
($\mu\approx 0.8$). Therefore, flux tubes aligned along the local vertical
should have $\gamma\sim 144^{\circ}$ inclination. The strongest magnetic field
patches inside MFCs have a median inclination close to $144^{\circ}$. However,
the histograms of Figure 8 show that the inclination angle with respect to
$144^{\circ}$ (local vertical) for areas marked with red and blue boxes have
different distributions and median values. This could be an indication that
flux tubes are beginning to diverge from the vertical at photospheric heights
as they form a magnetic canopy in the upper atmosphere (Figure 11).

Figure 11: Schematic representation of the unipolar plage magnetic field
configuration showing the basic geometry of the fibrils inside and at the
boundaries of the plage. Unipolar strong MFCs close to each other inside the
plage create low-lying canopy/flux tubes with funnel-like cross-sections and
shorter fibrils. At the edges of plage where $B_{1}<B$, magnetic field lines
can be pushed away towards the edge of the plage and QS. This creates an
asymmetric configuration of the funnel-like canopy where flux tubes and
fibrils from the edge of the plage are directed preferably towards the QS.
Dotted horizontal lines mark the base of the photosphere ($\tau=1$) and the
upper photospheric layer ($\tau=0.1$) where Fe i 6301/6302 Å lines have a high
sensitivity.

###  4.4 The chromospheric models

The Stokes V images of Ca II at $\Delta\lambda=-0.2$ Å and the LoS magnetic
field map obtained from inversion of the Ca II spectra show that the
enhancement in circular polarization and $B_{LoS}$ outside the MFCs is
detected in the areas where fibrils are oriented toward the LoS (North-west)
direction (see region marked with the white boxes in the top panels of Figure
9). Figure 10 compares the Stokes I and V profiles of representative pixels
located on the plage MFC and fibril. The Stokes V of MFC shows strong signal
at the Si I 8536 Å and Fe i 8538 Å photospheric lines as well as in the Ca II
chromospheric line, indicating that the plage MFC is dominated by both
photospheric and chromospheric magnetic field components. However, the fibril
pixels only show strong Stokes V for the Ca II line, suggesting the presence
of purely chromospheric magnetic field. Given the large viewing angle for this
region, the strong signal in Stokes V implies a large inclination of the field
with respect the local vertical.

Fibrils appear dominated by redshifted plasma in the LoS velocity map (bottom
right panel of Figure 9) suggesting the presence of gravity-driven downflows
from the top of the fibril toward the footpoints. The domination of downflows
indicates that plage fibrils observed in Ca II are cool and dense plasma which
in turn supports the opacity broadening discussed earlier. Interestingly, the
map of mass density derived from the spectral inversions displays areas of
enhanced density in the plage fibrils (bottom left panel of Figure 9).
Although one has to be cautious in interpreting such a map, as the density is
derived from the assumption of hydrostatic equilibrium (HE), this represents a
tantalizing clue on the nature of the fibrils, that will deserve further
investigations.

Finally, we note that field aligned, rapid chromospheric plasma downflows
along spicules have been recently reported by Bose et al. (2021). By analyzing
their morphological and dynamical properties, Bose et al. (2021) suggested
that the detected downflows might be the chromospheric counterparts of the
frequently observed redshifts/downflows predominantly seen in the TR/low
coronal lines (Doschek et al., 1976; Dadashi et al., 2011).

##  5 Concluding remarks

High-resolution H$\beta$ filtergrams obtained with DKIST/VBI show that the
plage chromosphere is dominated by fine-scale fibrils. Due to their enhanced
line width and line depth, the fibrillar features are clearly visible in both
broadband filtergrams as well as in monochromatic line core and wing images.
This demonstrates that H$\beta$ observations are an excellent diagnostic to
identify and track fine-scale structure in the chromosphere.

Our results also suggest that H$\beta$ fibrils can be optically thin
structures, making this line a very appropriate choice for the well-known
cloud modeling inversions red proposed originally by Beckers (1964). Cloud
modeling remains one of the most important inversion techniques for the Balmer
lines and works at its best for optically thin structures (Tziotziou, 2007).

A correlation between the H$\beta$ line depth and width indicates that opacity
broadening could be the main reason for the spectral line broadening observed
frequently in spicules and fibrils. Whether this mechanism is supported by an
increase in electron density due to enhanced Ly$\alpha$ flux as proposed by
Molnar et al. (2019) or by an overall increase in density as proposed by
Leenaarts et al. (2012), remains to be determined. It is possible that
footpoint heating, manifested as a temperature enhancement of the MFCs (Figure
7 and 9) could lead to hot plasma upflows in the chromosphere along magnetic
flux tubes; rapid cooling of this plasma through radiation losses could then
lead to the formation of denser fibrils, consistent with the pervasive
dowflows observed in the Ca II 8542 Å line (Figure 8). Hot plage fibrils
footpoints have been reported recently by Kriginsky et al. (2023) using
spectral inversions of the same line. Semiempirical models constructed from
the inversions seem to indicate the existence of dense fibrils dominated by
downflowing plasma in the Ca II 8542 Å line. However, assessing the exact
contribution of the opacity broadening in the fibril line widths requires
advanced radiative magnetohydrodynamic computations including synthesizing
fibrils spectra in H$\beta$. This will be studied in a future paper where we
plan to perform 3D, non-LTE radiative transfer calculations of the H$\beta$
line.

The analyses of photospheric and chromospheric polarization data show that
morphological characteristics, such as orientation, inclination and the length
of fibrils, are defined by the topology of the magnetic field in the lower
solar atmosphere. Future DKIST observations with improved S/N for linear
polarization signals in chromospheric lines will provide vector magnetograms
for the 3D geometry of the plage chromosphere.

The research reported herein is based in part on data collected with the
Daniel K. Inouye Solar Telescope (DKIST) a facility of the National Science
Foundation. DKIST is operated by the National Solar Observatory under a
cooperative agreement with the Association of Universities for Research in
Astronomy, Inc. DKIST is located on land of spiritual and cultural
significance to Native Hawaiian people. The use of this important site to
further scientific knowledge is done so with appreciation and respect. DK
thanks V. Martínez Pillet and T. Zaqarashvili for helpful discussions. DK
acknowledge Georgian Shota Rustaveli National Science Foundation project
FR-22-7506. DK acknowledge Science and Technology Facilities Council (STFC)
grant ST/W000865/1. MM & RJC acknowledge support from STFC under grants
ST/P000304/1, ST/T001437/1, ST/T00021X/1 and ST/X000923/1. 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).
DKIST(VBI & ViSP), SST(CHROMIS), SDO(AIA & HMI)

## References

  * Anan et al. (2010) Anan, T., Kitai, R., Kawate, T., et al. 2010, PASJ, 62, 871
  * Anan et al. (2021) Anan, T., Schad, T. A., Kitai, R., et al. 2021, ApJ, 921, 39
  * Beck et al. (2007) Beck, C., Bellot Rubio, L. R., Schlichenmaier, R., & Sütterlin, P. 2007, A&A, 472, 607
  * Beck et al. (2019) Beck, C., Gosain, S., & Kiessner, C. 2019, ApJ, 878, 60
  * Beck et al. (2016) Beck, C., Rezaei, R., Puschmann, K. G., & Fabbian, D. 2016, Sol. Phys., 291, 2281
  * Beckers (1964) Beckers, J. M. 1964, PhD thesis, National Solar Observatory, Sunspot New Mexico
  * Beckers (1968) —. 1968, Sol. Phys., 3, 367
  * Beckers (1972) —. 1972, ARA&A, 10, 73
  * Berger et al. (2007) Berger, T. E., Rouppe van der Voort, L., & Löfdahl, M. 2007, ApJ, 661, 1272
  * Bernasconi et al. (1995) Bernasconi, P. N., Keller, C. U., Povel, H. P., & Stenflo, J. O. 1995, A&A, 302, 533
  * Bose et al. (2021) Bose, S., Joshi, J., Henriques, V. M. J., & Rouppe van der Voort, L. 2021, A&A, 647, A147
  * Buehler et al. (2015) Buehler, D., Lagg, A., Solanki, S. K., & van Noort, M. 2015, A&A, 576, A27
  * Buehler et al. (2019) Buehler, D., Lagg, A., van Noort, M., & Solanki, S. K. 2019, A&A, 630, A86
  * Campbell et al. (2021) Campbell, R. J., Mathioudakis, M., Collados, M., et al. 2021, A&A, 647, A182
  * Carlsson et al. (2019) Carlsson, M., De Pontieu, B., & Hansteen, V. H. 2019, ARA&A, 57, 189
  * Cauzzi et al. (2009) Cauzzi, G., Reardon, K., Rutten, R. J., et al. 2009, A&A, 503, 577
  * da Silva Santos et al. (2023) da Silva Santos, J. M., Reardon, K., Cauzzi, G., et al. 2023, ApJ, 954, L35
  * Dadashi et al. (2011) Dadashi, N., Teriaca, L., & Solanki, S. K. 2011, A&A, 534, A90
  * de la Cruz Rodríguez & van Noort (2017) de la Cruz Rodríguez, J., & van Noort, M. 2017, Space Sci. Rev., 210, 109
  * de Pontieu et al. (2007) de Pontieu, B., McIntosh, S., Hansteen, V. H., et al. 2007, PASJ, 59, S655
  * De Pontieu et al. (2011) De Pontieu, B., McIntosh, S. W., Carlsson, M., et al. 2011, Science, 331, 55
  * de Wijn et al. (2022) de Wijn, A. G., Casini, R., Carlile, A., et al. 2022, Sol. Phys., 297, 22
  * Doschek et al. (1976) Doschek, G. A., Feldman, U., & Bohlin, J. D. 1976, ApJ, 205, L177
  * Durrant (1988) Durrant, C. J. 1988, The atmosphere of the sun
  * Erdélyi & Fedun (2007) Erdélyi, R., & Fedun, V. 2007, Science, 318, 1572
  * Foukal (1971a) Foukal, P. 1971a, Sol. Phys., 19, 59
  * Foukal (1971b) —. 1971b, Sol. Phys., 20, 298
  * Henriques et al. (2016) Henriques, V. M. J., Kuridze, D., Mathioudakis, M., & Keenan, F. P. 2016, ApJ, 820, 124
  * Jaeggli et al. (2022) Jaeggli, S. A., Schad, T. A., Tarr, L. A., & Harrington, D. M. 2022, ApJ, 930, 132
  * Jess et al. (2009) Jess, D. B., Mathioudakis, M., Erdélyi, R., et al. 2009, Science, 323, 1582
  * Keller et al. (2004) Keller, C. U., Schüssler, M., Vögler, A., & Zakharov, V. 2004, ApJ, 607, L59
  * Kriginsky et al. (2023) Kriginsky, M., Oliver, R., & Kuridze, D. 2023, A&A, 672, A89
  * Kuridze et al. (2015) Kuridze, D., Henriques, V., Mathioudakis, M., et al. 2015, ApJ, 802, 26
  * Kuridze et al. (2012) Kuridze, D., Morton, R. J., Erdélyi, R., et al. 2012, ApJ, 750, 51
  * Kuridze et al. (2021) Kuridze, D., Socas-Navarro, H., Koza, J., & Oliver, R. 2021, ApJ, 908, 168
  * Kuridze et al. (2016) Kuridze, D., Zaqarashvili, T. V., Henriques, V., et al. 2016, ApJ, 830, 133
  * Lagg et al. (2016) Lagg, A., Solanki, S. K., Doerr, H. P., et al. 2016, A&A, 596, A6
  * Langangen et al. (2008) Langangen, Ø., De Pontieu, B., Carlsson, M., et al. 2008, ApJ, 679, L167
  * Leenaarts et al. (2012) Leenaarts, J., Carlsson, M., & Rouppe van der Voort, L. 2012, ApJ, 749, 136
  * Lemen et al. (2012) Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, Sol. Phys., 275, 17
  * Löfdahl et al. (2021) Löfdahl, M. G., Hillberg, T., de la Cruz Rodríguez, J., et al. 2021, A&A, 653, A68
  * Madjarska et al. (2011) Madjarska, M. S., Vanninathan, K., & Doyle, J. G. 2011, A&A, 532, L1
  * Martínez Pillet et al. (1997) Martínez Pillet, V., Lites, B. W., & Skumanich, A. 1997, ApJ, 474, 810
  * Molnar et al. (2019) Molnar, M. E., Reardon, K. P., Chai, Y., et al. 2019, ApJ, 881, 99
  * Morosin et al. (2020) Morosin, R., de la Cruz Rodríguez, J., Vissers, G. J. M., & Yadav, R. 2020, A&A, 642, A210
  * Neckel (1999) Neckel, H. 1999, Sol. Phys., 184, 421
  * Pietarila et al. (2009) Pietarila, A., Hirzberger, J., Zakharov, V., & Solanki, S. K. 2009, A&A, 502, 647
  * Pietrow et al. (2020) Pietrow, A. G. M., Kiselman, D., de la Cruz Rodríguez, J., et al. 2020, A&A, 644, A43
  * Prasad et al. (2022) Prasad, A., Ranganathan, M., Beck, C., et al. 2022, A&A, 662, A25
  * Rezaei et al. (2007) Rezaei, R., Schlichenmaier, R., Beck, C. A. R., et al. 2007, A&A, 466, 1131
  * Rimmele et al. (2020) Rimmele, T. R., Warner, M., Keil, S. L., et al. 2020, Sol. Phys., 295, 172
  * Roberts (1945) Roberts, W. O. 1945, ApJ, 101, 136
  * Rouppe van der Voort et al. (2009) Rouppe van der Voort, L., Leenaarts, J., de Pontieu, B., et al. 2009, ApJ, 705, 272
  * Ruiz Cobo & del Toro Iniesta (1994) Ruiz Cobo, B., & del Toro Iniesta, J. C. 1994, A&A, 283, 129
  * Ruiz Cobo et al. (2022) Ruiz Cobo, B., Quintero Noda, C., Gafeira, R., et al. 2022, A&A, 660, A37
  * Rutten (2003) Rutten, R. J. 2003, Radiative Transfer in Stellar Atmospheres
  * Rutten (2021) —. 2021, arXiv, arXiv:2103.02369
  * Scharmer (2017) Scharmer, G. 2017, in SOLARNET IV: The Physics of the Sun from the Interior to the Outer Atmosphere (Lanzarote: IAC), 85
  * Scharmer et al. (2003) Scharmer, G. B., Bjelksjo, K., Korhonen, T. K., et al. 2003, Proc. SPIE, 4853, 341
  * Scherrer et al. (2012) Scherrer, P. H., Schou, J., Bush, R. I., et al. 2012, Sol. Phys., 275, 207
  * Secchi (1877) Secchi, A. 1877, Le Soleil (Paris: Gauthier-Villars)
  * Spruit (1976) Spruit, H. C. 1976, Sol. Phys., 50, 269
  * Sterling (2000) Sterling, A. C. 2000, Sol. Phys., 196, 79
  * Topka et al. (1992) Topka, K. P., Tarbell, T. D., & Title, A. M. 1992, ApJ, 396, 351
  * Trujillo Bueno & del Pino Alemán (2022) Trujillo Bueno, J., & del Pino Alemán, T. 2022, ARA&A, 60, 415
  * Tsiropoula et al. (2012) Tsiropoula, G., Tziotziou, K., Kontogiannis, I., et al. 2012, Space Sci. Rev., 169, 181
  * Tziotziou (2007) Tziotziou, K. 2007, Astronomical Society of the Pacific Conference Series, 368, 217
  * Uitenbroek (2001) Uitenbroek, H. 2001, ApJ, 557, 389
  * Van Noort et al. (2005) Van Noort, M., Rouppe Van Der Voort, L., & Löfdahl, M. G. 2005, Sol. Phys., 228, 191
  * Wöger (2014) Wöger, F. 2014, Proc. SPIE, 9147, 91479I
  * Wöger et al. (2021) Wöger, F., Rimmele, T., Ferayorni, A., et al. 2021, Sol. Phys., 296, 145
  * Wöger et al. (2008) Wöger, F., von der Lühe, O., & Reardon, K. 2008, A&A, 488, 375
  * Zaqarashvili & Erdélyi (2009) Zaqarashvili, T. V., & Erdélyi, R. 2009, Space Sci. Rev., 149, 355