Insight into the Solar Plage Chromosphere with DKIST

The strongly coupled hydrodynamic, magnetic, and radiation properties of the plasma in the solar chromosphere make 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 Hβ filter and the Visible Spectro-Polarimeter (ViSP) on the Daniel K. Inouye Solar Telescope to investigate the fine-scale structure of the plage chromosphere. To aid in 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 Hβ is an excellent diagnostic for the enigmatic fine-scale structure of the chromosphere. A correlation between the parameters of the Hβ line indicates that opacity broadening created by overdense fibrils could be the main reason for the spectral line broadening frequently observed 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 toward the observer.

1. INTRODUCTION 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 1968Beckers , 1972)).Such data made possible to perform first high-resolution measurements of spicules characteristics such as morphology, ther-Corresponding author: D. Kuridze dkuridze@nso.edumodynamical 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 ap- pear 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).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)  cal 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 highresolution 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.Inver- a pixel scale along slit, b width of the slit.
sions 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. 2015Buehler et al. , 2019)) Morosin et al. (2020) found that the photospheric magnetic field in the plage region were expanding horizontally toward the chromosphere and forming a volumefilling canopy.They derived a value of ∼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, multiwavelength 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).Nonthermal 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. 2012Kuridze et al. , 2016)).
In this paper we use data obtained with the high-resolution Visible Broadband Imager (VBI; Wöger et al. 2021) 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 fieldof-view (FoV) covered by the observations were (x, y) = (−362 ′′ , −406 ′′ ), with heliocentric angle µ ≈ 0.843 (see Figure 1).Details about the data and instrumentation are given in the next subsections, and in Table 1.

ViSP data
At each telescope pointing, the ViSP spectropolarimeter performed a large raster scan with the 0. ′′ 2142 wide slit oriented along the solar N-S direction.Each scan consisted of 490 slit positions separated by a slit step of 0. ′′ 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 -6307.8Å and 8535.4 -8544.9Å, respectively (arm 2 was not used for these observations).The spatial samplings along the slit for arm 1 and arm 3 are 0. ′′ 0298 pixel −1 and 0. ′′ 0194 pixel −1 , with a slit length of ∼ 75 ′′ and 48 ′′ , respectively.Hence, the FoV of each raster scan covered 107 ′′ ×75 ′′ for arm 1 and 107 ′′ ×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).

VBI data
During each ViSP raster scan, we used the VBI blue branch to obtain filtergrams in G-band, Ca II K and Hβ.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±0.048,1.01±0.02and 0.464±0.01Å for the G-band, Ca II K and Hβ, respectively (Wöger 2014).Single exposure times were ∼0.7, 25 and 4 ms for the G-band, Ca II K and Hβ with a frame rate of up to 30 Hz.In the following, we limit our analysis to G-band and Hβ data.
The instantaneous FoV of VBI-blue is 45 ′′ ×45 ′′ with a spatial sampling of 0. ′′ 011 pixel −1 .For these observations, we employed the so-called "field-sampling mode" to cover the full DKIST FoV of 2 ′ × 2 ′ with a mosaic of 3×3 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 ∼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 3×3 mosaics obtained at each of the four different telescope pointings were stitched together to produce a large mosaic covering the plage region.Adjacent metatiles have overlaps of about 20 ′′ resulting in an overall FoV of about 175 ′′ ×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.

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 Solar-Soft auto align images function via cross-correlation.

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 Hβ.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 Hβ with a spatial sampling of 0. ′′ 0378 pixel −1 and a FoV of about 62 ′′ ×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 ∼0.′′ 13 at this wavelength.The Hβ 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 halfmaximum) 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 Hβ data we used a spatially averaged profile over the disk center, quiet-Sun area marked with a white rectangle in Figure 3 (I av (λ)).The FTS atlas Hβ profile (I F T S (λ)) (Neckel 1999) convolved with the CHROMIS instrumental profile was used as the calibration reference.The ratio of the reference and observed intensities (I F T S (λ)/I av (λ)) was used for calibration and applied to the data (Figure 3).The Hβ 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 Hβ images is expected as the VBI/Hβ filter has a Lorentzian transmission profile centered at the line core and covers a significant part of the line wings, with a FWHM of ∼0.46 Å (bottom right panel of Figure 3).

Overview
To investigate why and how fine-scale chromospheric features appear as high-contrast dark structures relative to the background in Hβ, we study the line profiles of fibrillar structures using high-resolution Hβ spectral imaging obtained with CHROMIS.The top and bottom right panels in Figure 3 display CHROMIS Hβ 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 Hβ 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.

Integration with VBI transmission profile
To more closely replicate the DKIST Hβ 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 wavelengthintegrated CHROMIS and DKIST Hβ 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 Hβ (called integrated Hβ from now on) shows similar scenes including magnetic bright points, granular patterns and fine-scale dark fibrillar structures as found in the VBI/Hβ filtergrams.We note that the granulation in the VBI Hβ 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.

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 mean λ0 ) over the "fibril free" area marked with the white box in Figure 3.For line core intensities (I λ0 ) we applied a threshold as the mean line core intensity (I mean λ0 ) minus 2 standard deviations (σ).Resulting detections are presented as red contours plotted over the Hβ 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).
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 ∆λ ≈ 0.4 Å in the bottom right panel of Figure 3).We calculated the line depth (I w − I λ0 )/I w where I λ0 is the intensity of the line core and and I w is the intensity of the line wing located at ∆λ = −1.2Å 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, where λ rw and λ bw correspond to the far red and blue line wing wavelengths located at ∆λ = ±1.2Å 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 ∼0.63.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 Hβ and line blends at the red wing, reliably.To quantify the width of the Hβ 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.

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).

Code setup
To interpret the ViSP observations, we use the recently developed DeSire inversion code (Ruiz Cobo et al. 2022).De-Sire 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 (∼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 4.4×10 −4 I c and 3.7×10 −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 τ ).

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.
The inversion output showing maps of the LoS field (B LoS ), field strength (B), inclination (γ), azimuth (ϕ), temperature (T ) and LoS velocity (v LoS ) at log τ = −1 (low photosphere) are presented in Figure 7. Azimuth disambiguation has not been performed for the magnetic field, and the inclination angle (γ) and azimuthal angle both describe the direction of the magnetic vector with respect to the LoS, with γ = 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 (σ s ) (Lagg et al. 2016;Campbell et al. 2021).The inversion reveals a large inclination angle, γ, in MFCs.This is due to the large viewing angle (i.e., small µ) 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 pan- els 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 τ = −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).

Inclination map
Figure 8 shows a co-aligned Hβ image and an inclination map at log τ = −1.8,corresponding to the middle photosphere.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.

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-pluscontinuum 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 ∆λ = −0.2Å, 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 τ = −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 enhance-ments 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).

DISCUSSION
We investigated the fine scale structure of the plage chromosphere by analyzing broadband imaging and full Stokes spectropolarimetric observations in the Hβ, 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).

The appearance of Hβ fibrils
The VBI Hβ 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 Hβ 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 Hβ image.

Opacity broadening of the fibrils Hβ 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 highresolution, 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 Hβ 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 Hβ line center is less than 1 which classifies the fibril plasma as optically thin in this line, and not much larger than 1 (τ ≳ 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 Hα 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 Lyα wing flux.They concluded that this population number can be affected significantly by the downward Lyα wing flux.Leenaarts et al. (2012) showed that the Hα 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 Hα against their deeper-formed background (Leenaarts et al. 2012).Increased opacity in the Hβ 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 Hβ, no correlation between line core intensity and line width of Hα has been reported by Cauzzi et al. (2009) (see Figure 6 therein).This difference is not surpris-  ing as the Hα is more optically thick.The oscillator strength of the Hα transition is around seven times larger than the oscillator strength of the Hβ transition.Therefore, the Hα 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 Hβ structures can be in the saturation (optically thick) regime and/or other broadening mechanisms that are dominant in some fibrils.

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 Hβ 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 Hα 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 τ = −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) andMartínez Pillet et al. (1997) we can define a "magnetic filling factor", f l 1 , 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 ≈ −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). 1 We 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.
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 (γ) 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 • (µ ≈ 0.8).Therefore, flux tubes aligned along the local vertical should have γ ∼ 144 • inclination.The strongest magnetic field patches inside MFCs have a median inclination close to 144 • .However, the histograms of Figure 8 show that the inclination angle with respect to 144 • (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).

The chromospheric models
The Stokes V images of Ca II at ∆λ = −0.2Å 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 Hβ 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 Hβ observations are an excellent diagnostic to identify and track fine-scale structure in the chromosphere.
Our results also suggest that Hβ 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 Hβ 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 Lyα 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 Hβ.This will be studied in a future paper where we plan to perform 3D, non-LTE radiative transfer calculations of the Hβ 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 pro-vide 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.   (Jaeggli et al. 2022)

Figure 1 .
Figure 1.Overview of the DKIST observations of the plage.Top row: Mosaics of high-resolution Hβ (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.

Figure 2 .
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 ∆λ = ±0.17Å 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.

Figure 3 .
Figure 3. Overview of the SST data.Monochromatic Hβ 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 Hβ 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.
Figure 1 displays co-aligned images of the plage region in Hβ 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 Hβ/G-band images.The Hβ 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 (Figure1).The existence of both photospheric and chromospheric features in the Hβ images is expected as the VBI/Hβ filter has a Lorentzian transmission profile centered at the line core and covers a significant part of the line wings, with a FWHM of ∼0.46 Å (bottom right panel of Figure3).

Figure 4 .
Figure 4.A qualitative comparison of the DKIST VBI image (left panel) and the wavelength integrated SST CHROMIS (right panel) Hβ 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 .
Figure 5. Top left: CHROMIS Hβ line core image overlaid with a mask where I mean λ 0 − I λ 0 ⩾ 2σ (see text for explanation).Top right: Superimposition of the extracted line profiles of detections shown in the top left panel.The average Hβ profile is overplotted as a blue solid line.Middle left: Map of pEWs of Hβ 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 Hβ 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.

Figure 6 .
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.

Figure 7 .
Figure7.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 τ = −1.The bottom panels depict histograms of the LoS magnetic field and magnetic field strength for all pixels with negative BLoS inside the areas marked with the red and blue boxes in the top row.Median values are displayed in the top corners.

Figure 8 .
Figure 8. Coaligned VBI Hβ 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 4σs (see text for explanation).The vertical lines mark the inclination angles between LoS and local vertical (γ ≈ 144 • ).

Figure 9 .
Figure 9.The top panels show the ViSP images in the Ca II 8542 Å Stokes I line core and Stokes V at ∆λ = −0.2Å.The DeSIRe output showing the temperature, LoS magnetic field, mass density and LoS velocity maps averaged over the interval between log τ = −2.8 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 .
Figure10.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 H2O telluric lines have been remove from the observed Ca II 8542 Å spectra.

Figure 11 .
Figure11.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 B1 < 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 (τ = 1) and the upper photospheric layer (τ = 0.1) where Fe I 6301/6302 Å lines have a high sensitivity.

Table 1 .
Summary of the DKIST instruments and data used in this work.Values refer to a single telescope pointing.

Table 2 .
Number of cycles and nodes employed in the inversions of Ca II and Fe I lines.
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).