The role of the chromospheric magnetic canopy in the formation of a sunspot penumbra

Images were recorded using an adaptation of the BBI instrument (von der Lühe et al., 2012). The two Andor Zyla cameras were equipped with a G-band filter and an optimized titanium monoxide (TiO-band) filter centered at the TiO molecular band at $7057\text{\,}\mathrm{\text{Å}}$. Observing in these molecular bands has proven to be successful for high-contrast imaging of the solar photosphere and sunspots (see, e.g. Berger & Berdyugina, 2003). The cameras have 2560 x 2160 pixels and were set up with a pixel scale of 0.023 arcseconds per pixel. The telescope diffraction limit $\frac{\lambda}{D}$ is $0.10\text{\,}\arcsec$ for the TiO-band wavelength and 0.06″ for G-band. Exposure times were $1.2\text{\,}\mathrm{ms}$ for the TiO-band images and $3.0\text{\,}\mathrm{ms}$ and $2.5\text{\,}\mathrm{ms}$ for the G-band images. The BBI data were calibrated with a standard pipeline, including a dark image correction and a flat field correction. The images were then reconstructed using the KISIP speckle code (Wöger et al., 2008), however, without taking into account the central obscuration of GREGOR, leading to small variations in contrast from the ground truth. After the reconstruction, a Butterworth filter was applied to all images to remove a pattern of vertical stripes arising from the camera. Finally, the G-band images were aligned to the respective temporally closest TiO-band image using a translational shift.

Spectropolarimetric data were obtained with the GRegor Infrared Spectrograph (GRIS, Collados et al., 2012). Three scans were performed with 180 scan positions for each map. A step size of $0.135\text{\,}\arcsec$ was chosen, so that the resulting slit-reconstructed maps have the same image scale in x and y direction. The first and, partially, the second scan were acquired under good seeing conditions and the third scan with only mediocre seeing conditions. The exposure time was $100\text{\,}\mathrm{ms}$ with 10 accumulations, leading to one scan taking roughly $18\text{\,}\mathrm{min}$. The spectral range was chosen to be around the He i 10830 $\text{\,}\mathrm{\text{Å}}$ triplet. In addition to this helium triplet, the spectral window included the Si i 10827 $\text{\,}\mathrm{\text{Å}}$ and the Ca i 10839 $\text{\,}\mathrm{\text{Å}}$ line. GRIS level1 data were created using the gris_v8 pipeline by M. Collados (IAC, private communication). This version corrects for a sub-pixel misalignment between the two beams. A slit-reconstructed continuum map of the first GRIS scan, cropped around the sunspot, is shown in Fig. 8. An absolute wavelength calibration was carried out taking into account Earth’s orbital motion, solar and terrestrial rotation, as well as the gravity redshift (Mart´ınez Pillet et al., 1997; Kuckein et al., 2012b), using telluric lines observed simultaneously within the spectral window.

We utilized the “sharp_cea” HMI data series (Bobra et al., 2014) that has a cadence of 720 seconds and offers de-projected atmospheric data. HMI data has a spatial resolution of $1\text{\,}\arcsec$ (Hoeksema et al., 2014). Data access and handling was done using the SunPy open source software package (The SunPy Community et al., 2020).

The Ca i 10839 $\text{\,}\mathrm{\text{Å}}$ line is a magnetically sensitive line ($g_{\rm eff}=1.5$) that forms in the deep photosphere. Felipe et al. (2018) obtained a mean formation height of $64\text{\,}\mathrm{km}$. As it has a narrow formation height and forms in the deep photosphere, we used the computationally fast Milne-Eddington inversion code VFISV (Borrero et al., 2011) to obtain atmospheric parameter by making use of the GRISinv¹¹1https://gitlab.leibniz-kis.de/sdc/gris/grisinv tool by Vigeesh et al. (KIS) optimised for VFISV inversions of GRIS data.

The Si I 10827 $\text{\,}\mathrm{\text{Å}}$ line is sensitive to atmospheric parameters in the upper photosphere. While the wings are formed under local thermodynamical equilibrium (LTE), only the central core shows effects of non-LTE formation mechanisms (Bard & Carlsson, 2008). However, as shown by, for example, Kuckein et al. (2012a) and Kuckein (2019), depth-dependent inversions can still be used to obtain atmospheric parameters under the LTE assumption, neglecting the smallest optical depths, to which the line core are sensitive to. The spectropolarimetric data of the Si I 10827 $\text{\,}\mathrm{\text{Å}}$ line from the GRIS instrument was inverted with the SIR inversion code (Ruiz Cobo & del Toro Iniesta, 1992). A python-based wrapper written by Ricardo Gafeira²²2https://gitlab.com/gafeira/parallel_desire_sir_rh was used to initialize the inversion and to run it in parallel on multiple CPUs. Each pixel was inverted eight times with different initial-model atmospheres. After these eight runs, the one with the lowest $\chi^{2}$ value (describing the squared difference between the observed spectral profile and the inversion fit) was chosen for each pixel. For each individual run, we used three cycles with (2, 3, 4) nodes in temperature, (1, 2, 2) nodes in the magnetic field strength, (1, 2, 3) nodes in the velocity, (1, 2, 2) nodes in the inclination angle of the magnetic field, and (1, 1, 1) node in the azimuth angle of the magnetic field. The built-in spatial straylight correction method from SIR was used with a quiet sun profile obtained from averaging over a quiet region on the western side of the FOV and an $\alpha$ value (setting the assumed relative amount of straylight) of $0.1$.

In order to obtain atmospheric parameters of the chromosphere, the He I 10830 $\text{\,}\mathrm{\text{Å}}$ triplet (observed with GRIS) was analyzed. Single-atmospheric-component inversions of the Stokes profiles were performed with the HAZEL inversion code (Asensio Ramos et al., 2008), assuming magnetic field parameters and the velocity to be constant in height within the slab. The HAZEL code takes Zeeman and Hanle effects into account. We used three cycles, of which the first one was only used to obtain the optical depth and the velocity from Stokes-$I$. In the second and third cycle, polarimetric spectra were added and the magnetic field vector was obtained. We included weights for Stokes-$Q$ and Stokes-$U$ twice the weight of Stokes-$V$. A straylight correction was performed in the same way as for the SIR inversion (see Sect. 3.2).

The $180\text{\,}\mathrm{\SIUnitSymbolDegree}$ ambiguity of the azimuth angle of the magnetic field was resolved using the GRAZAM tool, which will be described in more detail in a future publication by González Manrique et al. (2023). This tool automatically processes the inversion maps (e.g. correcting the orientation of the maps, etc.) and writes the input data for the AZAM code (Lites et al., 1995), which includes tools to manually edit azimuth maps with the computer mouse. Initially, a radially symmetric distribution of the magnetic field, centered in the sunspot umbra, was assumed. The remaining discontinuities in the maps were resolved by hand. This procedure was carried out separately for the VFISV map, the HAZEL map, and the SIR maps at different optical depths. On the disk center side of the sunspot (top right in the image plane), the magnetic field is parallel to the line-of-sight (LOS) in some pixels of the penumbra. Linear polarization signals are, therefore, small and the azimuth angle cannot be estimated well during the inversions. This uncertainty propagates through the transformation from the LOS reference to the local-reference-frame (LRF) and makes the disambiguation difficult in this region. In the inclination map in Fig. 8 from the VFISV inversion, a spurious discontinuity (sharp jump from dark blue to green-yellow) is visible in the top right of the image. These discontinuity lines are also present in HMI data (not shown here).

Although we used a carefully inferred absolute wavelength array (see Sect. 2.2) as an input for the inversions, the velocity maps resulting from both the SIR and the VFISV inversions, initially showed an offset: The average over quiet sun pixels did not match the convective blueshift which is expected for a solar $\mu$ value (cosine of the heliocentric angle) of $0.639$, at which the sunspot was observed. We corrected the velocity offset by adding a constant value to the inversion maps for all $\log\tau$ values from the SIR results and for the one map of the VFISV result. This velocity value was chosen such that the quiet sun average velocity matches the reference value $v_{\textrm{ref}}$ that was measured with highest accuracy for several solar lines by Löhner-Böttcher et al. (2019). As they did not measure the Si I 10827 $\text{\,}\mathrm{\text{Å}}$ line, we have chosen the Fe I 5434 $\text{\,}\mathrm{\text{Å}}$ as a reference. This line has a formation height of $550\text{\,}\mathrm{km}$ (Löhner-Böttcher et al., 2019, Table 1), which is similar to the formation height of the Si I 10827 $\text{\,}\mathrm{\text{Å}}$ line core ($541\text{\,}\mathrm{km}$, as calculated by Bard & Carlsson, 2008). For the spectral resolution of $100\,000$ and a heliocentric position $\mu=0.6$, a convective blueshift $v_{\textrm{ref}}=$-6\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$$ is given by Löhner-Böttcher et al. (2019, Table A.1). We have chosen our constant such, that the velocity map at $\log\tau=-2.7$ matches this value, which corresponds to the height where the maximum of the velocity response function is located in the quiet sun for this line (Felipe et al., 2018; González Manrique et al., 2020). For the less frequently studied Ca I 10839 $\text{\,}\mathrm{\text{Å}}$ line, Felipe et al. (2018) obtained a mean formation height of $64\text{\,}\mathrm{km}$. Löhner-Böttcher et al. (2019) did not measure a line that matches this value, but the C I 5381 $\text{\,}\mathrm{\text{Å}}$ and the Fe II 6149 $\text{\,}\mathrm{\text{Å}}$ lines with formation heights of $40\text{\,}\mathrm{km}$ and $130\text{\,}\mathrm{km}$ (blue shift values of $-821\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$ and $-404\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$, respectively), are close. We interpolated and used the value $v_{\textrm{ref}}=$-710\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$$ for the Ca I 10839 $\text{\,}\mathrm{\text{Å}}$ line.
After applying our correction, the average velocities in the umbra were below $100\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$ at $\log\tau=-2.0$ for the SIR inversions of the Si I 10827 $\text{\,}\mathrm{\text{Å}}$ line and below $50\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$ for the VFISV inversions of the photospheric Ca I 10839 $\text{\,}\mathrm{\text{Å}}$ line. This is in line with the expectation of significantly suppressed convection in the photospheric umbra (see, e.g. Löhner-Böttcher et al., 2018) and we therefore regard our correction as consistent and successful.

We analyzed the evolution of the sunspot from 2020-10-15 to 2020-10-18 with HMI data. As shown in the continuum maps in Fig. 4, the sunspot formed at the beginning of this time range. On its western (right) side, the penumbra remained stable after the formation. On its eastern side, small pores or parts of the umbra kept changing shape, but no stable penumbra formed. Additional data from multiple days later (shown below the horizontal line in Fig. 4) yielded that, from 2020-10-20 (four days after our observations) onward, the sunspot had a penumbra that almost surrounded the whole umbra, but still left a small gap on the eastern side.

In our GREGOR observations, no penumbra was visible on the left (East) side of the sunspot. The BBI images reveal that granulation was present with some of the granules being slightly elongated. In addition, on the same side, thin bright filaments (hereinafter referred to as TBFs) were seen that are mostly orientated east-west, that is, radially outward from the umbra. They are remarkably straight, almost no curvature is observed, and they seem to span multiple granules in some cases. This can be seen in the time series shown in Fig. 6. These TBFs can be clearly recognized and create the visual impression of forming separately from the granulation. Although they are also recognizable in the G-band images, they are better seen in TiO-band. Fig. 7 shows an example of a TBF in G-band and TiO-band with a ruler that shows a length value in arcseconds.

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  Length: between $0.8\text{\,}\arcsec$ and $2.2\text{\,}\arcsec$ (average $1.4\text{\,}\arcsec$)

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  Width: seen as roughly $0.1\text{\,}\arcsec$. This is at the telescope diffraction limit $\frac{\lambda}{D}$ of $0.10\text{\,}\arcsec$ for TiO-band.

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  Lifetime: between $2\text{\,}\mathrm{min}$ and $10\text{\,}\mathrm{min}$ (average $4\text{\,}\mathrm{min}$)

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  No inner structures is seen within the TBFs at this resolution.

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  The TBFs appear as a single entity and do not exist in bundles.

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  In 5 of the 9 events, a bright point-like feature is forming or moving close to one end of the filament. They resemble penumbral grains. In 4 out of these 5 cases, the bright point was located at the eastern end of the TBF and moved towards east (away from the umbra). The bright point-like features were better visible in the TiO-band images than in the G-band images.

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  The maximum brightness values (in TiO-band) inside the TBFs varies between 1.0 and 1.4 (average: 1.17) of the average quiet sun value.

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  TBFs were observed only on 2020-10-16. In imaging data from 2020-10-17 (also available, but not shown in this work), no TBFs were unambiguously identified. Only one bright elongated feature with a length of less than $1\text{\,}\arcsec$ was observed on that date, that could also be part of an abnormal granulation.

In a literature search, we found publications where structures similar to the TBFs can be seen in the FOV of solar images (e.g. Rimmele, 2004, Fig. 2a) and even in simulations (Moreno-Insertis et al., 2018, Fig. 2). They are, however, not discussed by the authors. Only the report by Yurchyshyn et al. (2012) describes a ‘small scale filamentary flux emergence’ event seen in TiO-band images which, in one image of a time sequence, looks similar to the TBFs described here. The length is stated to be approximately $1\text{\,}\mathrm{Mm}$ and it also had a bright dot appearing on one end. Close to this structure, a patch of horizontal magnetic field is observed in co-aligned HMI data. In the later stage of development, a bundle of multiple filaments appear in this location. Such bundles have also been observed by others (Lim et al., 2011), but are usually confined to (sometimes abnormal) granules. The TBFs in our case however, never appeared in bundles and were not confined to granular structures.

Using the inversion results from VFISV, SIR and HAZEL, the topology of the magnetic field vector and the LOS velocity can be analyzed not only in two dimensions, but also with respect to the atmospheric height. In Fig. 8, cropped maps of the LOS velocity, the magnetic field strength and its inclination angle in the LRF of all three inversion codes are shown. For the depth-dependent model from the SIR inversions, maps at optical depths of $\log\tau=(-1.5,-2.0,-2.5)$ are shown. In the magnetic field parameter maps from the HAZEL inversion, the white pixels are neglected, as described in Sect. 3.3. As expected, all maps show that the magnetic field is mostly vertical to the solar surface in the umbra, together with high values of the magnetic field strength. In the deepest atmospheric layer (VFISV maps), the field strength values are the highest with umbral values of more than $2000\text{\,}\mathrm{G}$, which is in line with previous observations (see Balthasar, 2018, and references therein). In the penumbra, the well-known filamentary pattern in field strength and inclination maps is seen clearly in the VFISV maps. In the SIR maps, this pattern is weaker and fades towards higher layers. It is remarkable, however, that filamentary structures are also present on the eastern side (in and around region A) of the sunspot, where no penumbra is seen in continuum, TiO-band, and G-band images. Like the penumbra on the western side (in and around region B), which shows a classical spine and instraspine pattern, the eastern side (region A) also shows elongated structures of inclined magnetic fields and low field strength alternating with elongated structures of more vertical fields and high field strength values. The filamentation on both sides of the umbra is best visible in the deep photospheric inclination and field strength maps from VFISV. Without the knowledge of the continuum image, it would be difficult to tell whether a penumbra is present in and around region A or not. A quantitative comparison between the magnetic field properties of region A and region B follows in Sect. 4.4.
The similarities between the eastern and the western side seem to be most prominent in lower layers. In the chromospheric HAZEL inversion maps, a clear difference between the eastern and the western region can be seen by a visual inspection of the cropped maps shown in Fig. 8. The magnetic field strength is higher on the eastern side of the sunspot and the field is more vertically directed than on the western side. The field strength in the eastern side is also higher than in the umbral part of the spot. Interestingly, the region with high field strength values and almost vertically directed fields is at the location where the dark structure seen in the line depression map meets the umbral contour (Fig. 3). In the maps showing the full FOV in Fig. 3, one can see that the dark structure in the line depression map covers a large region at the north-eastern side of the FOV. It probably extends beyond the FOV, towards the direction of the opposite polarity of the AR.

In this section, we investigate whether the visually apparent similarity between the deep photospheric magnetic topology on the western side of the sunspot (with penumbra) and on the eastern side of the sunspot (without penumbra) is reflected in the result of a quantitative analysis or not. We chose two rectangular regions of interest with equal height and width on either side of the sunspot. They are depicted with dashed boxes A and B in Fig. 8. The widths were chosen such that the full penumbra is covered in box B, while the left-right locations were chosen such that they both border on the umbra on the spot-facing side. The heights and the up-down location of the boxes are also the same and were chosen such that a) no dark umbral-like structure at the bottom of region A is included, and b) the spurious line of discontinuity (see Sect. 3.4) in the VFISV inclination map above region B is excluded.

In the LOS velocity maps of the deep photospheric VFISV inversions (Fig. 8), the penumbra on the right side of the image is mostly blueshifted. As the disk center direction is pointing towards the top right of the images and the observations were done at a heliocentric angle of $55\text{\,}\mathrm{\SIUnitSymbolDegree}$, this corresponds to a horizontal flow direction towards the top-right, an up-flow, or a combination of both. The flow on the right side of the sunspot is therefore consistent with the standard outward-directed photospheric Evershed flow. On the left side of the sunspot (in and around region A), large patches of redshifts are present which cover the entire TBF (magenta contour), but also smaller patches of blueshifts. The predominant redshifts have smaller magnitude than the blueshifts in and around region B, but could also represent outward-directed flows. A comparison to the inclination map shows that the red velocity patches mostly correspond to regions with more horizontal fields. Close to the umbral boundary, a band of small blueshifts is present. Also the velocity pattern in and around region A is therefore, in principle, compatible with an outward-directed Evershed flow, including up-flows close to the umbra (see, e.g. Borrero & Ichimoto, 2011). A discussion whether these flows represent an Evershed flow follows in Sect. 5. We also note that the blueshifts in and close to region A are mostly confined to bright features seen in the TiO-band image.
In the higher atmospheric layers shown by the maps of the SIR inversions at $\log\tau=-2.0$, redshifts are predominant in the penumbra in and around region B, which is consistent with the start of the in-flows in the superpenumbra. In and around region A, both blueshifts and redshifts are present.
The velocity maps from the HAZEL inversion show large-scale structures, as shown in Fig. 3: Outside the dark region seen in the helium line depression map, blueshifts are predominant on the East side and redshifts are predominant on the West side. This would also be consistent with the in-flow in the superpenumbra. Inside the dark region seen in the helium line depression map, both blueshifts and redshifts are present and the structure seem to be more complex.

As described in Sect. 4.3, one contour of one TBF (seen in the TiO-band images) can be co-temporally analyzed in the GRIS inversion results shown in Fig. 8. The contour covers 447 pixels in the BBI images and therefore also in the co-aligned and interpolated inversion maps. This corresponds to roughly 13 pixels in maps with the original GRIS pixel size (see image scales of the instruments in Sect. 2). Although the TBF is located in the region in which filamentation is seen in the VFISV maps and the filamentation is parallel to the TBFs, we cannot unambiguously connect the TBF to one specific filament in the magnetograms. However, all TBFs that we identified were located in the region showing filamentation in inversion maps (in and around region A) and the orientations of TBFs and the filaments in the inversion maps were mostly parallel (see orange dotted lines in Fig. 8). In order to further characterize the TBFs, we calculated average atmospheric parameters within the magenta contour outlining the TBF in Fig. 8.