On the Magnetic Nature of Quiet-Sun Chromospheric Grains

Ca ii K grains, i.e., intermittent, short-lived (about 1 minute), periodic (2–4 minutes), pointlike chromospheric brightenings, are considered to be the manifestations of acoustic waves propagating upward from the solar surface and developing into shocks in the chromosphere. After the simulations of Carlsson and Stein, we know that hot shocked gas moving upward interacting with the downflowing chromospheric gas (falling down after having been displaced upward by a previous shock) nicely reproduces the spectral features of the Ca ii K profiles observed in such grains, i.e., a narrowband emission-like feature at the blue side of the line core. However, these simulations are one-dimensional and cannot explain the location or the pointlike shape of the grains. Here, we report on the magnetic nature of these events. Furthermore, we report on similar events occurring at the largest flux concentrations, though they are longer-lived (up to 8 minutes) and exhibit the typical signature of steep velocity gradients traveling across the atmosphere. The spectral signatures of the studied events resemble their counterparts in sunspots, the umbral flashes. We then propose that magnetohydrodynamical waves are not only channeled through the magnetic field in sunspots, but they pervade the whole atmosphere. The propagation along magnetic fields can explain the pointlike appearance of the calcium grains observed in the quiet chromosphere.


Introduction
In the chromosphere, the dominant 5 minute frequency of the p-mode photospheric oscillations is transformed into a dominant frequency of about 3 minutes.In the core of strong chromospheric lines, such as the Ca II H and K or the Ca II infrared (IR) triplet around 854.2 nm, these oscillations are observed as threadlike brightenings structured at mesogranular scales (8-10 Mm).Over this pattern, Ca II K filtergrams soon revealed intermittent, pointlike, enhanced brightenings.The first time they were recorded by Hale & Ellerman (1904), they were dubbed "minute bright calcium flocculi," to account for their small-scale and pointlike appearance.They are now known as Ca II K grains and are associated with sudden narrowband emission features at the blue side of the line core.Similar features are found in the Ca II IR lines, in phase with those of the Ca II K line (Cram et al. 1977;Martínez-Sykora et al. 2015;Mathur et al. 2022).
The calcium grains are intermittent, but they appear in a given location with periodicities of 2-4 minutes.This is why they have been suggested to be the manifestations of acousticshock-like waves propagating upward in the solar atmosphere (e.g., Cram et al. 1977;Beck et al. 2008).This idea was based on the works by Carlsson & Stein (1992, 1997), where they synthesized Ca II K intensity profiles similar to those of the bright grains in a one-dimensional hydrodynamical simulation in non-local thermodynamical equilibrium (NLTE), assuming complete frequency redistribution.They imposed a photospheric piston that induced upward propagating acoustic waves that turned into shocks at chromospheric layers.The interaction of the upflowing shocks and the downflowing atmosphere (displaced upward by previous shocks) caused local heating and, in turn, the peculiar shape of the Ca II K intensity profiles.However, these simulations are one-dimensional and cannot answer the question of why the grains are indeed grains and why they occur where they occur.In fact, Wedemeyer et al. (2004) show that propagating acoustic wave fronts are spherical within three-dimensional hydrodynamical simulations.In order to explain the transformation from spherical wave fronts into grains, some works suggest acoustic wave interference (Rutten & Uitenbroek 1991), while others claim a one-to-one relationship with magnetic fields (Sivaraman & Livingston 1982, and references therein).However, the magnetic nature of the calcium grains has been refuted by subsequent works (Lites et al. 1999;Beck et al. 2008;Vecchio et al. 2009;Mathur et al. 2022).The actual nature of the chromospheric grains is still unresolved nowadays.Most works claim the need for better observations to attain the answer to this problem.Here we present the first clear evidence of the magnetic nature of Ca II grains as seen in the near-infrared (NIR) line at 854.2 nm.We propose that magnetohydrodynamical waves are ubiquitous in the solar atmosphere.

Description of the Data
This study is based on filter-polarimetry data obtained on 2015 August 19 at the Swedish Solar Telescope (Scharmer et al. 2003a) at the Observatorio del Roque de los Muchachos (La Palma, Spain).The target of the observations was the quiet Sun at the disk center.We recorded two 8 minute time series of full vector polarimetry with the CRisp Imaging Spectro-Polarimeter (Scharmer 2006;Scharmer et al. 2008).The area covered at the Sun was 50″ × 53″, sampled with a pixel size of 0 059.We scanned, sequentially, the photospheric Fe I line at 617.3 nm and the chromospheric Ca II line at 854.2 nm.Here, we focus mainly on the analysis of the Ca II line and on one of the time series (the results are equivalent in the other one).This line was scanned at 21 wavelength positions: ±0.175, ±0.0945, ±0.0735, ±0.0595, ±0.0455, ±0.035, ±0.028, ±0.021, ±0.014, ±0.007, and 0 nm.The 0 nm reference was set to the position of the minimum of the spectral line as measured during the etalon calibration process in the morning (UT 07:10).
At each wavelength position, we modulated with four polarimetric configurations, and this was repeated 12 times to accumulate enough photons.All in all, scanning the 21 wavelength points took, approximately, 16 s.The scan of the Fe I line took about 32 s, resulting in a temporal cadence of about 48 s.The seeing conditions were not excellent, but good enough for the adaptive optics system (which is an update of the previous one (Scharmer et al. 2003b)) to work properly, allowing for high spatial resolution data (∼0 35; as retrieved from the two-dimensional Fourier power spectrum).
The data reduction was performed by applying the dedicated CRISPRED pipeline (de la Cruz Rodríguez et al.Since the pixel size of our data is 0 059, the maps were spatially oversampled for the actual spatial resolution.We thus performed a binning of 3 × 3 pixels, ending up with a pixel size of 0 177 and an increase of the signal-to-noise ratio of about a factor of 3.After the reduction process, the polarimetric sensitivity is about σ = 7 × 10 −4 I c in both Fe I and Ca II lines, as derived from the mean value in the FOV of the standard deviation over time of Stokes V at the wavelength point at the far wing (Ca II) or the continuum (Fe I).For more details on these observations, we refer to Pastor Yabar et al. (2020).

The Magnetic Nature of Calcium Grains
A visual inspection of the data reveals that the intensity profiles of the Ca II line are very often asymmetric, possibly due to the ubiquitous presence of significant velocity and magnetic field gradients along the line of sight from the photosphere to the chromosphere.More interestingly, many profiles show emission-like features in a narrow wavelength range.Among them, the majority show such an emission feature in the inner blue wing, lasting for 0.8-1.6 minutes approximately.These profiles have already been identified in the literature as the NIR counterparts of the Ca II K grains  3. (Cram et al. 1977;Martínez-Sykora et al. 2015;Mathur et al. 2022).
Figure 1 shows the time evolution of the intensity at Δλ = −0.21Å (where the emission-like feature is found) and the photospheric and chromospheric Stokes V amplitudes (A V ) related to a Ca grain event (marked with a yellow circle at the top of panel (e) in Figure 2).In order to decrease the impact of the noise in the calculation of the Stokes V amplitude, we proceed as follows.To compute the amplitude of the Ca II line at the wavelength of the grain, we average the amplitude of Stokes V in the three pixels centered at Δλ = −0.21Å.We then compute the absolute value to compare with the amplitude of the whole profile.For the whole profile, we consider the maximum value between zero and the absolute value of the amplitude minus the noise level (7 × 10 −4 I c ).The same procedure is applied to compute the Fe I Stokes V amplitude.The bottom panel shows that there is a magnetic signature at the photosphere during the whole time series.At the chromosphere, we see a fainter but significant Zeeman signal during most of the time series.The top panel shows that the brightening of the Ca II grain happens at the external parts of the photospheric magnetic structure.It is seen, for the first time, at the beginning of the time series, and then after 5.6 minutes.This time interval is consistent with the periodicity found in  3, the middle one marks the example displayed in Figure 4, and the bottom one marks the position of the example found in Figure 5. Panel (f) displays the initial time at which the calcium grains appear.
Ca II K grains.However, we see that it occurs at different places of the magnetic structure.For this reason, we show in Figure 3 the time evolution of the Stokes I and V profiles of the grain at different locations in each time step, as marked with yellow dots in Figure 1.
In Δt = 6.4 minutes in Figure 3 we see an emission-like spectral feature at the blue side of the line core.A glimpse of the same feature is visible in the rest of the snapshots.But the most interesting thing is that a counterpart of this emission-like feature is also observed in circular polarization in all snapshots.The feature is, in general, much more evident in Stokes V than it is in Stokes I.This is likely explained by the impact of the point-spread function of the atmosphere, telescope, and instrument.The intensity of a single pixel is highly contaminated by the intensity from the pixels around, while the polarization does not suffer as much since the azimuthal average tends to zero quite fast (Pastor Yabar et al. 2020).This effect can also explain why the calcium grain feature is narrower in V than in Stokes I or its derivative.
With the time series we have, we cannot compute a periodicity for the grains, but we have detected many events reappearing with a time span of around 4 minutes.Therefore, it is reasonable to consider that the events analyzed here are the NIR counterparts of the Ca II K grains and are then connected to the same oscillations.Here, we propose that the waves producing these brightenings are of a magnetic nature, as evidenced by the clear detection of circular polarization.Figure 1 shows that the photospheric Stokes V signal is cospatial with a Stokes V signal in the chromosphere.Very likely, the magnetic field connecting the photopshere with the chromosphere can act as a guide for the waves, explaining the pointlike appearance of the grains.
These short-lived grains appear, indeed, in the less magnetized areas of the quiet Sun.In the most magnetized areas of the quiet Sun (but not only those of the network), we have detected deformations in the intensity profiles similar to those of calcium grains, but with some differences: (1) as time evolves, they appear to travel across the wavelength, from the blue wing to the line core, (2) they can appear (although much less frequently) in the red wing of the line, and (3) they are much longer lived.Though they exhibit some differences in the observed characteristics, we think they are of the same origin as calcium grains.For this reason, we refer to any of the cases reported in this Letter as calcium grains.
Figure 4 shows the time evolution of the pixel centered at the middle yellow circle in panel (e) of Figure 2. In the initial frame, a feature appears at the blue side of the line core.It then disappears, reappearing at Δt = 4 minutes.As in the previous case, this can be compatible with the periodic nature of these events as reported in previous works (e.g., Beck et al. 2008;Vecchio et al. 2009).The feature "moves" across the profile toward the core and, at Δt = 7.2 minutes, the feature is at the line core.There are clear Stokes V signatures associated with the grain event.
Figure 5 shows an example of a calcium grain appearing in the red wing (Δt = 2.4 − 3.2 minutes) and "moving" toward the blue wing as it evolves (Δt = 5.6 − 6.4 minutes).These are the less frequent cases.de la Cruz Rodríguez et al. (2015a) analyzed a similar profile observed in an emergent loop in an active region.They find that the profile can be reproduced with cold upflowing material in a downflowing hot chromosphere.In our case, the example is located at the center of the bottom circle in panel (e) of Figure 2, embedded in the largest unipolar flux concentration.In general, we do not see a correlation between the calcium grains and bipoles at the photosphere (see also Figure 2).

Discussion and Conclusions
Our data set has suitable high quality in terms of spatial resolution and polarimetric sensitivity to report the magnetic nature of the Ca II NIR grains.We have found Ca II grains with associated Stokes V signatures in the whole FOV, irrespective of the magnetization level.Panel (a) of Figure 2 shows, as dotted lines, the cumulative distribution of the amplitude of Stokes V for the pixels harboring grains.These pixels have been found with a k-means procedure (considering only Stokes I) that will be described and discussed in further detail in a subsequent paper.About 60% (70%) of the pixels have amplitudes larger than the noise level in the Ca II (Fe I) line, which turns out to be very remarkable.If we consider a 3σ level, about 10% (20%) of the pixels have a magnetic detection in the Ca II (Fe I) lines.
If we average the signals of all the pixels in each patch (solid lines), more than 90% of the patches with grains have Stokes V amplitudes larger than the noise level at the Ca II line.About 55% have signals above a 3σ threshold.This is clear evidence of the magnetic nature of calcium grains.
Panel (b) of Figure 2 shows the histograms of the Stokes V amplitudes at the pixels with grains (dotted lines) and without them (solid lines).Both in the Ca II and the Fe I lines, larger amplitudes are more likely identified with grains.Panel (c) of Figure 2 displays the histograms of the continuum intensity for the photosphere and the intensity at the outer wings for the chromospheric Ca II line.At the photosphere, the grains appear everywhere, both in granules and intergranules, but the brightest intensities at the wings of the Ca II line show more probability of harboring grains.This is likely connected to what we find in panel (d) of Figure 2, where we show the histogram of the line strength or depth, i.e., the intensity continuum (or outer wing for the calcium) minus the intensity at the core.The smaller depths of the Ca line are more likely to harbor grains.This is not a surprise, since bright areas in the core of such spectral lines are commonly associated with stronger magnetic fields (e.g., plages).
Panel (f) of Figure 2 shows the initial time in which a grain is detected in the Ca line.Interestingly, the patches are not uniform and show different initial times forming subpatches.Sometimes, grains appear earlier at the center of the patch and then spread outwards (see, e.g., the patches at [44, 50.6] arcsec, [17.5, 33.5] arcsec, and [36.8, 0.7] arcsec).In other cases, the subpatches with different initial times are not so nicely organized (e.g., in the patches at [36.5, 12.4] arcsec and [15.4, 31.8]).With the information we have, we cannot explain the observed patterns and we cannot discern if (1) they are due to the expansion of the magnetic fields and the fact that the waves that travel parallel to the magnetic field vector have a longer path to reach the chromosphere, or (2) that the magnetic field properties change with timescales smaller than the time that the waves need to reach the chromosphere, modifying the conditions for the wave to propagate.In Figure 1 we see that the two consecutive emissions in the blue wing of the Ca II line appear at different positions of the Fe I Stokes V patch, in this case, favoring the second scenario.
All in all, we find that the calcium grains we have analyzed can be the manifestation of the same phenomenon as the umbral flashes, i.e., magnetohydrodynamical waves traveling upward across the atmosphere.In this case, they travel along weaker and much shorter-lived magnetic fields compared to that of sunspots.This likely leads to the different observables we have presented.The so-called calcium grains appear as very short-lived (less than 2 minutes), while the ones seen in larger magnetic flux concentrations live for at least 4-5 minutes, and we can clearly see the emission-like feature "moving" in the wavelength.Better observations with a much longer time series and, likely, larger spectral resolution and better polarimetric sensitivity are needed to really constrain the physical origin of these grains.For the moment, further work with this data will be published, including NLTE inversions to understand how the stratification of the solar atmosphere evolves during calcium grain production.
2015b).This software performs the dark current subtraction, flat-field correction, demodulation, removal of residual crosstalk, removal of polarimetric fringes, and the correction of the filter transmission profile.We used a destretching module (kindly implemented by Dr. de la Cruz Rodríguez), instead of the standard reduction, which typically involves image restoration by means of Multi-Object MultiFrame Blind Deconvolution (Van Noort et al. 2005) because the polarization signals at quiet-Sun regions are very weak and image restoration techniques tend to increase the noise level.Additional procedures were applied to reduce the polarized spectral fringes using Fourier filtering.Stokes I, Q, U, and V are normalized to the average quiet-Sun continuum at the disk center, computed by fitting the Fourier Transform Spectrometer atlas (Wallace et al. 2011) to the average intensity profile.An exhaustive inspection of the data reveals that there are no reliable Stokes Q and U signals in the field of view (FOV).

Figure 1 .
Figure 1.Time evolution of a region centered at [6, 49] arcsec in the FOV.The background image in the top panel represents the intensity at Δλ = −0.21Å, where the emission-like feature of the grain appears.The values of the intensity range between 0.2 I c and 0.6 I c .The background in the second panel from the top displays the absolute value of the average Stokes V amplitude in three pixels centered at Δλ = −0.21Å.The background image in the third panel from the top is the absolute value of the amplitude of Stokes V of the full profile of the Ca II line.The background image in the bottom panel is the absolute value of the Stokes V amplitude of the Fe I line.The salmon contours in all panels contain Stokes V amplitudes of the Fe I line larger than or equal to 3 × 10 −3 I c .More details on its computation can be found in the text.The values of the Stokes V amplitudes of both the Ca II and the Fe I lines range from zero to 2 × 10 −3 I c .The yellow dots mark the positions of the profiles drawn in Figure 3.

Figure 2 .
Figure 2. Panel (a) represents the cumulative functions of the amplitude of Stokes V/I divided by the noise level (7 × 10 −4 ) for those pixels that harbor calcium grains.Dotted lines display the values of the original data, while solid lines are the result of averaging each individual patch.In all panels, blue lines correspond to the Fe I data, and orange ones to the Ca II data.Panels (b), (c), and (d) display the histograms for the Stokes V/I amplitude, continuum intensity (Fe I) or wing intensity (Ca II), and intensity line depth.Solid lines are the pixels with calcium grains while dotted lines are the rest of the pixels.Panel (e) displays the map of Stokes V/I amplitude at the photosphere.The contours encircle those pixels with calcium grains, as obtained with the k-means algorithm.The yellow circles in panel (e) mark the positions of the three examples shown in the work.The topmost circle marks the position of the example shown in Figure3, the middle one marks the example displayed in Figure4, and the bottom one marks the position of the example found in Figure5.Panel (f) displays the initial time at which the calcium grains appear.

Figure 3 .
Figure 3.Time evolution of the Stokes I (upper inset) and Stokes V (bottom inset) for the pixels marked with yellow dots in the top panel of Figure 1.

Figure 4 .
Figure 4. Time evolution of the Stokes I (upper inset) and Stokes V (bottom inset) for a pixel centered at the middle yellow circle in panel (e) of Figure 2.

Figure 5 .
Figure 5.Time evolution of the Stokes I (upper inset) and Stokes V (bottom inset) for a pixel centered at the bottom yellow circle in panel (e) of Figure 2.