Spatial and Temporal Analysis of Quiescent Coronal Rain over an Active Region

For the co-alignment between the AIA and SJI channels, we first resample the AIA data to the SJI plate scale. The co-aligning is then achieved by matching the solar limb and on-disk features seen in co-temporal images of AIA 1600 Å and SJI 2832 Å, which form under similar conditions. Once the x and y shifts are obtained at various time instances, an interpolation is performed for any other time sequence and applied to all other channels.

As discussed in Wülser et al. (2018), IRIS observations are influenced by a modest level of scattered light that is pointing dependent and often difficult to characterize, especially for off-limb observations. Due to this scattered light and imperfect flat-fielding, the rastering mode of IRIS results in a background contribution that shows apparent motion relative to the solar image and thereby causes a nontrivial, time-dependent noise in the SJI images that periodically increases the intensity in the image. This artificial periodic intensity is 17.2 minutes in both SJI 1400 and 2796 Å, and it is more pronounced in SJI 2796 Å closer to the limb but is clearer relative to the coronal rain intensity high above the limb in SJI 1400 Å. We partially corrected for this noise pattern by calculating the minimum intensity evolution over a raster for each pixel in both SJI channels. The SJI cube is then divided by the minimum intensity value at each pixel and time step.

The AIA 304 Å channel has a temperature response peak at ≈10⁵ K from He ii λ304 emission. However, the bandpass also incorporates a secondary peak at ≈10^6.2 K due to Si xi λ303.32. When observing coronal rain off limb, the intensity of both components can be similar because the Si xi component coming from the surrounding diffuse hot corona is greater in extent along the line of sight than the He ii component coming from the small, clumpy coronal rain (Antolin & Rouppe van der Voort 2012; Froment et al. 2020). Besides temperature, both plasma emissions also differ strongly in their morphology. While the cool emission is clumpy, the hot emission is diffuse. We therefore use a morphology-based approach called blind source separation to separate both components, as outlined in Dudok de Wit et al. (2013). We have tested the combination of several AIA channels as source components with different numbers of morphological components, and we find that the combination of four source AIA channels (335, 304, 211, and 193 Å) with three main morphological components is enough to isolate the clumpy coronal rain structure from a given 304 Å image.

To apply our semiautomatic coronal rain detection routine, we first remove the region around the solar limb to avoid its large brightness contrast. We also remove the spicular region above the limb, defining a minimum height (6 Mm) for the off-limb FOV in order to avoid most of the spicules and other low-lying, cool chromospheric features, which are typically seen at heights of 4–10 Mm above the solar surface (Beckers 1968). Then, we apply an automatic detection routine called the rolling Hough transform (RHT; Schad 2017) based on the Hough transform (Hough 1962; a technique for detecting lines, circles, and curvilinear structures) in order to detect and quantify the apparent motion of the raining material. Along the temporal axis, a running mean filter is applied to ensure that the rain clumps trace out some path for each individual time step. This local path is then used to determine a flow direction in the plane of the sky (POS). For the SJI 1400 Å, SJI 2796 Å, and AIA 304 Å channels, we used 10-step (≈7.18 minutes), 13-step (≈6.99 minutes), and 17-step (≈3.4 minutes) running mean filters, respectively. Such values are chosen according to the observed speeds in coronal rain and thus the time it takes to see a significant change locally in the image. Subsequently, the code applies a bidirectional difference filter along the temporal axis to assist in flow segmentation. For the IRIS channels, we use a five-step filter (≈3.6 minutes in SJI 1400 Å and ≈2.7 minutes in SJI 2796 Å) and a 21-step filter (≈4.2 minutes) for AIA 304 Å to account for the faster cadence. After that, we use 29 pixels for the circular RHT kernel width (D_w ) for all channels (i.e., the circular region with a diameter D_w centered on each image pixel to be evaluated at one time). Choosing a wider kernel size leads to less detection of small rain clumps but reduces the background noise. Therefore, we choose this value according to the observed minimum length of the rain. Finally, the standard deviation accounting for the background noise σ_noise is 2, 2.1, and 0.008 for SJI 2796 Å, SJI 1400 Å, and AIA 304 Å, respectively (the different noise values in 304 Å are due to the "cool 304" preprocessing of images explained above).

Using all these input parameters, the RHT routine produces four main outputs (each output has 3D dimensions with position x, y and time t) providing spatial and temporal information for each. These are the mean axial direction, peak of the RHT function, resultant length, and error in the mean axial direction. The mean axial direction (θ_xy for the spatial part and θ_t for the temporal part) shows the spatial and temporal directions of each detected pixel. To accurately define these mean directions, the RHT function (H_xy (θ) in the spatial part and H_t (θ) in the temporal part) is used to accumulate pixels to define a mean direction. For this purpose, an adaptive threshold is defined according to the peak of the RHT function ($\max [{H}_{{xy}}(\theta )]$ and $\max [{H}_{t}(\theta )]$), which is the second output of the RHT routine. Any values below this threshold do not contribute to the mean direction. The resultant length $(\bar{R})$ is a measure of dispersion between 0 and 1. Values close to 0 or 1 indicate an ill-defined or well-defined mean axial direction, respectively. The last output is the error (_xy and _t ) in the mean axial direction. A detailed explanation of all these parameters can be found in Schad (2017). In total, we detected 4.33 × 10⁶, 2.11 × 10⁶, and 3.25 × 10⁶ rain pixels in SJI 2796 Å, SJI 1400 Å, and AIA 304 Å, respectively. These numbers are smaller than those detected in the same AR in Şahin & Antolin (2022) (6.5 × 10⁷, 4.9 × 10⁶, and 6.33 × 10⁶ in AIA 304 Å, SJI 1400 Å, and SJI 2796 Å, respectively). This is because of the stricter conditions we have used in the RHT routine since we are interested in higher accuracy when calculating trajectories and projected speeds in our analysis. Accordingly, we have also required the following set of conditions. We only include the pixels for which ${\overline{R}}_{{xy}}\geqslant 0.8$, $\max [{H}_{{xy}}(\theta )]\geqslant 0.75$, ${\overline{R}}_{t}\geqslant 0.8$, $\max [{H}_{t}(\theta )]\geqslant 0.75$ for all channels, as well as ${\overline{| \theta }}_{t}| \leqslant 84^\circ$ for AIA 304 Å and ${\overline{| \theta }}_{t}| \leqslant 88^\circ$ for both SJI channels, since these values ensure relatively small errors for projected velocities. The remaining rain pixels for our analysis are 6.71 × 10⁵, 1.90 × 10⁵, and 2.83 × 10⁵ in SJI 2796 Å, SJI 1400 Å, and AIA 304 Å, respectively.

For the long-period pulsation analysis, we study 3-day data at a cadence of 5 minutes (between 2017 June 1 05:00 UT and 2017 June 4 05:15 UT) with AIA using a different version of the automatic detection algorithm used in Auchère et al. (2014) and Froment et al. (2015), modified for off-limb observations (Froment et al. 2020). In this routine, the power spectral density is calculated for each time series associated with each pixel of the FOV, without specifically searching for pulsations in a particular region or structure. A 4 × 4 pixel binning is applied to increase the signal-to-noise ratio. Please see the abovementioned papers for additional information regarding the detection algorithm.

The average spatial (${\overline{\theta }}_{{xy}}$) and temporal (${\overline{\theta }}_{t}$) mean angle maps over an entire time sequence from the RHT analysis are shown in Figure 2. The spatial mean angle ${\overline{\theta }}_{{xy}}$ is related to the inclination of the rain in the POS, while the temporal mean angle ${\overline{\theta }}_{t}$ shows the dynamical change along the trajectory. All the colored pixels in these maps correspond to coronal rain pixels. As seen, coronal rain occupies a wide POS area over the AR. It is worth noting that much more rain is seen to occupy the FOV (about a factor of 10 more rain pixels exist). However, as explained in the previous section, we choose to set strict conditions for the detection of coronal rain in order to more accurately capture the dynamics and trajectories.

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The observed rain trajectories match well the expected large-scale magnetic field topology of the AR, given the sunspot at the center of the FOV. It is worth noting that this is a first-of-its-kind high-resolution coronal field line tracing on a large scale with coronal rain. In the temporal mean angle maps (bottom maps in Figure 2), the green and red colors (negative values) represent downward motion, which, as expected from the action of gravity on coronal rain, is much more dominant. The total pixel numbers of downflow motions are 6 × 10⁵, 1.6 × 10⁵, and 1.9 × 10⁵ for SJI 2796 Å, SJI 1400 Å, and AIA 304 Å, respectively, which represent 90.05%, 83.44%, and 89.11% of the total detected rain pixels. Upward motions are also ubiquitous (6.7 × 10⁴ (9.95%), 3.1 × 10⁴ (16.56%), and 3.1 × 10⁴ (10.89%) for SJI 2796 Å, SJI 1400 Å, and AIA 304 Å, respectively), particularly near the sunspot, as seen in the bottom panel (blue). This is expected because gas pressure can also play an important role in coronal loops (Antolin et al. 2010), a result supported by recent 2.5D numerical simulations (Li et al. 2022).

In Figure 3, we investigate the difference in coronal rain occurrence across the channels. On the top and bottom panels, we show, respectively, maps of "percentage difference" in coronal rain occurrence and scatter plots of the spatial mean angle, together with the Pearson correlation coefficient. Here we use the absolute spatial mean angle values and an equal number of time steps across channels to obtain maps of the difference in coronal rain occurrence. Since SJI 1400 Å has the lowest cadence, we select it as a reference channel and find the closest time to it on SJI 2796 Å and AIA 304 Å. For each pair of cubes among this set of three, we first calculate the total number of rain pixels (defined as nonzero spatial mean angle values) over time in each x and y position and gather them in a new cube. Then, we find the locations common to both new cubes (one for each channel) where we have nonzero values. Finally, we take the difference between them and divide it by the total number of images to obtain a percentage difference in coronal rain occurrence. As shown by the scatter plots, coronal rain emission in all channels is highly correlated (R = 0.84 between SJI 1400 Å and 2796 Å, 0.79 for AIA 304 Å and SJI 1400 Å, and 0.85 for AIA 304 Å and SJI 2796 Å). This indicates that at a global level coronal rain is multithermal, with chromospheric emission colocated on average with transition region emission. However, the normalized difference maps in the top panels reveal strong localized differences in all channels. From the top right and left panels, we see more rain in 2796 Å than in 1400 and 304 Å toward the footpoints. There is also more rain emission in SJI 1400 Å than in AIA 304 Å (top middle panel). These differences may also be due to intensity (opacity of the line) and contrast with the background, additional noise (low instrumental sensitivity, especially for AIA 304 Å), and the spatial resolution of the instrument.

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To investigate the differences in trajectories across the temperature range, we show in Figure 4 the average (top) and extremum (bottom) difference maps of absolute spatial mean angle values. Similar to Figure 3, we used an equal number of images for the channels. Here we first find the locations common to both channels where we have nonzero values, and then we take the difference between them. Then, for a given time t we take a time length around t equal to the mean running filter (chosen for the RHT routine) so that significant change is seen locally. We calculate the average and extremum (maximum in absolute values, retaining the sign of the difference) of the differences over this time range (over nonzero instances) between the two channel pairs and store the average and extremum in two new cubes. We repeat this process for all spatial pixels, and then we calculate the average and extremum over time for these two cubes in the top and bottom panels of Figure 4, respectively, over all nonzero time instances. The differences across channels are below 10° on average, while the extrema hover around 10°, with isolated cases of up to 20° (the figure is saturated at 11° to best observe the trends). The ∣1400∣ − ∣2796∣ panels reveal that differences occur on average in regions characterized by inclined structures or at the apexes of loops. We also observe increased variations close to the sunspot or solar surface. On the other hand, the other panels (∣304∣ − ∣1400∣ and ∣304∣ − ∣2796∣) show a more spatially uniform distribution of the differences. It is likely that the reduced accuracy of the RHT method in the near loop apexes, attributable to the slower speeds of clumps in these regions, contributes to the observed differences in these locations. However, for structures characterized by higher speeds, such as those near the sunspot and inclined structures, the observed differences are more likely to be genuine. We can think of two possibilities. They may be the result of the superposition of loops along the LOS, particularly for SJI 1400 Å, which is usually optically thin. Similarly, the narrow width of the rain may reduce the optical thickness of SJI 2796 Å. Another possibility is multithermal plasma moving differently in the same pixel elements, which would lead to shear motions.

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In this section, we show the dynamical results obtained through the RHT analysis. In Figure 5 (top panels), we show projected velocity maps resulting from the individual measurements of the rain clumps. The velocity along each curvilinear path obtained from the RHT temporal mean angle $({\overline{\theta }}_{t})$ is (Schad 2017)

$\begin{eqnarray}&&{v}_{| | }=\tan {\overline{\theta }}_{t}\left(\displaystyle \frac{\delta x}{\delta t}\right).\end{eqnarray} \tag{ 1 }$

Here δ x is the spatial sampling on the date, which is 244.72 km for the SJI channels and 244.75 km for the AIA channel, and δ t is the average cadence, which is 43.1, 32.3, and 12 s for SJI 1400 Å, SJI 2796 Å, and AIA 304 Å, respectively.

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The projected velocity is also related to the spatial mean angle ${\overline{\theta }}_{{xy}}$ through the horizontal (Equation (2)) and vertical velocities (Equation (3)):

$\begin{eqnarray}&&{v}_{x}={v}_{| | }\cos {\overline{\theta }}_{{xy}}\end{eqnarray} \tag{ 2 }$

$\begin{eqnarray}&&{v}_{y}={v}_{| | }\sin {\overline{\theta }}_{{xy}}.\end{eqnarray} \tag{ 3 }$

The projected velocity can also be decomposed in terms of the tangential (Equation (4)) and radial (Equation (5)) velocity components:

$\begin{eqnarray}&&{v}_{\tan }={v}_{x}(-\cos (\alpha ))+{v}_{y}(-\sin (\alpha ))\end{eqnarray} \tag{ 4 }$

$\begin{eqnarray}&&{v}_{\mathrm{rad}}={v}_{x}(-\sin (\alpha ))+{v}_{y}\cos (\alpha ),\end{eqnarray} \tag{ 5 }$

where α denotes the angle between the radial and horizontal directions in radians. The projected velocity is then

$\begin{eqnarray}&&{v}_{p}=| {v}_{| | }| =\sqrt{{v}_{\tan }^{2}+{v}_{\mathrm{rad}}^{2}}.\end{eqnarray} \tag{ 6 }$

The average projected velocity of SJI 2796 Å, SJI 1400 Å, and AIA 304 Å is shown in Figure 5 with respect to rain direction (downflows and upflows). As seen in these maps (first two rows from the top), most of the coronal rain clumps accelerate during the fall. Correspondingly, higher velocities can be clearly seen in the center of the AR (near the sunspot) in all three channels for downflow motions. Interestingly, this is also the case for the upflows, which suggest an increasingly larger role of gas pressure at lower heights (see Section 5). In the last two bottom panels in Figure 5, we show the differences between projected velocities across the channels by following the same method as for Figure 4. We note a salt-and-pepper distribution of highly localized red and blue values, which may again correspond to times for which a rain pixel is detected in one channel but not the other channel. However, some interesting large-scale differences emerge. For instance, in the ∣1400∣ − ∣2796∣ panel, more blue pixels are seen near the sunspot, suggesting higher velocities (≈20 km s⁻¹ higher) in 1400 Å than in 2796 Å. The ∣304∣ − ∣2796∣ panel shows larger patches of the loops that are consistent with one color, and higher speeds seem to be found in 304 Å near the sunspot, consistent with the previous result. The ∣304∣ − ∣1400∣ panel shows more red than blue, suggesting higher 1400 speeds. This result suggests the presence of multithermal shear flows and/or density-dependent (and temperature-dependent) speeds. However, the drag effect, which is dependent on density, predicts the opposite result, with higher speeds for denser (and therefore cooler) rain.

The number of snapshots in the data sets (SJI 2796 Å, SJI 1400 Å, and AIA 304 Å) is different between the channels. In addition, we have different exposure times, which change the characteristics of the rain (particularly the length of rain clumps). Therefore, we calculated the rain area per second in each channel using the number of snapshots, pixel size, and exposure times (units are ${\mathrm{arcsec}}^{2}\,{{\rm{s}}}^{-1}$) as

$\begin{eqnarray}&&\mathrm{Rain}\ \mathrm{area}\ \mathrm{per}\ \mathrm{second}=({N}_{\mathrm{pixels}}/{n}_{t})\times ({dxdy}/{D}_{t}),\end{eqnarray} \tag{ 7 }$

where N_pixels is the total number of pixels in a given channel, n_t is the number of snapshots, dxdy is the pixel size, and D_t is the exposure time.

The histogram of projected velocities in the left panels of Figure 6 shows a broad distribution of downflow and upflow projected velocities, with peaks below 50 km s⁻¹ and long tails to high-velocity downflows (up to 200 km s⁻¹). The overall shape of the distributions is very similar across the channels, and consequently, the median velocities are very similar as well, with 43.59 ± 36.36 km s⁻¹, 37.88 ± 28.42 km s⁻¹, and 41.06 ± 34.05 km s⁻¹ in SJI 1400 Å, SJI 2796 Å, and AIA 304 Å, respectively, for the downflow projected velocity. On the other hand, these are 49.17 ± 45.88 km s⁻¹, 45.36 ± 47.07 km s⁻¹, and 62.27 ± 51.54 km s⁻¹ for the upflow projected velocity in SJI 1400 Å, SJI 2796 Å, and AIA 304 Å, respectively. The variation of the median projected velocities for both downflow and upflow motions with projected height is shown in the right panels of Figure 6 for SJI 1400 Å (red), SJI 2796 Å (blue), and AIA 304 Å (green), where zero height corresponds to the solar limb, also shown in Figure 5 with dashed lines. The median projected velocities for the downflow motions are quite similar at all heights, particularly between SJI 2796 Å (blue) and AIA 304 Å (green); SJI 1400 Å has slightly larger velocity values at higher heights (≥18 Mm). This is in agreement with the results from Figure 5. This plot also indicates that the rain experiences small acceleration at higher heights (close to loop apexes) and then continues downward with an almost constant velocity, which is expected from gas pressure forces (Oliver et al. 2014). Relative to the downward motion, the upflow projected velocities show much more variation with height, suggestive of strong gas pressure changes associated with the rain's fall. The high speeds found in the histogram of Figure 6 therefore correspond to highly localized measurements that can be due to apparent effects or errors in the RHT routine and not to large-scale bulk flows due to gravity.

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In order to study the time evolution of the coronal rain dynamics, we plot in Figure 7 the time–distance diagrams of the spatial mean angles seen in SJI 1400 Å (top), SJI 2796 Å (middle), and AIA 304 Å (bottom). Here we overlay all time–distance maps for each radial axis and present the positive (right panels) and negative (left panels) spatial mean angle inclinations separately. Coronal rain (clumps and showers) is continuously observed during the entire time duration of the observations and across the full radial extent of the IRIS data. Although there are many overlapping rain trajectories over time, Figure 7 reveals that the spatial mean angle changes with height and in time (for individual trajectories), suggesting a change in the rain's projected velocity as it falls. This change suggests an acceleration, but it is likely an apparent acceleration caused by the small angle between the LOS and the plane of the loop (which leads to slow speeds for rain near the loop apex). On the other hand, Figure 6 shows a linear increase in velocity with decreasing height, indicating a small constant acceleration. This result can be explained by gas pressure restructuring produced by the condensation formation (Oliver et al. 2014; Martínez-Gómez et al. 2020). The change in the slope could actually correspond not to acceleration but to a change in the angle between the LOS and the vector tangent to the flow. If the LOS makes a small angle with the loop plane, the angle between the LOS and the vector tangent to the flow would be close to zero at the apex of the loop, which makes the projected velocity very small, while toward the loop leg, the angle would increase toward 90°, which makes the projected velocity close to the total velocity.

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In Figure 8, we show the 2D probability distribution function (pdf) of the tangential, radial, and downflow projected velocities relative to the height of the rain material. As seen in Figure 2, rain clumps appear on both sides of the AR in a roughly equal manner, and this is seen as a bimodal distribution in the tangential velocity maps (top panels). In the middle and bottom panels, we can see that the downward velocities are consistently lower than the freefall velocity limit (taking an average starting position from the rest of 45 Mm), in agreement with previous results (Schrijver 2001; De Groof et al. 2004; Antolin et al. 2010).

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We now turn to the statistical determination of the size of individual rain clumps. The width of the clumps is calculated in the following way. Given a clump pixel at a particular time and location, we first obtain the spatial mean angle information. We then draw a perpendicular line to the trajectory of the clump at that pixel and fit a Gaussian to the intensity profile interpolated over the perpendicular line (see the orange line in Figure 9). From the fit, we obtain the FWHM, which we take as the width for the rain clump at that pixel.

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We also set a condition on the intensity of the profile to avoid background noise, and we set an intensity threshold below which we neglect the intensity profiles. The thresholds for each channel are calculated by selecting a small region without any visible structure and calculating the average intensity over the entire observational sequence. As we mentioned in Section 3, the noise level across the image and during one raster is nonuniform because of the scattered light and imperfect flat-fielding. Although this nonuniformity is corrected to some degree in our data calibration (see Section 3), it is not entirely removed. We therefore take into account a spatially and temporally nonuniform secondary noise threshold that is used for the calculation of the length. Given a rain pixel detected by the RHT, the width calculation procedure explained above includes a Gaussian fitting whose FWHM sets the width. As seen in Figure 9, this procedure also sets an intensity threshold, the intensity at half maximum (filled circles corresponding to the positions of the dotted lines in panel (d)), which we use as the nonuniform intensity threshold for the length calculation (intensity values corresponding to the positions of the dotted lines in panel (e)).

To calculate the clump length, given a pixel location, we first take the center point of the Gaussian fit used to calculate the clump's width at that location. Using the spatial mean angle at this center point, we draw a path along the same trajectory and determine the locations along this path at which the intensity of the clump falls below the nonuniform noise threshold explained above. These naturally lead to two points above and below the center point, which define the extrema for the length calculation. The average of all the length calculations for all pixels of a given clump would provide an accurate measurement of the clump's length. An example of this method is shown in Figure 9.

The histogram plots in Figures 10(a) and (b) show the width and length distributions of all the pixels of the traced coronal rain clumps in all three channels. The distributions are similar in shape across all channels and are slightly asymmetric with a small tail at higher values. The average widths are found to be 0.84 ± 0.24 Mm for SJI 2796 Å, 0.74 ± 0.22 Mm for SJI 1400 Å, and 1.26 ± 0.35 Mm for AIA 304 Å. The lengths, on the other hand, are found to be 5.35 ± 3.99 Mm, 4.78 ± 3.52 Mm, and 6.91 ± 4.96 Mm for the same channel ordering. The widths between SJI 1400 Å and SJI 2796 Å are therefore similar, but the widths found in AIA 304 Å are significantly larger. This may be explained by the lower spatial resolution in AIA 304 Å and the fact that the rain widths are only a few times higher than the instrument's resolution (≈0.87 Mm for the AIA channels and ≈0.48 Mm for the SJI channels). A similar result but to a lower degree is seen for the lengths, which are an order of magnitude larger than the widths. Panels (c) and (d) show the width and length variations with height above the solar surface (z = 0). The widths are fairly constant as the rain falls; however, the lengths vary significantly, becoming shorter as the rain falls (passing from ≈15 to 6 Mm). The reason for the shortening length of the clumps is probably due to the fact that they cross below the limb, and we are therefore unable to track them further. Another reason may be that the rain also elongates (i.e., becomes less clumpy), which is supported by the increasing trend in Figure 10(d) between 20 and 40 Mm, in which case the temporal segmentation approach is less accurate.

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We now check for the existence of long- and short-period intensity pulsations using the 3-day data at a cadence of 5 minutes (between 2017 June 1 05:00 UT and 2017 June 4 05:15 UT). In Figure 11, we show the contours of some of the detected pulsation regions in AIA 171 Å (cyan) and AIA 193 Å (dark blue) over an AIA 171 image of the AR with the overlaid 2796 Å spatial mean angle map from coronal rain given in Figure 2. These contours correspond to regions with more than 10σ of normalized power. The pulsations are mostly found at the top or apex of the coronal loop structures, probably due to the reduced superposition of bright coronal structures at higher heights.

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To further check the existence of periodicity, we repeated the Fourier power calculation for manually selected smaller areas inside these regions and found periods between 3 and 9 hr. In Figure 12 we show one example of such analysis, with the pink square in the AIA 171 Å map of the selected subregion that we focused on for the detailed analysis. The AIA 171 Å light curve in the top right panel shows the time evolution over the 2.4-day period of the intensity variation summed over the pink square. The bottom panels show the corresponding Fourier spectra (right) and the map of normalized power (left) for the AIA 171 Å passband in logarithmic scale at the frequency of the highest power peak 75.97 μHz (3.65 hr) with the same FOV as in the top left panel. The solid red curve in the Fourier spectrum is the estimate of the average local power (and therefore a representative of the noise level), and the blue curve is the 10σ detection threshold. In the 131 Å and 193 Å channels, we find power peaks at the frequency of 76.8 μHz, with a normalized power of 11.33σ and 8.77σ, respectively. For the remaining channels (94, 211, and 335 Å), there is no significant power. The power in 171 Å is the highest, with 14.30σ. Even though it has not been shown in this study, we have also checked this periodicity with a wavelet analysis that shows a 95% confidence level for a significant power distribution (13.94σ) for a time range between 18:55:09 and 3:15:09.

In Figure 7, there seem to be quasi-periodic downflows in the time–distance series over the entire FOV. To investigate this possibility and, more generally, the existence of short periodicity, we focus on the data sets and time range where rain is visible in both AIA and IRIS channels (i.e., 5.45 hr data in SJI 2796 Å, SJI 1400 Å, and AIA 304 Å). We look for the existence of periodicities by first fixing a height above the limb and summing the intensities at that height both over the entire FOV and also locally by constraining the range in the Y-axis. We construct light curves at every 8 Mm height starting from the solar limb and summing over a height thickness of 8 Mm. We then check for strong power peaks in the corresponding Fourier spectrum. In Figure 13, we show a region at 15–23 Mm heights (red square) in SJI 2796 Å, SJI 1400 Å, AIA 304 Å, AIA 171 Å, and AIA 131 Å images (left columns), where a significant Fourier power is found (right columns). AIA 171 Å has a peak of 11.04σ, which corresponds to the frequency of 2749.71 μHz (6.06 minutes). In AIA 131 Å, two peaks of 12.36σ and 13.84σ powers were found at the frequency of 1934.98 μHz (8.61 minutes) and 2902.48 μHz (5.74 minutes). There is further no peak at exactly those frequencies in AIA 304 Å. A peak of 10.78σ power was found at the frequency of detection of 1018.41 μHz (16.36 minutes) in the AIA 304 Å channel. In SJI 2796 Å and SJI 1400 Å, the power and confidence level at the same frequency are significantly lower (4.12σ and 6.26σ, respectively). As mentioned previously, due to the IRIS rastering mode, the apparent motion caused by the light scattering and imperfect flat-fielding introduces a nonuniform background noise. This effect periodically increases the intensity nonuniformly over the AR (with the center part being more affected). The periodicity of this apparent motion is 17.2 minutes for both SJI 1400 Å and SJI 2796 Å. Although the Fourier periodicity found is not exactly this one, it is possible that part of the power found in nearby frequencies is due to this apparent motion. To clear up this possibility, in Figure 14 we show the time–distance map over the blue path shown in Figure 13, which was done with the help of the CRisp SPectral EXplorer (CRISPEX) tool (Vissers & Rouppe van der Voort 2012). To reduce the influence of the apparent motion effect, we first identify in the time–distance map the IRIS raster in each channel (1400 and 2796 Å) with no (or minimal) coronal rain (indicated by the red rectangles in Figure 14). We then subtract the intensity in these rectangle areas from all the other IRIS rasters in the time–distance maps (see the second and fourth panels) in order to distinguish more clearly the coronal rain. The same short-timescale rain showers can be clearly seen in SJI 1400 Å and SJI 2796 Å. These repetitive downflows are also seen in the time distance map of AIA 304 Å, AIA 171 Å, and AIA 131 Å.

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