On the 5-Minute Oscillations of Photospheric and Chromospheric Swirls

Swirls are widely observed in different layers of the solar atmosphere (e.g., Wang et al., 1995; Bonet et al., 2008; Attie et al., 2009; Balmaceda et al., 2010; Wedemeyer-Böhm & Rouppe van der Voort, 2009; Bonet et al., 2010; Wedemeyer-Böhm et al., 2012; Su et al., 2014; Kato & Wedemeyer, 2017; Liu et al., 2019b, c; Shetye et al., 2019). Besides their ubiquity, they have been suggested to be related to a number of different magnetohydrodynamic (MHD) processes from the photosphere through to the corona, including MHD waves and pulses (e.g., Carlsson et al., 2009; Fedun et al., 2011; Shelyag et al., 2013; Shukla, 2013; Mumford & Erdélyi, 2015; Leonard et al., 2018; Murawski et al., 2018; Kohutova et al., 2020; Battaglia et al., 2021), spicules or jets (e.g., Kitiashvili et al., 2012, 2013; Liu et al., 2019c; Oxley et al., 2020; Scalisi et al., 2021b, a; Bate et al., 2022; Dey et al., 2022), and (magnetic) bright points or magnetic concentrations (e.g., Balmaceda et al., 2010; Jess et al., 2010; Liu et al., 2019a; Shetye et al., 2019; Murabito et al., 2020). Further observations and numerical simulations suggest that swirls might be able to channel enough energy from the lower to the upper solar atmosphere (e.g., Wedemeyer-Böhm & Rouppe van der Voort, 2009; Liu et al., 2019c; Yadav et al., 2021; Battaglia et al., 2021).

Detailed studies of individual swirls, or a small collection of swirls, have shown intriguing and important properties. For example, Wedemeyer-Böhm & Rouppe van der Voort (2009) analysed 10 clear small-scale swirling candidates observed in the chromosphere by the Swedish 1-m Solar Telescope (SST; Scharmer et al., 2003) and found that these swirls could be related to the so-called magnetic tornadoes channelling energy into the solar corona. A series of investigations were conducted to establish the properties, including its associated waves and oscillations, of a persistent quiet-Sun swirl that had a lifetime exceeding 1.7 hours (Tziotziou et al., 2018, 2019, 2020). However, owing to their ubiquity ($>10^{5}$ swirls in the photosphere at any time, e.g., Liu et al., 2019b) and small scale (with an average radius of several hundred kilometres), statistical studies of manually selected swirls have proven difficult and may introduce unwanted human bias. Several automated detection methods have recently been developed. Kato & Wedemeyer (2017) presented two detection algorithms both based on a line integral convolution (LIC) imaging technique with one using enhanced vorticity and the other the vorticity strength to identify swirls. Their methods have been tested on a simulated chromosphere generated by the CO⁵BOLD (Freytag et al., 2012) numerical MHD code. Another method, recently proposed by Dakanalis et al. (2021), employs a series of processes including image pre-processing, tracing of curved structures, segmentation and clustering, with the last two processes being widely used in machine learning techniques. This method was tested with both synthetic data and observations obtained by the SST and was further suggested to be applicable for quasi-linear fibrillar structure detections following some modifications.

Employing the velocity field information estimated from successive images by Fourier local correlation tracking (FLCT; Welsch et al., 2004; Fisher & Welsch, 2008), Liu et al. (2019b) developed an automated swirl detection algorithm (ASDA¹¹1https://github.com/PyDL/ASDA). ASDA was applied to both photospheric and chromospheric observations (Liu et al., 2019b, c) acquired by the Solar Optical Telescope (SOT; Tsuneta et al., 2008) on board Hinode (Kosugi et al., 2007), and the CRisp Imaging SpectroPolarimeter (CRISP; Scharmer, 2006) on the SST (Scharmer et al., 2003). A total number of more than $10^{5}$ swirls were found in the photosphere at any moment of time, with an average radius of $\sim 300$ km, rotating speed of $\sim 1$ km s^-1, and a lifetime of around 20 s. Correlation analysis between photospheric and chromospheric swirls, together with three-dimensional MHD numerical simulations, suggested that ubiquitous Alfvén pulses could be excited by photospheric swirls and travel to the chromosphere (Liu et al., 2019c). The co-existence of intensity swirls and magnetic swirls (Liu et al., 2019a) in the simulated photosphere generated by the Bifrost code (Gudiksen et al., 2011; Carlsson et al., 2016) suggested that the necessary condition for the generation of Alfvén pulses in the solar atmosphere might be fulfilled. This scenario was confirmed by the MHD numerical simulation using the radiative MHD code CO⁵BOLD (Battaglia et al., 2021). Recent advances in analytical and numerical simulations (Oxley et al., 2020; Scalisi et al., 2021b, a; Singh et al., 2022) suggest that these Alfvén pulses could further drive upward mass motions, e.g., spicules, that propagate in the upper solar atmosphere.

Besides these recent advances in observations, numerical simulations and theories of solar atmospheric swirls, we are not aware of many works that study the collective behaviours of swirls and their relationship with global phenomena of the Sun, such as the 5-minute global acoustic oscillations and the solar activity cycle. In this paper, we present evidence of the 5-minute oscillation of photospheric and chromospheric swirls. This paper is organised as follows: data and methods will be briefly introduced in Sect. 2, before we present results in Sect. 3 and draw the conclusions in Sect. 4.

Five sets of data are utilised in this study. The first three sets of data consist of wide-band photospheric images at Fe i 630.25 nm, chromospheric images at the H$\alpha$ line core with a central wavelength of 656.3 nm, and chromospheric images at the Ca ii line core with a central wavelength of 854.2 nm by SST/CRISP (Scharmer et al., 2003; Scharmer, 2006; Scharmer et al., 2008) between 08:07:22 UT and 09:05:44 UT on 21^st June 2012. The target was a quite-Sun region close to the disk centre ($x_{c}=-3$^′′, $y_{c}=70$^′′) with a FOV of 55^′′$\times$55^′′. The spatial and temporal resolutions are 0.1^′′and 8.25 s, respectively. The black-white background in Figure 1a) depicts an example of the SST chromospheric images at the H$\alpha$ line core.

The other two sets of data consist of blue-continuum (FG-Blue) photospheric images with a central wavelength of 450.45 nm, and photospheric/chromospheric images at the Ca ii H line with a central wavelength of 396.85 nm taken by Hinode/SOT (Kosugi et al., 2007; Tsuneta et al., 2008) between 05:48:03 UT and 08:29:59 UT on the 5^th March 2007. Each of them contains 1515 images of a quiet-Sun region close to the disk centre ($x_{c}$=5.3^′′, $y_{c}$=4.1^′′) with a field-of-view (FOV) of $\sim 56$^′′$\times 28$^′′. The spatial and temporal resolutions are 0.1^′′and 6.42 s, respectively. Figure 1c) depicts an example of the SOT FG-blue photospheric images. We note that the broadband Ca ii H observations by Hinode/SOT cover a wide range of altitudes from the photosphere to the chromosphere (Rutten et al., 2004; Carlsson et al., 2007).

The automated swirl detection algorithm ASDA (Liu et al., 2019b) was applied to every two successive images in each data set. ASDA contains two essential steps to perform the detection of swirls: 1) velocity field estimation using FLCT (Welsch et al., 2004; Fisher & Welsch, 2008) and 2) vortex identification using two parameters ($\Gamma_{1}$ and $\Gamma_{2}$) proposed by Graftieaux et al. (2001). For each point in the velocity field, 49 points around it are used to calculate $\Gamma_{1}$ and $\Gamma_{2}$ for identifying the centres and edges of swirls, respectively. A detailed description of ASDA and how the parameters including location, radius, rotating speed, expanding/shrinking speed and lifetime of swirls are extracted from the $\Gamma_{1}$ and $\Gamma_{2}$ values could be found in Liu et al. (2019b). In summary, $\Gamma_{2}$ is used to identify swirl candidates and regions they cover, while $\Gamma_{1}$ is used to quantify swirl strength. Red and blue curves in Figure 1a) and c) are swirls detected by ASDA from the example SST H$\alpha$ chromospheric observation and SOT FG-blue photospheric observation, with clockwise rotations (red) and anti-clockwise rotations (blue), respectively. Figure 1b) and d) are the distributions of the $\Gamma_{2}$ values calculated from the example observations. Figure 2 depicts examples of individual swirls detected using ASDA from both SST and Hinode/SOT observations, with rows 2-6 displaying zoom-in views of the orange dashed boxes in the first row. Black and white backgrounds are the intensity observations and green streamlines are velocity fields estimated using FLCT. Red and blue contours are the edges of the example swirls with clockwise and counter-clockwise rotations, respectively. Panels in the second row are images and velocity fields $\sim$5 minutes before the example swirls, with curved streamlines at similar locations to where the swirls will form indicating their prerequisites. The third to the sixth rows are the first, middle and last frames of the example swirls, respectively. Consistent with the statistical findings in Liu et al. (2019b) and Liu et al. (2019a), these swirls are located at intergranular lanes (dark features in the first, third, fourth and fifth columns). The last row shows the photospheric and chromospheric conditions $\sim$5 minutes after the example swirls.

To explore the relationship between photospheric and chromospheric swirls, bypassing a number of difficulties such as selection effects, the inclined magnetic field from the photosphere to the chromosphere, and the irregular shape of swirls, Liu et al. (2019c) proposed a new method to calculate the correlation coefficient between photospheric and chromospheric swirls. In this work, to quantify the collective behaviour of swirls in the same data set (i.e., the same layer in the solar atmosphere), we have adapted the above method, as follows:

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  For the $\Gamma_{2}$ maps of all images in a given layer, set all points to be 0 except those greater (less) than $2/\pi$ ($-2/\pi$), which are set to be 1 (-1).
  

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  Take the first $\Gamma_{2}$ map from the above as the reference and mark it as $\Gamma_{t1}$. Define $T_{1}$ as the sum of the absolute values of all points in $\Gamma_{t1}$.

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  Take the second $\Gamma_{2}$ map and mark it as $\Gamma_{t2}$. Define $T_{2}$ as the sum of the absolute values of all points in $\Gamma_{t2}$.

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  Multiply $\Gamma_{t1}$ and $\Gamma_{t2}$ point-by-point to obtain the correlation map $C$. Their correlation coefficient $CC$ is then define as $(\sum{C})/T$, where $T=max(T_{1},T_{2})$.
  

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  Repeat the above processes for the rest frames to obtain their correlation coefficients with the first frame of the data set.

We can see from the definition of CC that it evaluates the similarity of swirl distribution between two frames. The above process is shown in Figure 3.

In this paper, we conducted a statistical study of oscillations related to photospheric and chromospheric swirls detected from five SST and SOT data sets using the automated swirl detection algorithm (ASDA). Periods with significant wavelet powers above their corresponding 95% confidence levels were found from the time series of the correlation coefficient ($CC$), the number of swirls per frame ($N$), average intensity ($\overline{I}$), average radius ($\overline{R}$), average rotating speed ($\overline{v_{r}}$) and average expanding/shrinking speed ($\overline{v_{e}}$) of swirls detected in all five data sets. These periods range from 1 min to 17 min, with an average value of 6.9$\pm$4.4 min. Two clusters of periods have been found using the k-means clustering algorithm with one from 3 min to 8 min and the other from 10 min to 14 min, with the latter being approximately twice the former. More than half ($\sim$54%) of these periods lie in or are very close to the 3 min to 8 min range. Similar periods have further been discovered from the $\Gamma_{1}$ and $\Gamma_{2}$ maps in the areas centred at five example swirls in the five different SST and SOT passbands using both the FFT and wavelet analysis.

The exact relation between the found $3-8$ min and $10-14$ min periods is unknown. Realistic numerical simulations might be needed to establish their physical relations. We also note that there are two periods less than $1$ min detected in the number of swirls ($N$) but not in other parameters (Table 1). Moreover, the maximum periods found in SOT observations are overall larger than those in SST observations for the same parameters. It is unclear whether the above differences are physical or artificial. Further studies are needed to investigate whether these are due to the fact that the utilised SOT observations cover a longer time span.

Nevertheless, these periods found in swirls remind us of the well-known $3-8$ minute $p$-mode oscillations of the Sun (e.g., Bahng & Schwarzschild, 1962; Ulrich, 1976; Zirker, 1980), which are the result of the globally coherent acoustic waves with pressure as the restoring force. Table 3 lists all significant periods found from the wavelet analysis of the average intensity across the whole field-of-view (FOV) of the SST and SOT observations. Most of the periods lie within the $5-8$ minute range (and $11-12$ minutes, which are twice that of the $5$-minute oscillations), providing evidence of the existence of global $p$-mode oscillations spanning the photosphere to the chromosphere. These periodicities also agree well with those found in the studied parameters of swirls detailed in this paper. Previously, oscillations with periods of the $p$-mode were also observed in a large variety of structures in the solar atmosphere from the photosphere to the corona, including but not limited to sunspots (e.g., Cally et al., 2016), coronal loops (e.g. De Moortel, 2006), plumes (e.g., Liu et al., 2015), and spicules (e.g., De Pontieu et al., 2004).

Our results suggest that the global $p$-mode oscillations modulate not only the occurrence manifested by periods in $CC$ and $N$, and periods in the investigated example swirls) but also the properties of photospheric swirls. Chromospheric swirls have also been found to possess almost identical periods. We note that employing simultaneous photospheric and chromospheric observations and 3D numerical simulations, Liu et al. (2019c) found that photospheric swirls could trigger Alfvén pulses which propagate upward into the chromosphere and lead to the observed chromospheric swirls. This suggests that the global $p$-modes could play a very important role in generating photospheric swirls thus Alfvén pulses, chromospheric swirls and spicules, recalling that many studies have found that spicules could be driven by rotational motions at their footpoints (Oxley et al., 2020; Scalisi et al., 2021b, a; Battaglia et al., 2021). Given that most photospheric swirls appear to be located at intergranular lanes (e.g., Wang et al., 1995; Bonet et al., 2008; Liu et al., 2019b), we suggest that they could be formed as a result of horizontal velocity flows (e.g., Murawski et al., 2018) that are modulated by the global $p$-modes. However, the exact physical processes of how photospheric swirls are formed due to global $p$-modes and how the vertical oscillations in the $p$-modes are converted into the horizontal rotations in swirls are still unclear. This may be answered by investigating realistic 3D numerical simulations similar to the ones in Liu et al. (2019a), where photospheric swirls were detected in the simulated photosphere undergoing $p$-mode oscillations.

If this scenario will be proven, a new way for the global $p$-mode oscillation to channel both energy (via triggering Alfvén pulses) and material (via triggering spicules) into the upper solar atmosphere will be established. Here, the $p$-mode oscillations themselves do not need to leak into the upper solar atmosphere in inclined magnetic field lines to trigger spicules as suggested by De Pontieu et al. (2004). Instead, they can also transport energy and mass into the upper atmosphere in less inclined magnetic lines via photospheric swirls.