On Quasi-biennial Oscillations in Chromospheric Macrospicules and Their Potential Relation to the Global Solar Magnetic Field

Macrospicules are likely formed in the chromosphere and have the potential to play an important role in the transfer of momentum and energy from the lower solar atmospheric regions to the transition region and the low corona. Several interesting features of MS have been found and reported since their first discovery (Bohlin et al. 1975). These jets are multithermal (Pike & Harrison 1997), rotating phenomena (Pike & Mason 1998), that can be observed both on-limb and off-limb (Scullion et al. 2010) with a density of about 10⁻¹⁰ cm⁻³ (Parenti et al. 2002). Their formation energy has been estimated (Bennett & Erdélyi 2015) and a possible connection to the active longitude of sunspots has been revealed (Gyenge et al. 2015).

To gain relevant information about the long-term variation of the physical properties of MS, a multi-year long database is needed. The raw data are provided by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) in the 30.4 channel. Identifying MS from the large variety of different chromospheric phenomena is a crucial point for this research, therefore firm criteria are necessary for defining what an MS may be. Kiss et al. (2017) discussed the range of such criteria in more details, the applied date selection method and how these jets are characterized as tetragons.

Accomplishment of the process of MS identification resulted in a catalog of 363 MS between 2010 June and 2017 July. The jets are categorized based on the solar environment around them at the solar limb: MS inside coronal hole and quiet-Sun regions are named coronal hole MS (CH-MS) and quiet-Sun MS (QS-MS), respectively. The numbers of CH-MS and QS-MS are found to be approximately equal: 184 and 169. A third, so-called coronal hole boundary class was also constructed in order to account for MS with uncertainty on their more exact locii, but their number is much smaller (9). Therefore, these latter jets are not taken into account for our further study. 363 MS were found on 334 observing days, indicating 1.08 MS to appear in the 2 hr time interval of a given day of observing.

For the tetragon approximation, four points were fitted to each MS. The geometric shape of tetragon grants a decent measure of the actual length, width, and area for each SDO/AIA during the entire lifetime of an MS. For our study, during the evolution of an individual MS, the maxima of these properties were recorded (e.g., maximum length, width, and area, respectively) in addition to lifetime (the time span between the first and the last SDO/AIA observation of a given jet). The temporal resolution of SDO/AIA at the wavelength of 30.4 nm is 12 s, therefore the actual velocity of the jet can be estimated by determining the length difference between two observations. The actual velocity of some individual MS may have outlier values, which are interpreted as errors. Therefore, an average velocity for each MS is used in the analysis instead of their maximum velocity.

Additional occasional interpolation is applied to the data of the maximum length, maximum width, maximum area, average velocity, and lifetime series, because the temporal resolution is not perfectly homogeneous. The average number of MS occurrence is varying slightly on a given day of observation. Wavelet analysis is sensitive to the non-homogeneous nature of the input data. Consequently, a homogenizing method was constructed to overcome this problem. For the analysis, we need only a single datum of each MS property per each epoch of observation. This approach addressed two issues: (i) if two or more MS were observed on one observing block, the average of all of their physical properties is calculated, and (ii) if no MS is identified during the observing sequence, then the value of each MS property on the given day is interpolated linearly from the closest existing values. We obtained the interpolated values by calculating the difference between neighboring data points, divided the difference proportionately to the number of the missing dates, and assigned a value by adding/extracting the fraction from the known data accordingly to the increasing/decreasing trend. During the build-up of the data set, 330 dates were picked for investigation. On 140 days, only one MS was observed; therefore, these dates remained unaffected by the homogenization process. In the case of 99 days, more than one MS were identified. On the remaining 91 dates, no MS observation was registered. Note that the homogenization will have no effect on the data at periods on the order of magnitude of QBOs. To study the temporal variation of oscillatory patterns of the homogenized data set of MS properties, wavelet analysis was used.

In this section, we summarize proxies capturing long-term solar activity, what we will utilize in this study.

(1) The sunspot number accounts for each sunspot and sunspot group on the visible surface of the Sun. This is one of the most important solar activity proxies for us today due to its 300 years of relatively continuous observations. All the data used here are provided on the website of the sunspot Index and Long-term Solar Observation, Royal Observatory, Belgium (http://sidc.be/silso/home).

(2) The sunspot area data indicates the total covered area of sunspot umbra and penumbra. These data are available at the late Debrecen Heliophysical Observatory http://fenyi.solarobs.csfk.mta.hu/en/databases/SDO/). This catalog is based on magnetograms of the Helioseismic and Magnetic Imager on board the SDO (Baranyi et al. 2016).

(3) The 10.7 cm radio flux is a bright emission of the upper chromosphere and the lower corona (Tapping 1987). Sources of this emission are the gyroresonances from thermal plasma trapped in magnetic field and bremsstrahlung of thermal plasma over active regions (Kundu 1965; Krueger 1979). There is a widely known correlation between the 10.7 cm radio flux and the solar sunspot activity. This emission is observed and integrated over the disk and the data made available by the Dominion Radio Astrophysical Observatory, National Research Council of Canada (http://www.spaceweather.gc.ca/solarflux/sx-en.php).

(4) With six base stations all around the Globe, the BiSON measures the line-of-sight velocity of the solar surface (Chaplin et al. 1996; http://bison.ph.bham.ac.uk/). The observations are disk-integrated, so-called Sun-as-a-star observations, which are sensitive to low-ℓ p-mode oscillations, where ℓ is the degree of an eigenmode. The helioseismic data are divided into 182.5 day time series and the frequency shift of each individual global acoustic mode is calculated for 0 ≤ ℓ ≤ 2 and 2400 ≤ ν ≤ 3500 μHz.

(5) The wavelength 94 Å is an optically thin, EUV intensity line. This emission is generated by the Fe xviii ions at around 6 MK. The 94 Å channel of SDO/AIA is mapping these Fe xviii ions in the solar corona in every 12 s with the cadence of 0.6 arcsec (≈435 km).

In their recent study, Kiss et al. (2017) investigated the temporal variation of the physical properties of MS obtained for the period between 2010 June and 2015 December. No obvious trends were seen, initially, in the data themselves. Therefore, the histograms of the data were analyzed. These histograms were constructed in log-normal distribution. The cross-correlations of MS physical properties (e.g., "Maximum length" versus "Average velocity") do show a strong oscillatory pattern. However, the time span of the database in Kiss et al. (2017) was not sufficiently long to obtain confident enough results about the nature of periodicities in these oscillations. In Kiss et al. (2018), they extended the data set with another year of observation. With this extension, they confirmed that there is evidence for QBOs in the cross-correlations of MS physical properties. These facts suggest examining further the temporal evolution of the raw data in more details, in order to find the origin of these QBO signatures. The work here is about mounting evidence toward this goal.

The database in comparison to Kiss et al. (2017) has now been extended by an additional year and a half, i.e., expanding the number of MS, with an additional sample of 62 (27 CH-MS and 35 QS-MS). In all the panels on the left-hand side of Figure 1, the temporally homogenized data of each investigated physical parameters of MS are given. To highlight the trends in these plots, the signals are smoothed. The temporal length of the running average is around a month. This temporal scale is long enough to mask the short-scale noise-like variations of the data. On the other hand, the window is short enough to prevent the influence on long-scale oscillations.

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The distributions of "Lifetime" and "Maximum width" do not show a clear oscillatory pattern; however, a strong one is visible in the cases of "maximum length," "average velocity," and "maximum area." Highest values of the cycles occur during the summer of each odd year: 2011, 2013, and 2015. This trend suggests a period of around two years, but a proper signal processing would be required to gain more precise (and with confidence) information about the oscillatory properties of these signals.

For this reason, wavelet analysis was applied to the homogenized data. The 7 year length of the data sets is sufficiently long enough to provide a power peak with the expected 2 year period outside the cone of influence (CoI). The right panel of each row, in Figure 1, shows the results of the wavelet analysis. "Lifetime" and "Maximum width" do not show power peaks at around two years. However, the wavelet of the remaining three properties of MS provides a much more promising outcome. A significant peak appears at around 1.8 years outside the CoI, which is interpreted as a signature of QBOs. These oscillations are dominant after 2012, hence some parts of these oscillation peaks are inside CoI. However, there are highly significant areas of QBOs outside of the CoI. Some power peaks with shorter periods are also visible in these figures, but they are not as significant as the QBOs.

The global wavelets are confirming the statements above (see, e.g., the right-hand side of the wavelet panels in Figure 1). "Lifetime" does not seem to provide any measurable oscillation peaks; furthermore, "maximum width" shows a more complex global wavelet with several non-significant power peaks. "Maximum length," "average velocity," and "maximum area" have clear and significant peaks at about two years (outside CoI).

Broomhall & Nakariakov (2015) compared the long-term variation of the global p-mode frequency shift to a few other solar activity proxies for a period between 1985 and 2014: namely, two indicators in the photosphere (i.e., sunspot number, sunspot area), two proxies in the solar atmosphere (i.e., 10.7 cm radio flux, 530.3 nm green coronal index) and two activity phenomena present farther away from the solar surface (interplanetary magnetic field, the galactic cosmic-ray intensity). After the removal of the dominant 11 year long cycle, QBOs were found in each data set. However, the actual details of these high-frequency oscillations were not compared to each other in that work.

Here, besides highlighting the high-frequency variation of the physical properties of MS, we also shed light on the temporal variations of different QBOs in comparison to each other. For this reason, we have also removed the 11 year cycle from the time series of five solar activity proxies (and labeled them with abbreviation in square brackets): the sunspot number [n_SN], area [n_SA], 10.7 cm radio flux [${{ \mathcal F }}_{10.7}$], average channel intensity of SDO/AIA 9.4 nm [I_SDO] and the p-mode frequency shift [d_p]. The residual data, after removing the solar cycle trend, are plotted in the bottom two panels of Figure 2. The trend removal was executed in the following way: a smoothing was utilized with a large windowsize (nearly 2.5 years), which has removed shorter-scale fluctuations but preserved the 11 year cycle. The smoothed graph clearly shows the 11 year oscillation. Next, this smoothed graph is extracted from the original data set and the residual is shown in the middle and bottom panels of Figure 2. All the SDO channels present QBO patterns; however, the 9.4 nm channels provide the most similarities to other solar activity proxies. "Maximum length," "maximum area," and "average velocity" of MS, reveal QBOs, that are clearly visible in the top panel of Figure 2. The duration of the MS data set allows us to carry out this study now between 2010 June and 2017 July.

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In the next step, we compare the oscillatory signatures of the MS data to other solar proxies. Local extrema (minima and maxima) can be determined for each MS data set. To find the epochs of all the MS extrema, the dates of the local extrema of the "maximum length," "maximum area," and "average velocity" data sets were averaged (solid vertical lines for maxima and dashed vertical lines for minima in Figure 2) and their standard deviations (gray vertical bars around the lines Figure 2) were estimated for error analysis. Dates for all MS extrema are given in Table 1 (labeled with Roman numbers I–VI). The dates of the extrema clearly indicated supporting evidence for the 2 year long oscillation, only the minima in 2014 may seem to be somewhat early.

In the following, we now compare these extrema with those of the other solar proxies:

• This maximum is close to one of the maxima of n_SN–n_SA–${{ \mathcal F }}_{10.7}$; though, it does not match them really well. With a good approximation, however, they are in-phase. I_SDO and d_p are in their rising phase.
• This minimum occurs around the time when there is a small "step" in each of the other proxies.
• This maximum is matching the local minimums of all other proxies. They are clearly out-of-phase.
• This minimum happens at the same time, when there is a local maximum in the n_SN–n_SA−d_p variations. In the case of ${{ \mathcal F }}_{10.7}$ and I_d, IV also marks the local maximum, however, these variables have a smaller secondary maximum. Overall, they are all out-of-phase.
• This maximum is similar to that of I. At this epoch, n_SN–n_SA are around their local minimum, but the matching is not perfect. ${{ \mathcal F }}_{10.7}$–I_d is in its decaying phase from their secondary maximum, closing up to the minimum. Overall, they are all out-of-phase.
• Close to the epoch of this minimum, a small-scale maxima is visible on the n_SN–n_SA–${{ \mathcal F }}_{10.7}$–I_SDO plots.

For the six extrema of the MS properties, four of them are in- or out-of-phase with the other solar proxies. Only at II is there no extrema, but a "step" is still visible in all the other proxies. This may suggest a change in the underlying process: before this time, I is in-phase with the other proxies and, after this time, III is out-of-phase with other proxies.

To corroborate this out-of-phase behavior, we implemented a cross-correlation analysis between the three MS time series and the five solar activity proxies as seen in Figure 3. To present a proof, anticorrelation should be found on the cross-correlation plots. Linear regression was utilized to analyze the correlation between every combination of them. By taking into account the entire time span of the data series, no strong anticorrelations were found (the average of r² values is −0.218). By considering the data points only after 2013 May (the epoch of III), the anticorrelation between the MS properties and the solar proxies is significantly stronger (the average of r² values is −0.3895). In 13 cases out of 15 cross-correlations, the absolute value of the correlation coefficients is larger. Figure 3 clearly shows that the blue points (data values before 2013 May) are robustly vertical, which weakens the correlation coefficient and, thus, the anticorrelation. This is a supporting evidence for the previously discussed out-phase nature.

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However, for a more detailed investigation of this variation of extrema, longer data would be needed. Therefore, this analysis may be a promising motivation for investigation in the future.