1 INTRODUCTION

The occurrence and cyclic evolution of coronal holes (CHs) depend on their relation to both the large-scale magnetic field and active regions (ARs). Coronal holes in ARs are related to the processes occurring in these regions, in particular, flares and coronal mass ejections. Coronal holes that are not related to ARs reflect the distribution of large-scale solar magnetic fields, and their dynamics is determined by global changes in the structure of the magnetic field of the Sun (Bilenko, 2004). A close relationship between CHs and ARs was found earlier (Levin, 1977; Bohlin and Sheeley, 1978; Sheeley and Harvey, 1981; Levin et al., 1977) and later confirmed (Obridko and Shelting, 2013, 2015; Malashchuk et al., 2012).

The role of ARs in the generation and subsequent evolution of CHs is beyond doubt. Nevertheless, the mechanism of the generation and evolution of polar and mid- and low-latitude CHs is not fully understood.

In the standard solar dynamo model (e.g., Hoyng, 1993), the initially dipole poloidal field in the solar minimum is wound by differential rotation into a strong toroidal field in the solar maximum. The polar CHs that dominate during the minimum are related to the poloidal field, while the higher sunspot number during the maximum is related to the toroidal field. The relationship between these two manifestations of the magnetic evolution of the Sun was first studied by Bravo and Otaola (1989). Later, Bravo and Stewart (1994, 1997) showed that there is a close relationship between the evolution of polar-CH areas estimated from K-coronameter observations and the sunspot number with a delay of about half of the solar cycle. Bravo and Stewart (1997) showed that the total area of CHs of all types is maximal in the minimum phase.

During the solar minimum, the regions of an open field over the poles (polar CHs) reach the maximum extension, and the number of low-latitude regions of the closed and strong field (active regions and sunspots) is minimal. As the cycle evolves, more sunspots appear and the polar CHs become smaller. Small, low-latitude CHs appear at this time, but the total area of the Sun covered by CHs decreases as the sunspot number increases.

During the declining phase of cycle 24, there were two pronounced intervals of dominant sunspot activity: first, in the southern (S) and then in the northern (N) hemispheres. The purpose of this article is to study the CH dynamics and to identify features of the changes in the polar and isolated CH areas in this cycle phase.

2 OBSERVATIONAL DATA, METHODS, AND STATISTICAL ANALYSIS

This article explores the temporal variations of the daily total CH area (daily total coronal hole area, SCH) during the declining phase of cycle 24. The study is based on observational data from the SDO/AIA instrument in the iron line (Fe XII 19.3 nm), from April 2014 to December 2019.

The solar corona is the source of very dynamic events that mainly take place in ARs and CHs. The exact location of these large-scale objects can be determined with the application of image-processing techniques to extreme ultraviolet (EUV) data. We used the Heliophysics Event Knowledgebase (HEK) (Hurlburt et al., 2012), which is available at http://www.lmsal.com/hek/hek_isolsearch.html, to locate CHs and determine their areas. Information on CHs was extracted with the spatial possibilistic clustering algorithm (SPoCA), which was described in detail by Barra et al. (2009) and Verbeeck et al. (2014). The SPoCA is a set of multichannel, fuzzy, clustering algorithms that automatically segment EUV solar images into a set of functions. The SPoCA separates ARs, quiet Sun, and CHs by minimizing fuzzy intraclass variance. It segments up to 0.99 R⊙, excluding off-disk structures. These databases made it possible to obtain an array of daily total CH areas for the period April 1, 2014–December 31, 2019. The unit of measurement of the CH area is Mm2.

In the course of the study, we processed more than 5.5 years (2092 days) of CH observations. During this period, we analyzed 8891 CHs, 553 of which crossed the equator. In our work, we assumed that the area of the CHs crossing the equator is divided into two parts, and each part belongs to the corresponding hemisphere, depending on its location. Taking this into account, 4619 CHs were detected in the N hemisphere and 4272 CHs were found in the S hemisphere. Table 1 shows that the statistical volume of the presented material is quite extensive and gives grounds for the study of the dynamics of different types of CHs during the cycle.

Table 1.   Statistical analysis of coronal holes detected in the period Apr. 1, 2014–Dec. 31, 2019
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We used the sunspot index, SN, as an index of solar activity to analyze our material. It is generally accepted that the solar-activity index SN reflects an 11-year solar cyclicity and is therefore related to the solar dynamo. Conversely, the studied CHs are open-flux regions that are also generated by the solar dynamo. Therefore, it is expedient to compare the SN with the parameters of cyclic CH variations, in particular, their area. The daily total SN for the N and S hemispheres were taken from the Royal Belgian Observatory website (http://sidc.oma.be/silso/datafiles#hemi). We call the data divided by hemispheres the northern and southern components.

In our work, we also analyzed

—The smoothed total values of the monthly SN and SCH components for the N and S hemispheres;

—Six-month components, i.e., monthly components of the corresponding values smoothed over half a year;

—The mean SCH value level, i.e., the linear approximation of the monthly components for the detection of a rough SCH trend in polar and isolated components.

Figure 1 shows the northern (black curve) and southern (gray curve) components of the monthly SNs smoothed over six months for the entire study period. It can be seen that the S hemisphere was dominant with respect to the sunspot number from the beginning of this period until March 2015, after which the sunspot activity shifted to the N hemisphere. This trend continued until the end of 2019, which is consistent with the results previously obtained by other authors: (http://sidc.oma.be/silso/monthlyhemisphericplot). The fact that there are two distinct periods in which the sunspot activity predominated in the declining phase is one of the features of cycle 24. Since we were interested in what happens with CHs in this phase of the cycle, we used this information to analyze SCH variation over time.

Fig. 1.
figure 1

Monthly SN components smoothed over half a year: northern (black line) and southern (orange line).

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3 TOTAL CORONAL HOLE AREAS

As a result of the processing of the array of CH areas extracted from the EUV images by the SPoCA, we obtained the temporal variations of the daily total CH area for the entire visible surface of the solar disk (Fig. 2a) and separately for both hemispheres (Figs. 2b and 2c). In all three panels of Fig. 2, the hollow squares are SCH and the black curves are the monthly smoothed values of the corresponding components.

Fig. 2.
figure 2

Temporal variations of the daily total CH area on the branch of activity decline of cycle 24: (a) for the entire visible surface of the Sun, (b) for the N hemisphere, and (c) for the S hemisphere. The hollow squares are the SCH, and the red curve is SCH smoothed over a month.

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The first stage of the study period (April 2014–March 2015) is marked by the dominance of the S hemisphere by SCH (Fig. 2c). However, starting from September 2015, it is replaced by the N hemisphere, as in the case of SN but with a delay of about half a year (Fig. 2b). The fact that the sunspot activity at this stage anticipates the increase in CH areas was noted in our previous work (Andreeva et al., 2020).

From April 2014 to mid-2017, the SCH amplitudes changed in a fairly wide range [0: 45 × 104 Mm2]. After that, the SCH amplitude range narrows by about two times. The noticeable increase in the CH area during this period is due to the reappearance of several giant CHs (GCHs), which remained for a series of solar rotations (SRs). One of them, the longest lasting GCH of the N hemisphere (Fig. 2b, June 2015–February 2017), was observed and studied in our work (Andreeva et al., 2018). During its evolution, the GCH occupied a significant part of the N hemisphere, ~ 8 × 1011 km2. The GCH evolution included the passage of two active centers through it, which affected the change of many of its parameters. The GCH had a significant impact on the processes of the N hemisphere.

The visible, quasi-synchronous behavior of CHs in the N and S hemispheres in Figs. 2b and 2c and Figs. 5a and 5c reflects the change in the slope of the solar rotation axis during the year.

4 TEMPORAL CHANGES IN THE TOTAL POLAR AND ISOLATED CORONAL-HOLE AREAS

Sanchez-Ibarra and Barraza-Paredes (1992) divided all CHs into two classes, equatorial and polar, with respect to their topological relationship to the polar regions. A typical polar CH (CH_pol) appears as a CH spike in the polar region extending to the low latitude region. In turn, equatorial CHs are observed at low latitudes within the royal zone, where ARs develop, and are isolated islands that are not related to polar CHs. The term equatorial holes does not seem to be optimal, because this class formally includes high-latitude objects that are located away from the equator but are not related to polar holes. From this perspective, the terms isolated (Yazev, 2010) or nonpolar CHs are more appropriate (Bilenko and Tavastsherna, 2016). Insley et al. (1995) pointed out that these two classes of CHs are two populations that differ in their rotation patterns and developmental characteristics during the cycle.

Polar CHs usually disappear during the solar cycle maximum and appear again, already with a magnetic flux of opposite polarity, thus demonstrating a change in the polar field. Isolated CHs behave differently: they appear during the early phases of increase in solar activity, though usually more frequently at the maximum, and disappear near the activity minimum.

After the polarity reversal, the spikes of polar holes merge with the regions resulting from the evolution of the AR tails following the polarity rule. In the initial phase of the cycle decline, the situation seems favorable for the formation of large, isolated equatorial holes (Yazev, 2010; Abramenko et al., 2006, 2010), because bipolar magnetic regions at low latitudes from different hemispheres can form large, unipolar cells upon merging. Finally, there is no significant number of ARs at the cycle minimum. Therefore, there is no basis for the formation of regions capable of generating CHs over time. During this period, the magnetic flux at the poles is maximal, and the polar regions are maximally developed (Yazev, 2010).

In this article, we studied two types of CHs, polar (CHs_pol) and isolated (CHs_isol). Figure 3 gives an example of such CHs. The first group is polar CHs, which are located at the solar poles (SPoCA 23 064, 23 027, 23 717, 23 632) and have a lifetime comparable to that of the solar cycle. Extensions of CHs, such as the elephant trunk (SPoCA 23 064), also belong to this category. The second type is isolated or nonpolar CHs (SPoCA 23 715, 23 716, 23 097), which are mostly limited to low, medium, and sometimes high latitudes, but not related to polar CHs. Their lifetime is comparable to several CRs.

Fig. 3.
figure 3

Inverted images of the Sun obtained by the SDO/AIA on Feb. 24, 2016, and July 17, 2016, in the Fe XII line (19.3 nm). The areas on the solar disk marked with CH are CHs extracted from the EUV image with SPoCA. Coronal holes with SPoCA 23027, 23064, 23632, and 23717 are polar, and those with SPoCA 23097, 23715, and 23716 are isolated. Dark formations on the solar disk marked with AR are active regions.

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Figs. 4a and 4b show the variations of the total polar and isolated CH areas for the entire visible surface of the solar disk, and they are shown separately for the N and S hemispheres in Fig. 5.

Fig. 4.
figure 4

Change in the daily total area (hollow squares) of all polar (a) and isolated (b) CHs on the visible surface of the solar disk in the period Apr. 1, 2014–Dec. 31, 2019. The solid black curves are the CH area smoothed over a month. The dashed lines are a linear approximation of the areas smoothed over a month, the mean levels of the total polar and isolated CH areas.

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Against the background of the daily total polar (a) and isolated (b) CH areas (squares), Fig. 4, shows their values smoothed over a month and approximated (the black solid curve and dashed straight line, respectively) for the entire visible surface of the solar disk. The direction of the dotted line reflects the trend of the mean level of the total CH area during the considered period. It can be seen that it increases in this phase of the cycle for polar CHs (Fig. 4a) and decreases for isolated CHs (Fig. 4b). In the entire studied period, the mean level of the polar CH areas varied within 11.5 × 104 < Sum SCH_pol < 14.5 × 104 Mm2 and the isolated areas varied within 0 < Sum SCH_isol < 7 × 104 Mm2.

The maximum amplitudes of polar CH areas are observed at the beginning of the decline phase and seem to be related to the ongoing restructuring after the second maximum of cycle 24 and the presence of several GCHs between April 2014 and September 2017. The GCH was first observed in the S hemisphere (Fig. 5c, April 2014–April 2015), then in the N hemisphere (Fig. 5c, June 2015–January 2017), and then again in the S hemisphere (Fig. 5c, August 2016–June 2017). The spikes in the amplitudes of the polar-CH areas at these moments are clearly visible in Fig. 5a. The amplitudes of the isolated-CH areas also had the maximum values during this period, but they were significantly smaller than those for polar-CH areas. After June 2017, the mean level of the total polar-CH areas approached 14 × 104 Mm2 (Fig. 4a). The situation stabilized, and the amplitude range of the polar-CH area significantly decreased.

Fig. 5.
figure 5

Daily total areas of polar (a, c) and isolated (b, d) CHs of the N (a, b) and S (c, d) hemispheres. The black lines are the monthly smoothed components of the daily total CH area.

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It can be seen from Fig. 4 that the total polar-CH areas predominated during the studied stage. The range of amplitude variation of the total daily polar-CH areas was 0–45 × 104 Mm2, while it was only 0–23 × 104 Mm2 for the isolated areas (squares in Figs. 4a and 4b). We determined the contribution of the areas of the two CH types to the total area for the studied period. It turned out that the total area of all CHs was 33 508.53 × 104 Mm2, 26 873.93 × 104 Mm2 of which were polar and 6669.43 × 104 Mm2 were nonpolar. In percentage terms, it was ~80% and ~20%. With this in mind, our result is consistent with the conclusion drawn by Bravo and Stewart (1997) that the total area of all CHs becomes maximal toward cycle minimum.

The following can be noted upon analysis of the temporal distribution of polar- and isolated-CH areas across hemispheres (Fig. 5): at the beginning of the studied period, giant, recurrent polar CHs followed each other with some periodicity during the first 4 years (Figs. 5a and 5c). There were very strong increases and decreases in SCH_pol (the black curve in Figs. 4a, 5a, and 5c). The situation stabilized after the middle of 2017, but the N hemisphere continued to predominate to a certain extent in terms of the area occupied by CHs.

5 CONCLUSIONS

The dynamics of CHs in the declining phase of cycle 24 was studied. Comparison of the variations in the daily total CHs areas with the index of sunspot number made it possible to reveal some features of the variation of the polar- and isolated-CHs areas in the period April 1, 2014–December 31, 2019.

During the studied period, there was an asymmetry in the distribution of SCH and SN across hemispheres; the dominance of the S hemisphere changed to that of the N hemisphere.

The division of all CHs from the considered period into polar and nonpolar ones showed that polar-CH areas predominated and increased, while nonpolar-CH areas constantly decreased toward the cycle minimum. The polar-CH areas accounted for ~80% of the total area of all considered CHs during the studied period.

The total area of polar CHs increases toward solar cycle minimum, which is consistent with the general concept of polar CHs as the main source of the Sun’s dipole magnetic field (Ikhsanov and Ivanov, 1999; Webber et al., 2014). This conclusion is consistent with previous studies (Bravo and Stewart, 1997; Dorotovič, 1996). In this case, the second subset, isolated CHs, shows an interesting behavior in the declining phase of the solar activity that was not previously observed. Their areas slowly decrease from the maximum to the minimum of the solar cycle. This trend is qualitatively consistent with a decrease in sunspot activity toward the minimum, which suggests a physical relationship between the two phenomena. However, the latter conclusion requires further verification with data from other solar cycles. Regardless of the result of such verification, it is already clear that the open magnetic flux from the entire Sun is not uniform in composition.

It was noted that the visible quasi-synchronous behavior of polar CHs in the N and S hemispheres reflects the change in the tilt of the Sun’s rotation axis during the year.