Intermediate-term periodicities in solar activity

The presence of intermediate-term periodicities in solar activity, at approximately 323 and 540 days, has been claimed by different authors. In this paper, we have performed a search for them in the historical records of two main indices of solar activity, namely, the daily sunspot areas (cycles 12–21) and the daily Zürich sunspot number (cycles 6–21). Two different methods to compute power spectra have been used, one of them being especially appropriate to deal with gapped time series. The results obtained for the periodicity near 323 days indicate that it has only been present in cycle 21, while in previous cycles no significant evidence for it has been found. On the other hand, a significant periodicity at 350 days is found in sunspot areas and Zürich sunspot number during cycles 12–21 considered all together, also having been detected in some individual cycles. However, this last periodicity must be looked into with care due to the lack of confirmation for it coming from other features of solar activity. The periodicity around 540 days is found in cycles 12, 14, and 17 in sunspot areas, while during cycles 18 and 19 it is present, with a very high significance, in sunspot areas and Zürich sunspot number. It also appears at 528 days in sunspot areas during cycles 12–21. On the other hand, it is important to note the coincidence between the asymmetry, favouring the northern hemisphere, of sunspot areas and solar flares during cycle 19, and the fact that the periodicity at 540 days was only present, with high significance, in that hemisphere during that solar cycle.     

The 73-day periodicity of the flare index during the current solar cycle 22

The flare index of the current solar cycle 22 is analysed to detect intermediate-term periodicities from Sep. 1, 1986 to Dec. 31, 1991. Power spectral analysis of the time series of solar flare index data reveals a periodicity around 73 and 53 days. We find that a periodicity of 73 days was in operation from 1988 November to the end of 1991 December. We also find that when the 73-day periodicity or the 154-day periodicity is in operation, the flare index is well correlated with the relative sunspot numbers. As a conclusion, we do not expect to see a resumption of the 154-day or 73-day periodicity, but we do expect only one of the periodicity near the integral multiples of 25^d.8 in the next solar cycles.     

Long-Term Solar Activity: Direct and Indirect Study

The series of directly observed sunspot numbers is nearly 400 years long. We stress that the recently compiled group sunspot number series is an upgrade of the old Wolf series and should always be used before 1850. The behavior of solar activity on longer time scales can be studied only using indirect proxies. Such proxies as aurorae occurrence or naked-eye sunspot observations are qualitative indicators of solar activity but can be hardly quantitatively interpreted. Cosmogenic isotope records provide a basis for quantitative estimate of the past solar activity. Here we overview the main methods of the long-term solar activity reconstruction on the centennial to multimillennia time scale. We discuss that regression-based reconstructions of solar activity lead to very uncertain results, while recently developed physics-based models raise solar activity reconstruction to a new level and allow studying its behavior on a multimillennia time scale. In particular, the reconstructions show that the recent episode of high solar activity is quite unusual in the multimillennia time scale.     

Periodicities in Solar Flare Index for Cycles 21 – 23 Revisited

The periodic analyses of solar flare data have been carried out by different authors for about three decades. Controversial results appear as depending on the analysis techniques and investigated time periods. Considering that different authors applied different methods to different data sets, it seems necessary to reanalyze the periodicity of solar flare index with a unified method. In this study we used two new methods to investigate the periodic behavior of solar flare index data, first for individual cycles 21, 22 and 23, and then for all of them. We used i) the multi taper method with red- and white-noise approximations, and ii) the Morlet wavelet transform for periodicity analysis. Apart from the solar rotation periodicity of about 27 days which is of obvious significance and is found in all examined cycles with at least a 90% significance level, we obtained the following prominent periods: 152 days for cycle 21, 73 days for cycle 22, and 62 days for cycle 23. Finally, we compare our results with the ones previously found. We emphasize the fact that a lesser number of periodicities is found in the range of low frequencies (long periods) while the higher frequencies show a greater number of periodicities. This result might be useful for better predictions of the solar cycles.     

The 73-day periodicity of the flare index during the current solar cycle 22

The flare index of the current solar cycle 22 is analysed to detect periodicities. Power spectral analysis of the time series of solar flare index data reveals a periodicity around 73 and 53 days. We find that a periodicity of 73 days was in operation from November 1988 to the end of December 1991. We also find that when the 73-day periodicity or the 154-day periodicity is in operation the flare index is well correlated with the relative sunspot numbers.     

Phase Coherence Analysis of Solar Magnetic Activity

Over 24 years of synoptic data from the NSO Kitt Peak Vacuum Telescope is used to investigate the coherency and source of the 27-day (synodic) periodicity that is observed over multiple solar cycles in various solar-related time series. A strong 27.03-day period signal, recently reported by Neugebauer et al. (2000), is clearly detected in power spectra of time series from integrated full-disk measurements of the magnetic flux in the 868.8 nm Fei line and the line equivalent width in the 1083.0 nm Hei line. Using spectral analysis of synoptic maps of photospheric magnetic fields, in addition to constructing maps of the surface distribution of activity, we find that the origin of the 27.03-day signal is long-lived complexes of active regions in the northern hemisphere at a latitude of approximately 18 deg. In addition, using a new time series analysis technique which utilizes the phase variance of a signal, the coherency of the 27.03-day period signal is found to be significant for the past two decades. However, using the past 120 years of the sunspot number time series, the 27.03-day period signal is found to be a short-lived, no longer than two 11-year solar cycles, quasi-stationary signal.     

A 14-day periodicity in the mean solar magnetic field

In the present paper we look for periodicities in the mean solar magnetic field observed at Stanford Observatory, using Fourier transform and autocorrelation techniques. Apart from the periodicity equal to that of the synodic rotational modulation of the Sun, other periods were also found by examining the time series formed at different epochs of the solar cycle. From the aforesaid analyses a 14-day periodicity has been confirmed, which is found to occur in all the cases taken under consideration.     

Confirmation of the 25.5-day fundamental period of the Sun using the north-south asymmetry of the flare index

Short-term periodicities of solar activity were studied. To perform the study, a north-south asymmetry time series was constructed by using the northern and the southern hemisphere flare index values for solar cycle 22. The statistical significance of this time series was calculated. It indicates that in most of cases the asymmetry is highly significant during cycle 22. Power spectral analysis of this time series reveals a periodicity around 25.5 days, which was announced before as a fundamental period of solar activity (Bai and Sturrock, 1991). To investigate the time agreement between the two hemispheres, the phase distribution was studied and a phase shift of about 0.5 was found. An activity trend from the north to the south was found.     

Periodicities in the occurrence rate of solar proton events

Power spectral analyses of the time series of solar proton events during the past three solar cycles reveal a periodicity around 154 days. This feature is prominent in all of the cycles combined, cycles 19 and 21 individually but is only weak in cycle 20. These results are consistent with the presence of similar periodicities between 152 and 155 days in the occurrence rate of major solar flares, the sunspot blocking function (P _s ), the 10.7 cm radio flux (F _10.7) and the sunspot number (R _z ). This suggests that the circa 154-days periodicity may be a fundamental characteristic of the Sun. Periods around 50–52 days are also found in the combined data set and in the three individual cycles in general agreement with the detection of this periodicity in major flares in cycle 19 and inP _s ,F _10.7, andR _z in cycle 21. The cause of the 155 day period remains unknown. The spectra contain lines (or show power at frequencies) consistent with a model in which the periodicity is caused by differential rotation of active zones and a model in which it is related to beat frequencies between solar oscillations, as proposed by Wolff.     

Solar activity around AD 775 from aurorae and radiocarbon

A large variation in ¹⁴C around AD 775 has been considered to be caused by one or more solar super‐flares within one year. We critically review all known aurora reports from Europe as well as the Near, Middle, and Far East from AD 731 to 825 and find 39 likely true aurorae plus four more potential aurorae and 24 other reports about halos, meteors, thunderstorms etc., which were previously misinterpreted as aurorae or misdated; we assign probabilities for all events according to five aurora criteria. We find very likely true aurorae in AD 743, 745, 762, 765, 772, 773, 793, 796, 807, and 817. There were two aurorae in the early 770s observed near Amida (now Diyarbakır in Turkey near the Turkish‐Syrian border), which were not only red, but also green‐yellow – being at a relatively low geomagnetic latitude, they indicate a relatively strong solar storm. However, it cannot be argued that those aurorae (geomagnetic latitude 43 to 50°, considering five different reconstructions of the geomagnetic pole) could be connected to one or more solar super‐flares causing the ¹⁴C increase around AD 775: There are several reports about low‐ to mid‐latitude aurorae at 32 to 44° geomagnetic latitude in China and Iraq; some of them were likely observed (quasi‐)simultaneously in two of three areas (Europe, Byzantium/Arabia, East Asia), one lasted several nights, and some indicate a particularly strong geomagnetic storm (red colour and dynamics), namely in AD 745, 762, 793, 807, and 817 – always without ¹⁴C peaks. We use 39 likely true aurorae as well as historic reports about sunspots together with the radiocarbon content from tree rings to reconstruct the solar activity: From AD ∼733 to ∼823, we see at least nine Schwabe cycles; instead of one of those cycles, there could be two short, weak cycles – reflecting the rapid increase to a high ¹⁴C level since AD 775, which lies at the end of a strong cycle. In order to show the end of the dearth of naked‐eye sunspots, we discuss two more Schwabe cycles until AD ∼844. The ¹⁴C record (from both Intcal and Miyake et al. 2013a) is anti‐correlated to auroral and sunspot activity, as expected from solar wind modulation of cosmic rays which produce the radiocarbon. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Short-term periodicities in sunspot areas during solar cycle 22

We have analyzed the daily record of sunspot areas during the current cycle 22 looking for the short-term periodicity of around 155 days which was present during some previous solar cycles. Two different methods have been used to compute the power spectra and the results indicate that such periodicity has been absent during the current solar cycle, which confirms the results obtained by other authors who used flares or flare-related data.However, we have found that, during some intervals of time, a periodicity close to 86 days is statistically significant. A similar periodicity was found by Landscheit (1986) in energetic X-ray flares, between 1970 and 1982 (second and first half of solar cycles 20 and 21, respectively), and by Bai (1992b) for important solar flares during solar cycle 20.     

The Sunspot and Auroral Activity Cycle Derived from Korean Historical Records of the 11th–18th Century

Historical records of sunspots and aurorae are valuable information to examine variations of solar activity and the terrestrial climate on a long-term scale. We have collected the historical records of Korea during the 11th–18th century. Through a power-spectrum analysis of these data, we have found solar activity cycles, which coincide with the Schwabe cycle and the Gleissberg cycle on short and long-term periods, respectively.     

Sunspot and Auroral Activity During Maunder Minimum

The extremely low sunspot activity during the period of the Maunder minimum 1645–1715 was confirmed by group sunspot numbers, a new sunspot index constructed by Hoyt and Schatten (1998a,b). Neither sunspots nor auroral data time behavior indicate the presence of 11-year solar cycles as stated by Eddy (1976). The evidence for solar cycles was found in the butterfly diagram, constructed from observations made at Observatoire de Paris. After Clivier, Boriakoff, and Bounar (1998) the solar cycles were reflected also in geomagnetic activity. Results are supported by the variation of cosmogenic isotopes ¹⁰Be and ¹⁴C. The majority of the observed 14 naked-eye sunspots occurred on days when telescopic observations were not available. A part of them appeared in the years when no spot was allegedly observed. Two-ribbon flares appear in plages with only very small or no sunspots. Some of these flares are geoactive. Most aurorae (90%), which were observed during the Maunder minimum, appeared in years when no spot was observed. Auroral events as a consequence of proton flares indicate that regions with enhanced magnetic field can occur on the Sun when these regions do not produce any sunspots.     

The 156-day quasi-periodicity in solar indices

This paper investigates a series of daily solar indices: the sunspot number W (1900–2008), solar flux at 2800 MHz F _10.7 (1947–2008), and a number of X-ray flares N _x (1981–2008). The methods of Fourier and wavelet analysis are used to reveal the so-called 156-day Rieger-type periodicity (RTP). The W index is observed to have a statistically significant RTP amplitude in the neighborhood of the solar maxima in most of the solar cycles under study, except for cycles 14, 15, and 23. The 156-day peak is observed to have its largest power during the declining phase of cycle 16, at the maximum of cycle 21, and during the increasing phase of cycles 20 and 23. Statistically significant RTPs are also observed at the minima of cycles 17, 18 and 19. We conclude that there is no stable dependence between RTP and the solar cycle. The wavelet analysis shows that the pattern of the RTP time dependence for the F _10.7 index is almost identical to that of the W index. The correlation coefficient between the RTP curves is 0.95. The correlation coefficients for the pairs of indices W-N _x and F _10.7-N _x are 0.36 and 0.32, respectively. No time lags are found between the RTP starting points for different indices. Thus, the 156-day quasi-periodicity involves, almost simultaneously, events that occur in active regions of the solar atmosphere at different heights. This paper discusses the possible nature of RTP.     

Sunspot Count Periodicities in Different Zurich Sunspot Group Classes Since 1986

We used two methods to investigate the periodic behavior of sunspot counts in four categories for the time period January 1986?–?October 2013. These categories include the counts from simple (A and B), medium (C), large (D, E, and F), and final (final-stage; H) sunspot groups. We used i) the multitaper method with red noise approximation, and ii) the Morlet wavelet transform for periodicity analysis. Our main findings are that 1) the solar rotation periodicity of about 25 to 37 days, which is of obvious significance, is found in all groups with at least a 95 % significance level; 2) the periodic behavior of a cycle is strongly related to its amplitude and group distribution during the cycle; 3) the appearance of periods follows the amplitude of the investigated solar cycles; and that 4) meaningful periods do not appear during the minimum phases of the investigated cycles. We would like to underline that the cyclic behavior of all categories is not exactly the same; there are some differences between these groups. This result can provide a clue for the better understanding of solar cycles.     

Magnetic flux emergence and geomagnetic activity,a close correlation

We analyse data of magnetic flux emergence for solar cycles 21 and 22, Helios 1 interplanetary shocks for cycle 21, and sudden storm commencements (SSCs) for cycles 11–22. A dominant variation of 3-year periodicity was found for all three phenomena during cycles 21 and 22. This indicates a correlation and a possible influence of the rate of solar magnetic flux emergence to produce the interplanetary phenomena studied in this work; in particular, the suggested role of coronal mass ejections as a means by which magnetic flux and stresses are taken out of the corona seems to be plausible. When taking cycles 11–22 in SSCs, the main periodicity changes to around 4 years; this may be an indication of flux emergence rate variations over the cycles.     

Different Periodicities in the Sunspot Area and the Occurrence of Solar Flares and Coronal Mass Ejections in Solar Cycle 23 – 24

In order to investigate the relationship between magnetic-flux emergence, solar flares, and coronal mass ejections (CMEs), we study the periodicity in the time series of these quantities. It has been known that solar flares, sunspot area, and photospheric magnetic flux have a dominant periodicity of about 155 days, which is confined to a part of the phase of the solar cycle. These periodicities occur at different phases of the solar cycle during successive phases. We present a time-series analysis of sunspot area, flare and CME occurrence during Cycle 23 and the rising phase of Cycle 24 from 1996 to 2011. We find that the flux emergence, represented by sunspot area, has multiple periodicities. Flares and CMEs, however, do not occur with the same period as the flux emergence. Using the results of this study, we discuss the possible activity sources producing emerging flux.     

Periodic variation and phase analysis of grouped solar flare with sunspot activity

Studies on the periodic variation and the phase relationship between different solar activity indicators are useful for understanding the long-term evolution of solar activity cycles.Here we report the statistical analysis of grouped solar flare(GSF) and sunspot number(SN) during the time interval from January 1965 to March 2009.We find that,(1) the significant periodicities of both GSF and SN are related to the differential rotation periodicity,the quasi-biennial oscillation(QBO),and the eleven-year Schwabe cycle(ESC),but the specific values are not absolutely identical;(2) the ESC signal of GSF lags behind that of SN with an average of 7.8 months during the considered time interval,which implies that the systematic phase delays between GSF and SN originate from the inter-solar-cycle signal.Our results may provide evidence about the storage of magnetic energy in the corona.     

Intermediate‐term variations in solar radius during solar cycle 23

In this study, we look for the mid‐term variations in the daily average data of solar radius measurements made at the Solar Astrolabe Station of TUBITAK National Observatory (TUG) during solar cycle 23 for a time interval from 2000 February 26 to 2006 November 15. Due to the weather conditions and seasonal effect dependent on the latitude, the data series has the temporal gaps. For spectral analysis of the data series, thus, we use the Date Compensated Discrete Fourier Transform (DCDFT) and the CLEANest algorithm, which are powerful methods for irregularly spaced data. The CLEANest spectra of the solar radius data exhibit several significant mid‐term periodicities at 393.2, 338.9, 206.5, 195.2, 172.3 and 125.4 days which are consistent with periods detected in several solar time series by several authors during different solar cycles. The knowledge relating to the origin of solar radius variations is not yet present. To see whether these variations will repeat in next cycles and to understand how the amplitudes of such variations change with different phases of the solar cycles, we need more systematic efforts and the long‐term homogeneous data. Since most of the periodicities detected in the present study are frequently seen in solar activity indicators, it is thought that the physical mechanisms driving the periodicities of solar activity may also be effective in solar radius variations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)