North-south distribution of solar flares during cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemispheres of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of the descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to the previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997–2000). The dominance of northern hemisphere shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.     

Quasi-Biennial Oscillations of Global Solar-Activity Indices

Quasi-biennial oscillations of solar activity are investigated using several global indices. The Singular Spectrum Analysis is used to separate out and study quasi-biennial oscillations; this method is one of the modifications of the main components method. The principal components of the solar cycle are stable 11-year, secular, and quasi-biennial variations. The periods and shapes of individual variations in each quasi-biennial train depend on the length and power of the particular 11-year cycle.     

Solar-Cycle Characteristics Examined in Separate Hemispheres: Phase,Gnevyshev Gap,and Length of Minimum

According to research results from solar-dynamo models, the northern and southern hemispheres may evolve separately throughout the solar cycle. The observed phase lag between the northern and southern hemispheres provides information regarding how strongly the hemispheres are coupled. Using hemispheric sunspot-area and sunspot-number data from Cycles 12 – 23, we determine how out of phase the separate hemispheres are during the rising, maximum, and declining period of each solar cycle. Hemispheric phase differences range from 0 – 11, 0 – 14, and 2 – 19 months for the rising, maximum, and declining periods, respectively. The phases appear randomly distributed between zero months (in phase) and half of the rise (or decline) time of the solar cycle. An analysis of the sunspot cycle double peak, or Gnevyshev gap, is conducted to determine if the double-peak is caused by the averaging of two hemispheres that are out of phase. We confirm previous findings that the Gnevyshev gap is a phenomenon that occurs in the separate hemispheres and is not due to a superposition of sunspot indices from hemispheres slightly out of phase. Cross hemispheric coupling could be strongest at solar minimum, when there are large quantities of magnetic flux at the Equator. We search for a correlation between the hemispheric phase difference near the end of the solar cycle and the length of solar-cycle minimum, but found none. Because magnetic flux diffusion across the Equator is a mechanism by which the hemispheres couple, we measured the magnetic flux crossing the Equator by examining Kitt Peak Vacuum Telescope and SOLIS magnetograms for Solar Cycles 21 – 23. We find, on average, a surplus of northern hemisphere magnetic flux crossing during the mid-declining phase of each solar cycle. However, we find no correlation between magnitude of magnetic flux crossing the Equator, length of solar minima, and phase lag between the hemispheres.     

Photospheric Magnetic Field: Relationship Between North–South Asymmetry and Flux Imbalance

Photospheric magnetic fields were studied using the Kitt Peak synoptic maps for 1976?–?2003. Only strong magnetic fields (B>100 G) of the equatorial region were taken into account. The north–south asymmetry of the magnetic fluxes was considered as well as the imbalance between positive and negative fluxes. The north–south asymmetry displays a regular alternation of the dominant hemisphere during the solar cycle: the northern hemisphere dominated in the ascending phase, the southern one in the descending phase during Solar Cycles 21?–?23. The sign of the imbalance did not change during the 11 years from one polar-field reversal to the next and always coincided with the sign of the Sun’s polar magnetic field in the northern hemisphere. The dominant sign of leading sunspots in one of the hemispheres determines the sign of the magnetic-flux imbalance. The sign of the north–south asymmetry of the magnetic fluxes and the sign of the imbalance of the positive and the negative fluxes are related to the quarter of the 22-year magnetic cycle where the magnetic configuration of the Sun remains constant (from the minimum where the sunspot sign changes according to Hale’s law to the magnetic-field reversal and from the reversal to the minimum). The sign of the north–south asymmetry for the time interval considered was determined by the phase of the 11-year cycle (before or after the reversal); the sign of the imbalance of the positive and the negative fluxes depends on both the phase of the 11-year cycle and on the parity of the solar cycle. The results obtained demonstrate the connection of the magnetic fields in active regions with the Sun’s polar magnetic field in the northern hemisphere.     

Multifractality as a Measure of Complexity in Solar Flare Activity

In this paper we use the notion of multifractality to describe the complexity in Hα flare activity during the solar cycles 21, 22, and 23. Both northern and southern hemisphere flare indices are analyzed. Multifractal behavior of the flare activity is characterized by calculating the singularity spectrum of the daily flare index time series in terms of the Hölder exponent. The broadness of the singularity spectrum gives a measure of the degree of multifractality or complexity in the flare index data. The broader the spectrum, the richer and more complex is the structure with a higher degree of multifractality. Using this broadness measure, complexity in the flare index data is compared between the northern and southern hemispheres in each of the three cycles, and among the three cycles in each of the two hemispheres. Other parameters of the singularity spectrum can also provide information about the fractal properties of the flare index data. For instance, an asymmetry to the left or right in the singularity spectrum indicates a dominance of high or low fractal exponents, respectively, reflecting a relative abundance of large or small fluctuations in the total energy emitted by the flares. Our results reveal that in the even (22nd) cycle the singularity spectra are very similar for the northern and southern hemispheres, whereas in the odd cycles (21st and 23rd) they differ significantly. In particular, we find that in cycle 21, the northern hemisphere flare index data have higher complexity than its southern counterpart, with an opposite pattern prevailing in cycle 23. Furthermore, small-scale fluctuations in the flare index time series are predominant in the northern hemisphere in the 21st cycle and are predominant in the southern hemisphere in the 23rd cycle. Based on these findings one might suggest that, from cycle to cycle, there exists a smooth switching between the northern and southern hemispheres in the multifractality of the flaring process. This new observational result may bring an insight into the mechanisms of the solar dynamo operation and may also be useful for forecasting solar cycles.     

Relative phase analyses of long-term hemispheric solar flare activity

Wavelet transform methods, including the continuous wavelet transform, cross-wavelet transform and wavelet coherence, have been proposed to investigate the phase synchrony of the monthly mean flare indices in the time interval 1966 January–2007 December in the solar northern and southern hemispheres, respectively. The Schwabe cycle is the only period of statistical significance, and its mean value is 10.7 yr for the monthly mean flare indices in the northern hemisphere but slightly smaller, 10.1 yr, in the southern hemisphere – this should lead to phase asynchrony between the two. Both the cross-wavelet transform and wavelet coherence analyses show asynchronous behaviour with strong phase mixing in the high-frequency components of hemispheric flare activity, and strong synchronous behaviour with coherent phase angles in the low-frequency components, corresponding to the period-scales around the Schwabe cycle. The northern flare activity should lead the southern for the low-frequency components.     

Solar-Cycle-Related Variations in the Solar Differential Rotation and Meridional Flow: A Comparison

We have analysed a large set of sunspot group data (1874 – 2004) and find that the meridional flow strongly varies with the phase of the solar cycle, and the variation is quite different in the northern and the southern hemispheres. We also find the existence of considerable cycle-to-cycle variation in the meridional velocity, and about a 11-year difference between the phases of the corresponding variations in the northern and the southern hemispheres. In addition, our analysis also indicates the following: (i) the existence of a considerable difference (about 180^°) between the phases of the solar-cycle variations in the latitude-gradient terms of the northern and the southern hemispheres’ rotations; (ii) the existence of correlation (good in the northern hemisphere and weak in the southern hemisphere) between the mean solar-cycle variations of meridional flow and the latitude-gradient term of solar rotation; (iii) in the northern hemisphere, the cycle-to-cycle variation of the mean meridional velocity leads that of the equatorial rotation rate by about 11 years, and the corresponding variations have approximately the same phase in the southern hemisphere; and (iv) the directions of the mean meridional velocity is largely toward the pole in the longer sunspot cycles and largely toward the equator in the shorter cycles.     

Variations of the Solar Differential Rotation Associated with Polarity Reversal

Variations of solar differential rotation have been studied using observations of solar quiescent Hα filaments obtained during 1965–1993 at the Abastumani Astrophysical Observatory. In both hemispheres of the Sun, propagation of a quasi-biennial pulse of residual rotation velocities of filaments was found. There is a pulse drift from high latitudes to the equator in the northern hemisphere in 1968–1970, 1979–1981, 1988–1990 and in the southern one in 1969–1971, 1979–1981, 1989–1991. Propagation of a pulse starts near the time of the polarity reversal of the circumpolar regions of the Sun. High-latitude double peaks of rapid motion were found in the northern hemisphere for cycle 20 and in the southern hemisphere for cycle 22. The relation of the appearance of suggested double pulse peaks of residual velocities with the threefold polarity changing of the circumpolar areas is suggested.     

Fluctuations of the Solar Dynamo Observed in the Solar Wind and Interplanetary Magnetic Field at 1 AU and in the Outer Heliosphere

Recent helioseismic observations have found strong fluctuations at a period of about 1.3 years in the rotation speed around the tachocline in the deep solar convection layer. Similar mid-term quasi-periodicities (MTQP; periods between 1–2 years) are known to occur in various solar atmospheric and heliospheric parameters for centuries. Since the deep convection layer is the expected location of the solar magnetic dynamo, its fluctuations could modulate magnetic flux generation and cause related MTQP fluctuations at the solar surface and beyond. Accordingly, it is likely that the heliospheric MTQP periodicities reflect similar changes in solar dynamo activity. Here we study the occurrence of the MTQP periodicities in the near and distant heliosphere in the solar wind speed and interplanetary magnetic field observed by several satellites at 1 AU and by four interplanetary probes (Pioneer 10 and 11 and Voyager 1 and 2) in the outer heliosphere. The overall structure of MTQP fluctuations in the different locations of the heliosphere is very consistent, verifying the solar (not heliospheric) origin of these periodicities. We find that the mid-term periodicities were particularly strong during solar cycle 22 and were observed at two different periods of 1.3 and 1.7 years simultaneously. These periodicities were latitudinally organized so that the 1.3-year periodicity was found in solar wind speed at low latitudes and the 1.7-year periodicity in IMF intensity at mid-latitudes. While all heliospheric results on the 1.3-year periodicity are in a good agreement with helioseismic observations, the 1.7-year periodicity has so far not been detected in helioseismic observations. This may be due to temporal changes or due to the helioseismic method where hemispherically antisymmetric fluctuations would so far have remained hidden. In fact, there is evidence that MTQP fluctuations may occur antisymmetrically in the northern and southern solar hemisphere. Moreover, we note that the MTQP pattern was quite different during solar cycles 21 and 22, implying fundamental differences in solar dynamo action between the two halves of the magnetic cycle.     

Phase Relationship Between Sunspot Number, Flare Index and Solar Radio Flux

To understand better the variation of solar activity indicators originated at different layers of the solar atmosphere with respect to sunspot cycles, we carried out a study of phase relationship between sunspot number, flare index and solar radio flux at 2800 MHz from January 1966 to May 2008 by using cross-correlation analysis. The main results are as follows: (1) The flare index and sunspot number have synchronous phase for cycles 21 and 22 in the northern hemisphere and for cycle 20 in the southern hemisphere. (2) The flare index has a noticeable time lead with respect to sunspot number for cycles 20 and 23 in the northern hemisphere and for cycles 22 and 23 in the southern hemisphere. (3) For the entire Sun, the flare index has a noticeable time lead for cycles 20 and 23, a time lag for cycle 21, and no time lag or time lead for cycle 22 with respect to sunspot number. (4) The solar radio flux has a time lag for cycles 22 and 23 and no time lag or time lead for cycles 20 and 21 with respect to sunspot number. (5) For the four cycles, the sunspot number and flare index in the northern hemisphere are all leading to the ones in the southern hemisphere. These results may be instructive to the physical processes of flare energy storage and dissipation.     

The Relative Phase Asynchronization between Sunspot Numbers and Polar Faculae

The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astronomical Observatory of Japan, for the interval of March 1954 to March 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar disk and for both hemispheres in solar cycles 19, 20, 21 and 22. We found that (1) the polar faculae begin earlier than sunspot activity, and the phase difference exhibits a consistent behaviour for different hemispheres in each of the solar cycles, implying that this phenomenon should not be regarded as a stochastic fluctuation; (2) the inverse correlation between polar faculae and sunspot numbers is not only a long-term behaviour, but also exists in short time range; (3) the polar faculae show leads of about 50–71 months relative to sunspot numbers, and the phase difference between them varies with solar cycle; (4) the phase difference value in the northern hemisphere differs from that in the southern hemisphere in a solar cycle, which means that phase difference also existed between the two hemispheres. Moreover, the phase difference between the two hemispheres exhibits a periodical behaviour. Our results seem to support the finding of Hiremath (2010).     

Solar-cycle Time Delay of Rotating Sunspots

As shown by statistical results, in the 23rd solar activity cycle the variation of the latitudes of rotating sunspots with time exhibits a butterfly pattern. We have studied the variations with phase for the mean square errors among the 4 fitting curves of the 2 wings of the butterfly diagram of sunspots and the 2 wings of the butterfly diagram of rotating sunspots in the 23rd solar activity cycle. The results show that a systematic time delay exists not only between the northern and southern hemispheres of the butterfly diagram of sunspots, but also between the northern and southern hemispheres of the butterfly diagram of rotating sunspots, even between the butterfly diagrams of the sunspots and rotating sunspots in the same hemisphere. This means that the 23rd-cycle sunspot activities in the northern and southern hemispheres happened not simultaneously, that a systematic time delay or advance (phase difference) exists between the northern and southern hemispheres, that the southern hemisphere lags behind the northern hemisphere, that a phase difference exists between the butterfly diagram of rotating sunspots and the butterfly diagram of sunspots in the 23rd cycle, and that the butterfly diagram of rotating sunspots lags behind that of sunspots. The observed delay is a little less than the theoretical value predicted by the dynamo model.     

Rhythm of physical sunspot cycles

The time series of the relative sunspot number is interpreted as a sequence of physical cycles of sunspot activity overlapping in the minimum. The cycle periodicity, i.e., the time interval between neighboring cycles, can be considered as a quantitative characteristic of the sequence. Estimates of this interval have been obtained for 11 and 22-year cycles. In the growth phase and in the century cycle maximum, the 22-year cycles follow one another with an interval of 21 ± 0.4 years, and in the decline phase, 23 ± 0.3 years. This division of intervals into two groups depending on the century cycle phase should be taken into consideration when developing a theory of solar activity cycles.     

On Mid-Term Periodicities in Sunspot Groups and Flare Index

In this work we study the mid-term periodicities (MTPs), between 1 and 2 years, of the sunspot groups and the flare index (FI), by separating the data into hemispheres and spectral bands (SBs) according to the most significant periodicities presented by these phenomena. We found that the MTP of sunspot groups has a diminished power during the Modern Minimum and an increased power during the Modern Maximum, with the exception of cycle 20. For flares, the MTP has a diminished power during the low activity cycle 20, and an increased power during cycles 21 and 22. Therefore, for both sunspot groups and FI, cycle 20 shows a very diminished power followed by the active and higher-power cycles 21 and 22; cycle 23 shows a weaker power than cycles 21 and 22. It is uncertain whether MTP can be a precursor of a long-term minimum of solar activity or not, as has been previously suggested. Also, there is no one-to-one correlation between the cycle intensity and the importance of MTP. Concerning the quasi-biennial periodicities and the theory of two kinds of dynamos, we notice the tendency that higher-power cycles mean weaker coupling in the model. Concerning the hemispheric north-south asymmetry, for sunspot groups the southern hemisphere dominates in most of the SBs, while for FI the northern hemisphere dominates for all the SBs. Additionally, the time lag found between the two hemispheres indicates that the degrees of coupling in the photosphere for sunspot groups and in the corona for flares are between moderate and strong. Finally, the modulation shown by the MTP time series suggests that these periodicities are the product of chaotic quasi-periodic processes and not of stochastic processes.     

Periodicity and Hemispheric Phase Relationship in High-Latitude Solar Activity

The counts of the monthly averaged polar faculae, from observations of the National Astronomical Observatory of Japan (NAOJ), are examined by using linear and nonlinear approaches to find the periodicity characteristics of the polar faculae in the northern and southern hemispheres and the phase relationship between them. Both the cross-wavelet transform (XWT) and wavelet coherence (WTC) indicate the prominent period with 95% confidence level, namely the Schwabe cycle of about 11 years. The Schwabe cycle is in phase in the two hemispheres. Within the 11-year frequency band, there is a small phase difference during the period of 1966 – 1975 when the activity of polar faculae in the northern hemisphere slightly leads the one in the southern hemisphere. A cross-recurrence plot analysis and the line of synchronization (LOS) extracted from the cross-recurrence plot show further the phase difference between the two hemispheres. The LOS deviates significantly from the main diagonal during the period of 1965 – 1970 and LOS >0, showing that the activity of polar faculae in the northern hemisphere leads in phase, which is in accordance with XWT and WTC analyses. Moreover, asynchronization is highest (about 30 months) during this period.     

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.     

Large-Scale Structure of the Sunspot Activity and the Background Magnetic Field Formation

Large-scale distribution of the sunspot activity of the Sun has been analyzed by using a technique worked out previously (Erofeev, 1997) to study long-lived, non-axisymmetric magnetic structures with different periods of rotation. Results of the analysis have been compared with those obtained by analyzing both the solar large-scale magnetic field and large-scale magnetic field simulated by means of the well-known flux transport equation using the sunspot groups as a sole source of new magnetic flux in the photosphere. A 21-year period (1964–1985) has been examined.The rotation spectra calculated for the total time interval of two 11-year cycles indicate that sunspot activity consists of a series of discrete components (modes) with different periods of rotation. The largest-scale component of the sunspot activity reveals modes with 27-day and 28-day periods of rotation situated, correspondingly, in the northern and southern hemispheres of the Sun, and two modes with rotation periods of about 29.7 days situated in both hemispheres. Such a modal structure of the sunspot activity agrees well with that of the large-scale solar magnetic field. Moreover, the magnetic field distribution simulated with the flux transport equation also reveals the same modal structure. However, such an agreement between the large-scale solar magnetic field and both the sunspot activity and simulated magnetic field is unstable in time; so, it is absent in the northern hemisphere of the Sun during solar cycle No. 20. Thus the sources of magnetic flux responsible for formation of the large-scale, rigidly rotating magnetic patterns appear to be closely connected, but are not identical with the discrete modes of the sunspot activity.     

The hemispheric variation of the flare index during solar cycles 20–23

In this paper, the monthly counts of flare index in the northern and southern hemispheres are used to investigate the hemispheric variation of the flare index in each of solar cycles 20–23. It is found that, (1) the flare index is asymmetrically distributed in each solar cycle and its asymmetry is a real phenomenon; (2) the flare index in the northern hemisphere begins earlier than that in the southern hemisphere in each of solar cycles 20–23, and the phase shifts between the two hemispheres show an odd‐even pattern; (3) although the flare index dominating in a hemisphere does not mean that it leads in phase in this hemisphere in individual solar cycle, these two features have an intrinsic relationship. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Use of ground-based coronal data to predict the date of solar-cycle maximum

Prediction of the exact date of the maximum of the 11-year solar activity cycle is a matter of disagreement among solar scientists and of some importance to satellite operators, space-system designers, etc. Most predictions are based on physical conditions occurring at or before the solar-cycle minimum preceding the maximum in question. However, another indicator of the timing of the maximum occurs early in the rise phase of the solar cycle. A study of the variation over two previous solar cycles of coronal emission features in Fe xiv from the National Solar Observatory at Sacramento Peak has shown that, prior to solar maximum, emission features appear above 50° latitude in both hemispheres and begin to move towards the poles at a rate of 8° to 11° of latitude per year. This motion is maintained for a period of 3 or 4 years, at which time the emission features disappear near the poles. This phenomenon has been referred to as the `Rush to the Poles'. These observations show that the maximum of solar activity, as seen in the sunspot number, occurs approximately 19 ± 2 months before the features reach the poles. In 1997, Fe xiv emission features appeared near 55° latitude, and began to move towards the poles. Using the above historical data from cycles 21 and 22, we will see how the use of progressively more data from cycle 23 affects the prediction of the date of solar maximum. The principal conclusion is that the date of solar maximum for cycle 23 could be predicted to within 6 months as early as 1997. For solar cycle 24, when this phenomenon first becomes apparent later this decade, the average parameters for cycles 21–23 can be used to predict the date of solar maximum.