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.     

Solar Rotation Rate during Solar Activity Cycle 23

We studied the solar rotation rate and its temporal change, using the sunspot data obtained during activity cycle 23 (1996 – 2006). The equatorial rotation rate is nearly the same as in the former cycle 22, while the latitudinal gradient of differential rotation considerably increased. Comparison of our results with others indicates the existence of a long-term periodicity of about eight cycles in differential rotation. In addition, no significant asymmetry in differential rotation between the northern and southern hemispheres during cycle 23 was found. The equatorial rotation rate and the latitudinal gradient of the differential rotation in the period of cycle 23 are approximately constant, except for the initial and final phases in the cycle.     

A statistical study of the spiral spots on the solar disc

After adding the data observed in the years from 1979 to 1982 to those obtained earlier (Ding et al., 1981), we re-examine the previous results and conclude:

1. The longitudinal distribution of spiral spots on the solar disc is generally the same as that of sunspot groups with areas of S _p ≥ 400, but their active longitudes seem to be more concentrated.
2. The distribution of spiral patterns in the southern and northern hemispheres shows that the differential rotation may be a fundamental solar dynamo for the formation of the spiral spots.
3. The statistical directions of the emerging twisted magnetic vectors in the active regions in the southern and northern hemispheres are synchronously inverse with a period of about two years. This period seems to be detected in other solar observations.

     

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.     

Small-scale background magnetic field on the sun in solar cycle 23

Based on SOHO/MDI data (an archive of magnetic maps with a resolution of ～2″), we have investigated the dynamics of the small-scale background magnetic field on the Sun in solar cycle 23. The cyclic variations and surface structure of the background magnetic field have been analyzed using the mean estimates of 〈B〉 and 〈B ²〉 of the observed magnetic field strength B for various solar surface areas and at various B levels. We have established that the cyclic variations of 〈2〉 at latitudes below 30° are essentially similar to those of the total radio flux F _10.7. A significant difference between the background magnetic fields in the northern and southern solar hemispheres persisting throughout the solar cycle has been detected. We have found the effect of background magnetic field growth toward the solar limb and concluded that the transversal component in the background magnetic field is significant. The relatively weak small-scale background magnetic fields are shown to form a special population with its own special laws of cyclic variation.     

Systematic Time Delay of Hemispheric Solar Activity

Five solar-activity indices – the monthly-mean sunspot numbers from January 1945 to March 2008, the monthly-mean sunspot areas during the period of May 1874 to March 2008, the monthly numbers of sunspot groups from May 1874 to May 2008, the monthly-mean flare indices from January 1966 to December 2006, and the numbers of solar filaments per Carrington rotation in the time interval of solar rotations 876 to 1823 – have been used to show a systematic time delay between northern and southern hemispheric solar activities in a cycle. It is found that solar activity does not occur synchronously in the northern and southern hemispheres, and there is a systematic time lag or lead (phase shift) between northern and southern hemispheric solar activity in a cycle. About an eight-cycle period is inferred to exist in such phase shifts. The activity on the Sun may be governed by two different and coupled processes, not by a single process.     

Seasonal changes on Jupiter: 2. Influence of the planet exposure to the Sun

From our investigation of the behavior of changes in the visible brightness of Jupiter observed since 1850, it follows that the 22.3-year Hale magnetic cycle of solar activity produces the dominating influence on the processes taking place in the troposphere at a level of forming the upper boundary of clouds. The maximum values of the integral brightness of Jupiter fall on the solar cycle with the highest value of the Wolf number for the last 165 years (around 1957). The lowest estimates of brightness were obtained in 1855, when the Wolf number in the 12th solar-activity cycle was smallest. The analysis of the reflectance of Jupiter’s hemispheres in the visible spectral range for 1962–2015 revealed the alternating increase in the brightness of southern and northern tropical and middle regions for one rotation period of Jupiter about the Sun. Such a change in brightness and the increase in the activity of different hemispheres of the planet may indicate the periodic global alteration in the circulation system, the structure of cloud layers, and the overcloud haze. This suggests the interrelation between the observed variations in the reflectance of the considered latitudinal belts of Jupiter and the change in the axial tilts of the planet itself and its magnetic field to the orbital plane, i.e., the seasonal alteration in the atmosphere. The comparison of the temporal dependence of the activity factor A _j of the Jovian hemispheres in the visible spectral range with the change in the solar-activity index R shows that, from 1962 to 1995, these parameters almost synchronously changed, though the response of the visible cloud layer somewhat lagged behind the regime of exposure of the atmosphere to the Sun. The analysis shows that, when the planet is moving along the orbit, the reflectance of Jupiter’s hemispheres varies in response to the 21-percent change in the exposure of different hemispheres with a lag of 6 years. Such a lag coincides with the radiation- relaxation time of the hydrogen–helium atmosphere under the Jovian conditions. Desynchronization in their behavior that occurred after 1997 may be explained by the unbalanced influence of the three mentioned causes on the atmosphere of the planet.     

North – South Asymmetry of Zonal and Meridional Flows Determined From Ring Diagram Analysis of Gong ++ Data

We study the North–South asymmetry of zonal and meridional components of horizontal, solar subsurface flows during the years 2001–2004, which cover the declining phase of solar cycle 23. We measure the horizontal flows from the near-surface layers to 16 Mm depth by analyzing 44 consecutive Carrington rotations of Global Oscillation Network Group (GONG) Doppler images with a ring-diagram analysis technique. The meridional flow and the errors of both flow components show an annual variation related to the B ₀-angle variation, while the zonal flow is less affected by the B ₀-angle variation. After correcting for this effect, the meridional flow is mainly poleward but it shows a counter cell close to the surface at high latitudes in both hemispheres. During the declining phase of the solar cycle, the meridional flow mainly increases with time at latitudes poleward of about 20^˚, while it mainly decreases at more equatorward latitudes. The temporal variation of the zonal flow in both hemispheres is significantly correlated at latitudes less than about 20^˚. The zonal flow is larger in the southern hemisphere than the northern one, and this North–South asymmetry increases with depth. Details of the North–South asymmetry of zonal and meridional flow reflect the North–South asymmetry of the magnetic flux. The North–South asymmetries of the flows show hints of a variation with the solar cycle.     

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.     

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.     

North–south asymmetry of different solar activity features during solar cycle 23

A study on north–south (N–S) asymmetry of different solar activity features (DSAF) such as solar proton events, solar active prominences [total, low (?40°) and high (?50°) latitudes], Hα flare indices, soft X-ray flares, monthly mean sunspot areas and monthly mean sunspot numbers carried out from May 1996 to October 2008. Study shows a southern dominance of DSAF during this period. During the rising phase of the cycle 23 the number of DSAF approximately equals on both, the northern and the southern hemispheres. But these activities tend to shift from northern to southern hemisphere during the period 1998–1999. The statistical significance of the asymmetry time series using a χ²-test of goodness of fit indicates that in most of the cases the asymmetry is highly significant, meaning thereby that the asymmetry is a real feature in the N–S distribution of DSAF.     

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)     

Distribution of latitudes and speeds of Coronal Mass Ejections in the northern and southern hemispheres in cycle 23

Distribution of latitudes and speeds of Coronal Mass Ejections (CMEs) in the northern and southern hemispheres in cycle 23, from September 1996 to December 2006, have been analyzed. By calculating the actual probability of the hemispheric distribution of the activity of the CME, we find that a southern dominance of the activity of the CME is shown to occur in cycle 23 from September 1996 to December 2006. The CME activity occurs at all latitudes and is most common at low latitudes. This should furnish evidence to support that CMEs are associated with source magnetic structures on a large spatial scale, even with transequatorial source magnetic structures on a large spatial scale. The latitudinal distribution of CMEs in the northern and southern hemispheres are no different from a statistical point of view. The speed distribution in the northern and southern hemispheres are nearly identical and to a good approximation they can be fitted with a single lognormal distribution. This finding implies that, statistically, there is no physical distinction between the CME events in the southern and northern hemispheres and the same mechanism of a nonlinear nature acting in both the CME events in the northern and southern hemispheres. Our conclusions seem to suggest that the northern-southern asymmetry of the CME events is related to the northern-southern asymmetry in solar dynamo theory (Jiang et al. 2007).     

The peculiarities of rotation of the solar polar regions

The sidereal rotation rate of the high-latitude solar regions is examined using long-lived photospheric polar faculae. The observations were carried out with the photoheliograph of Kislovodsk Mountain Station of the Pulkovo Observatory from 1982 to 1986. The following facts have been established: (a) There is a differential rotation of the polar faculae close to the maximum of solar activity, while the amount of latitude gradient of solar rotation decreases towards the sunspot minimum; (b) small differences of rotation in the northern and southern hemispheres of the Sun are observed; (c) some deviations of differential rotation curves constructed for each Carrington rotation from the mean curve of differential rotation are revealed. The total amplitude of the maximum positive and negative excesses is about 40–50 m s^–1. The positive surplus velocities of solar rotation (the amplitude of which is about 20–25 m s^–1) move in the form of a wave from heliographic latitudes 40° with a velocity of 1.6 m s^–1. The latitude width of this flow is B 15°. This wave of abnormally high velocity starts in the year of minimum solar activity and reaches the pole 11 years later. The picture is symmetrical relative to the equator.     

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).     

N–S Asymmetry in the Solar Differential Rotation During 1957–1993

The properties of the differential rotation of the Sun are investigated by using H filaments as tracers. Annual average angular velocities of 716 quiescent filaments are determined from H photoheliograms of the Abastumani Astrophysical Observatory film collection for the years 1957–1993. The existence of north-south (N–S) asymmetry in H filaments rotation is confirmed statistically. The connection of asymmetry with the solar activity cycles is established. It is found that the northern hemisphere rotates faster during the even cycles (20 and 22) while the rotation of southern hemisphere dominates in odd ones (cycles 19 and 21). The mechanism of the solar activity should be responsible for the N–S asymmetry of the solar differential rotation. A theoretical explanation for the N–S asymmetry in the Suns rotation is offered. It is suggested that the asymmetry in the rotation of the two hemispheres of the Sun is balanced by the dynamo mechanism, which acts in parallel to the mechanism offered here. It is concluded that the N–S asymmetry of the solar rotation should cause a difference in activity level between the northern and southern hemispheres.     

Long-Term Variations in the Solar Differential Rotation

Using Greenwich data (1879–1976) and SOON/NOAA data (1977–2002) on sunspot groups we found the following results: (i) The Sun's mean (over all the concerned cycles during 1879–1975) equatorial rotation rate (A) is significantly larger (≈0.1%) in the odd-numbered sunspot cycles (ONSCs) than in the even-numbered sunspot cycles (ENSCs). The mean rotation is significantly (≈10%) more differential in the ONSCs than in the ENSCs. North–south difference in the mean equatorial rotation rate is larger in the ONSCs than in the ENSCs. North–south difference in the mean latitude gradient of the rotation is significant in the ENSCs and insignificant in the ONSCs. (ii) The known very large decrease in A from cycle 13 to cycle 14 is confirmed. The amount of this decrease in the mean A was about 0.017 μrad s⁻¹. Also, we find that A decreased from cycle 17 to cycle 18 by about 0.008 μrad s⁻¹ and from cycle 21 to cycle 22 by about 0.016 μrad s⁻¹. From cycle 13 to cycle 14 the decrease in A was more in the northern hemisphere than in the southern hemisphere, it is opposite in the later two epochs. The time gap between the consecutive drops in A is about 44 years, suggesting the existence of a `44-yr' cycle or `double Hale cycle' in A. The time gap between the two large drops, viz., from cycle 13 to cycle 14 and from cycle 21 to cycle 22, is about 90 years (Gleissberg cycle). We predict that the next drop (moderate) in A will be occurring from cycle 25 to cycle 26 and will be followed by a relatively large-amplitude `double Hale cycle' of sunspot activity. (iii) Existence of a 90-yr cycle is seen in the cycle-to-cycle variation of the latitude gradient (B). A weak 22-yr modulation in B seems to be superposed on the relatively strong 90-yr modulation. (iv) The coefficient A varies significantly only during ONSCs and the variation has maximum amplitude in the order of 0.01 μrad s<sup>−1</sup> around activity minima. (v) There exists a good anticorrelation between the mean variation of B during the ONSCs and that during the ENSCs, suggesting the existence of a `22-yr' periodicity in B. The maximum amplitude of the variation of B is of the order of 0.05 μrad s⁻¹ around the activity minima. (vi) It seems that the well-known Gnevyshev and Ohl rule of solar activity is applicable also to the cycle-to-cycle amplitude modulation of B from cycle 13 to cycle 20, but the cycles 12 (in the northern hemisphere, Greenwich data) and 21 (in both hemispheres, SOON/NOAA data) seem to violate this rule in B. And (vii) All the aforesaid statistically significant variations in A and B seem to be related to the approximate 179-yr cycle, 1811–1989, of variation in the Sun's motion about the center of mass of the solar system.     

Non-Axisymmetric Magnetic Fields and Flip-Flops on the Sun and Cool Stars

The modulation of solar activity closely follows the solar rotation period suggesting the existence of long-lived active regions at preferred longitudes. For instance, two preferred active longitudes in both southern and northern hemispheres are found to be persistent at the century time scale. These regions migrate with differential rotation and periodically alternate their activity levels showing a flip-flop cycle. The pattern and behaviour of active longitudes on the Sun is similar to that on cool, rapidly rotating stars with outer convective envelopes. This suggests that the magnetic dynamo, including non-axisymmetric magnetic fields and flip-flop cycles, is also similar in these stars. This allows us to overview the phenomenon of stellar magnetic activity and to study it in detail on the Sun.     

Solar rotation during the Maunder Minimum

We have measured solar surface rotation from sunspot drawings made in a.d. 1642–1644 and find probable differences from present-day rates. The 17th century sunspots rotated faster near the equator by 3 or 4%, and the differential rotation between 0 and ±20° latitude was enhanced by about a factor 3. These differences are consistent features in both spots and groups of spots and in both northern and southern hemispheres. We presume that this apparent change in surface rotation was related to the ensuing dearth of solar activity (the Maunder Minimum) which persisted until about 1715.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Coronal Holes and Open Magnetic Flux over Cycles 23 and 24

As the observational signature of the footprints of solar magnetic field lines open into the heliosphere, coronal holes provide a critical measure of the structure and evolution of these lines. Using a combination of Solar and Heliospheric Observatory/Extreme ultraviolet Imaging Telescope (SOHO/EIT), Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA), and Solar Terrestrial Relations Observatory/Extreme Ultraviolet Imager (STEREO/EUVI A/B) extreme ultraviolet (EUV) observations spanning 1996?–?2015 (nearly two solar cycles), coronal holes are automatically detected and characterized. Coronal hole area distributions show distinct behavior in latitude, defining the domain of polar and low-latitude coronal holes. The northern and southern polar regions show a clear asymmetry, with a lag between hemispheres in the appearance and disappearance of polar coronal holes.