Group Sunspot Numbers: Sunspot Cycle Characteristics

We examine the `Group' sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group sunspot numbers to Zürich (International) sunspot numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zürich numbers follow the 10.7-cm radio flux and total sunspot area measurements only slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zürich numbers. We find that the `Waldmeier Effect' – the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle – is much more apparent in the Zürich numbers. The `Amplitude–Period Effect' – the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum – is also much more apparent in the Zürich numbers. The `Amplitude–Minimum Effect' – the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zürich numbers and the Group numbers. The `Even–Odd Effect' – in which odd-numbered cycles are larger than their even-numbered precursors – is somewhat stronger in the Group numbers but with a tighter relationship in the Zürich numbers. The `Secular Trend' – the increase in cycle amplitudes since the Maunder Minimum – is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80-year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zürich numbers are slightly more useful for characterizing the on-going levels of solar activity.     

Solar differential rotation derived from sunspot observations

Sunspot drawings obtained at National Astronomical Observatory of Japan during the years 1954–1986 were used to determine the differential rotation of the Sun. From the limited data set of three solar cycles it was found that three factors (the level of cycle activity, the cycle phase, and sunspot type) affect the solar rotation rate. The differential rotation varies from cycle to cycle in such a way that the rotation velocity in the low activity cycle (cycle 20) is higher than in the high-activity cycle (cycle 19). The equatorial rotation rate shows a systematic variation within each cycle. The rate is higher at the beginning of the cycle and decreases subsequently. Although quite small, the variation of solar differential rotation with respect to Zürich sunspot type was found. The H and J types show the slowest rotation among all the sunspot types.     

10.7-cm Solar radio flux and the magnetic complexity of active regions

During sunspot cycles 20 and 21, the maximum in smoothed 10.7-cm solar radio flux occurred about 1.5 yr after the maximum smoothed sunspot number, whereas during cycles 18 and 19 no lag was observed. Thus, although 10.7-cm radio flux and Zürich suspot number are highly correlated, they are not interchangeable, especially near solar maximum. The 10.7-cm flux more closely follows the number of sunspots visible on the solar disk, while the Zürich sunspot number more closely follows the number of sunspot groups. The number of sunspots in an active region is one measure of the complexity of the magnetic structure of the region, and the coincidence in the maxima of radio flux and number of sunspots apparently reflects higher radio emission from active regions of greater magnetic complexity. The presence of a lag between sunspot-number maximum and radio-flux maximum in some cycles but not in others argues that some aspect of the average magnetic complexity near solar maximum must vary from cycle to cycle. A speculative possibility is that the radio-flux lag discriminates between long-period and short-period cycles, being another indicator that the solar cycle switches between long-period and short-period modes.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

Sunspot turning-points and aurorae since A.D. 1510

Dates of solar maxima and minima extending back to c. 1610 were estimated by Wolf and Wolfer at Zürich (Waldmeier, 1961) in the nineteenth century, and those back to c. 1710 have been generally accepted. Slight modifications have already been suggested by the author (Schove, 1967) for the seventeenth century, although, in that century, even the existence of the eleven-year cycle has been questioned (Eddy, 1976). In the course of any sunspot cycle we find a pattern of the aurorae in place and time characteristic of sunspot cycles of the particular amplitude-class. These patterns since c. 1710 can be linked to the precise dates of the Zürich turning-points by a set of empirical rules. A sunspot rule is based on the Gnevyshev gap, the gap in large sunspots near the smoothed maximum. These rules are here applied to the period c. 1510–1710 to give improved determination of earlier turning-points, and approximately confirm the dates given for the seventeenth century by Wolfer and for most of the later sixteenth century by Link (1978). Some turning-points for the fifteenth century and revised sunspot numbers for the period 1700–48 are also given.     

A possible relationship between spectral bands in sunspot number and the space-time organization of our planetary system

For the particular purpose of this paper, Zürich relative sunspot numbers of the time spans 1749–1982, 1749–1865, and 1866–1982, have been analysed anew by two different methos. It is shown that the spectral bands in the power spectra of sunspot numbers between 1 and 234 years obtained from these analyses can be clearly related to the modified configuration frequencies of the giant planets and their harmonics. In particular, the clearly dominant spectral band in sunspot number, the solar cycle of 10.8 years, is given by the configuration period of Jupiter and Saturn (19.859 yr) times the ratio of their distances from the Sun (0.545).     

On the R z -sunspot relative number variations

The Zürich sunspot relative number R _z series has been analysed by the cyclogram method. The amplitude and the frequency variations of the Fourier 11 yr component between 1700–1983 A.D., were determined in a continuous way.Four distinct time intervals with significantly different characteristics of the periodicities are observed and discussed.Their second harmonics are also considered. The periodicity changes are contemporary to those of the 11 yr cycles.Around the year 1903 it seems that an important event has happened in the Sun. In fact the 11.4 yr cycle periodicity, that was very stable since at least 1825 started to change gradually to smaller values and similarly it happened to the second harmonic which also stopped and abruptly changed of phase of 90°.     

Variations in the solar rotation rate derived from Ca+ K plage areas

Daily calcium plage areas for the period 1951–1981 (which include the solar cycle 19 and 20) have been used to derive the rotation period of the Sun at latitude belts 10–15 ° N, 15–20 ° N, 10–15 ° S, and 15–20 ° S and also for the entire visible solar disk. The mean rotation periods derived from 10–20 ° S and N, total active area and sunspot numbers were 27.5, 27.9, and 27.8 days (synodic), respectively. A power spectral analysis of the derived rotation rate as a function of time indicates that the rotation rate in each latitude belt varies over time scales ranging from the solar activity cycle, down to about 2 years. Variations in adjacent latitude belts are in phase, whereas those in different hemispheres are not correlated. The rotation rates derived from sunspot numbers also behave similarly though the dependence over the solar cycle are not very apparent. The total plage areas, integrated over the entire visible hemisphere of the Sun shows a dominant periodicity of 7 years in rotation rate, while the other time scales are also discernible.     

Fitting the sunspot cycles 10–21 by a modified F-distribution density function

It has been found that sunspot cycles 10–21, represented by quarterly mean values of Zürich sunspot number, can be suitably described by the F-distribution density function provided it is modified by introducing five characteristic parameters, in order to achieve an optimal fitting of each cycle. The average cycle calculated from cycles 10–21 has been used as a basis to forecast time and magnitude of the maximum of each cycle, as a function of various numbers of the first quarterly mean values in the beginning N = 8 to 16 quarters. The standard deviations at a 99% significance level calculated from the observed values depend on N, and vary from 1.6 to 1.1 quarters and 65 to 16 units of sunspot number. A rather sufficient forecast is obtained from N = 12 quarters (with inaccuracy of ± 1.5 quarters and ± 24 units); the forecast for cycle 22 yielded, for N = 12, the values t _m = (15.4 ± 1.5) quarters ( 1990.I) and f(t _m ) = (175 ±24 units).     

A new pattern for the north–south asymmetry of sunspots

We study the solar cycle evolution during the last 8 solar cycles using a vectorial sunspot area called the LA (longitudinal asymmetry) parameter. This is a useful measure of solar activity in which the stochastic, longitudinally evenly distributed sunspot activity is reduced and which therefore emphasizes the more systematic, longitudinally asymmetric sunspot activity. Interesting differences are found between the LA parameter and the more conventional sunspot activity indices like the (scalar) sunspot area and the sunspot number. E.g., cycle 19 is not the highest cycle according to LA. We have calculated the separate LA parameters for the northern and southern hemisphere and found a systematic dipolar-type oscillation in the dominating hemisphere during high solar activity times which is reproduced from cycle to cycle. We have analyzed this oscillation during cycles 16–22 by a superposed epoch method using the date of magnetic reversal in the southern hemisphere as the zero epoch time. According to our analysis, the oscillation starts by an excess of the northern LA value in the ascending phase of the solar cycle which lasts for about 2.3 years. Soon after the maximum northern dominance, the southern hemisphere starts dominating, reaching its minimum some 1.2–1.7 years later. The period of southern dominance lasts for about 1.6 years and ends, on an average, slightly before the end of magnetic reversal.     

Periodic variation of the north-south asymmetry of solar activity phenomena

We report here a study of various solar activity phenomena occurring in both north and south hemispheres of the Sun during solar cycles 8–23. In the study we have used sunspot data for the period 1832–1976, flare index data for the period 1936-1993, Hα flare data 1993–1998 and solar active prominences data for the period 1957–1998. Earlier Verma reported long-term cyclic period in N-S asymmetry and also that the N-S asymmetry of solar activity phenomena during solar cycles 21, 22, 23 and 24 will be south dominated and the N-S asymmetry will shift to north hemisphere in solar cycle 25. The present study shows that the N-S asymmetry during solar cycles 22 and 23 are southern dominated as suggested by Verma.     

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.     

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.     

On the use of ‘first spotless day’ as a predictor for sunspot minimum

Defining the first spotless day of a sunspot cycle as the first day without spots relative to sunspot maximum during the decline of the solar cycle, one finds that the timing of that occurrence can be used as a predictor for the occurrence of solar minimum of the following cycle. For cycle 22, the first spotless day occurred in April 1994, based on the International sunspot number index, although other indices (Boulder and American) indicated the first spotless day to have occurred earlier (September 1993). For cycles 9–14, sunspot minimum followed the first spotless day by about 72 months, having a range of 62–82 months; for cycles 15–21, sunspot minimum followed the first spotless day by about 35 months, having a range of 27–40 months. Similarly, the timing of first spotless day relative to sunspot minimum and maximum for the same cycle reveals that it followed minimum (maximum) by about 69 (18) months during cycles 9–14 and by about 90 (44) months during cycles 15–21. Accepting April 1994 as the month of first spotless day occurrence for cycle 22, one finds that it occurred 91 months into the cycle and 57 months following sunspot maximum. Such values indicate that its behavior more closely matches that found for cycles 15–21 rather than for cycles 9–14. Therefore, one infers that sunspot minimum for cycle 23 will occur in about 2–3 years, or about April 1996 to April 1997. Accepting the earlier date of first spotless day occurrence indicates that sunspot minimum for cycle 23 could come several months earlier, perhaps late 1995.The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

The north-south asymmetry of sunspot areas during solar cycle 22

We have analyzed the asymmetry of sunspot areas during the current solar cycle 22, finding that it has been statistically significant and that the shape of the underlying trend within the full asymmetry time series (1874–1993) indicates that the dominance of solar activity has started to shift, during the current cycle, from the northern hemisphere to the southern one.     

Solar neutrino in relation to solar activity

Here we have carried out a power-spectrum analysis of solar nuclear gamma-ray (NGR) flares observed by SMM and HINOTORI satellites. The solar NGR flares show a periodicity of 152 days, confirming the existence of a 152–158 days periodicity in the occurrence of solar activity phenomena and also indicating that the NGR flares are a separate class of solar flares. The power-spectrum analysis of the daily sunspot areas on the Sun for the period 1980–1982 shows a peak around 159 days while sunspot number data do not show any periodicity (Verma and Joshi, 1987). Therefore, only sunspot area data should be treated as an indicator of solar activity and not the daily sunspot number data.     

Preferred longitudes of sunspot groups and high-speed solar wind streams: Evidence for a ‘solar memory’

Correlation analysis of the mean longitude distribution of sunspot groups (taken from the Greenwich Photoheliographic Results) and high-speed solar wind streams (inferred from the C9 index for geomagnetic disturbances) with the Bartels rotation period P = 27.0 days shows anti-correlation for individual cycles.In particular, the longitudes of post-maximum stable streams of cycle 18 and 19 are well anticorrelated with the preferred longitudes of sunspot groups during the maximum activity periods of these cycles. This is further analyzed using the daily Zürich sunspot number, R, between 1932 and 1980, which reveals a conspicuous similarity of cycle 18 and 19 as well as cycle 20 and 21.We conclude that there is a solar memory for preferred longitudes of activity extending at least over one, probably two cycles (i.e. one magnetic cycle of 22 years). We conjecture that this memory extends over longer intervals of time as a long-term feature of solar activity.     

Do polar faculae on the sun predict a sunspot cycle?

The paper reports the results of the analysis of the data on polar faculae for three solar cycles (1960–1986) at the Kislovodsk Station of the Pulkovo Observatory and on polar bright points in Ca ii K line for two solar cycles (1940–1957) at the Kodaikanal Station of the Indian Institute of Astrophysics. We have noticed that the monthly numbers of polar faculae and polar bright points in Ca ii K line and monthly sunspot areas in each hemisphere of the following solar cycle have a correlation with each other. A new cycle of polar faculae and polar bright points in the Ca ii K line begins after the polar magnetic field reversal. We find that the smaller the period between the ending of the polar field reversal and the beginning of a new sunspot cycle is, the more intense is the cycle itself. The intensity of the forthcoming solar cycle (cycle 22) and the periods of strong fluctuations in activity expected in this cycle are also discussed.     

Relative sunspot numbers in the first half of eighteenth century

We revised relative sunspot numbers in the time interval 1700–1748 for which Wolf derived their annual means. The frequency of daily observations, counting simultaneously the number of sunspots and the number of sunspot groups necessary for determinating Wolf's relative sunspot numbers, is in this time interval very low and covers, on average, 4.8% of the number of all days only. There also exist incomplete observations not convenient to determine relative sunspot numbers. To enlarge the number of daily relative sunspot numbers we used the nonlinear, two-step interpolation method derived earlier by Letfus (1996, 1999). After interpolation, the mean value increased to 13.8%. Waldmeier (1968) found that the scaling factor k can be derived directly from the observed number of spots f and from the number of sunspot groups g. From the observations made at Zürich (Wolf and his assistants, Wolfer), at Peckeloh, and at Moncalieri during the years 1861–1928, we derived a new, more correct empirical relation. The resulting annual relative sunspot numbers are given in Table II. However, only for 26 years (53.0%) from the total number of 49 years was it possible to derive annual relative sunspot numbers. The observations were missing for the other years. This corresponds with results of Wolf, which gives the annual relative sunspot numbers for all 49 years. For the years when the data were missing, he marked these values as interpolated or very uncertain ones. Most of the observations originate from two data series (Kirch, Plantade), for which Wolf derived a higher scaling factor (k=2.0) than followed from the newly derived relation (k=1.40). The investigated time interval covers four solar cycles. After our results, the height of the first cycle (No. –4), given by Wolf, should be lowered by about two-thirds, the following two cycles (Nos. –3 and –2) lowered by one-third, as given by Wolf, and only the height of the fourth one (No. –1) should be unchanged. The activity levels of the cycles, as represented by group sunspot numbers, are lower by about one-fourth and, in the case of the first one (No. –4) even by two-thirds of the levels derived by us. The group sunspot numbers, derived from a much greater number of observations, have also greater credibility than other estimates. The shapes of the cycles, as given by Wolf, can be considered only as their more or less idealized form.     

Long-term changes in the cosmic-ray diurnal anisotropy

A detailed study has been conducted on the long-term changes in diurnal anisotropy of cosmic rays for the two solar cycles (20 and 21) during the period 1965–1990; this shows that the amplitude of the anisotropy is related to the characteristics of high and low amplitude days. The occurrence of high amplitude days are found to be positively correlated with the sunspot cycle while the low amplitude days are correlated negatively with the sunspot cycle. Further, the variability of the time of maximum of the aniotropy indicates that it essentially is composed of two components; one in the 1800 hours (corotation) direction and the other, an additional component in the 1500 hours direction (45° east of the S-N line) apparently caused by the reversal of the solar polar magnetic field. Our observations also suggest that the direction of the anisotropy of high- and low-amplitude days contribute significantly to the long-term behaviour of the diurnal anisotropy as it produces an additional component of cosmic rays in the radial (1200 hours) direction.     

Long-term variations in north-south asymmetry of solar activity

We present a new set of data on relative sunspot number (total, northern hemisphere, and southern hemisphere), taken for the 37-yr period 1947 to 1983; this constitutes a particularly coherent and consistent set of data, taken by the same observer (Hisako Koyama) using the same observing instrument. These data are combined with earlier data (White and Trotter, 1977) on the variation of sunspot areas for both solar hemispheres from 1874 to 1971. The combined data, covering 110 years and 10 solar cycles, are examined for periodicity in solar activity north-south asymmetry. We show that, in general, northern hemisphere activity, displayed as either An/(An + As) or Rn/(Rn + Rs), peaks about two years after sunspot minimum. This peak is greater during even cycles, pointing to a 22-yr periodicity in north-south asymmetry in solar activity, suggesting that the asymmetry is related to the 22-yr solar magnetic cycle. We demonstrate that the largest and most protracted period of northern-hemisphere activity excess in the last 110 years has occurred from 1959 to 1970; we show that there is a strong correlation between northern activity excess and a cosmic-ray density gradient perpendicular to the ecliptic plane, pointing southward, which is evident in cosmic-ray diurnal variation data from the Embudo underground cosmic-ray telescope.