22-year cycle or 11-year cycle in the latitude drift of sunspot groups?

Some earlier investigations seem to indicate that sunspots show an average drift in latitude which varies sinusoidally with the period of the double sunspot cycle (about 22 years), while the same investigations do not show similar variability with the period of the single sunspot cycle (about 11 years). Other studies, however, show that the drift of sunspots varies with the period of the single sunspot cycle. There seems to be a discrepancy between the two results. The problem is reinvestigated on the basis of long-lived sunspot groups, but treating the material in a way different from that used before. This procedure, which uses central values of the proper motions of the groups instead of their average values, gives an additional proof of the reality of the 11-year period of the drift. It also seems to produce the 22-year period, but there is such a difference between the variabilities of the drift found on the basis of the two methods that the 22-year cycle of the drift is made doubtful.     

Polar coronal holes and the sunspot cycle. A new method to predict sunspot numbers

Twenty years ago, Ohl (1966, 1968) found a correlation between geomagnetic activity around the minimum of the solar cycle and the Wolf sunspot number in the maximum of the following solar cycle. In this paper we shall show that such a relation means indeed a relation between the polar coronal holes area around the minimum of the solar cycle and the sunspot number in the maximum of the next. In fact, a very high positive correlation exists between the temporal evolution of the size of polar coronal holes and the Wolf sunspot number 6.3. years later.     

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude of a cycle and the length of the previous cycle. This allows for an estimate of the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7–12 years of the cycle. The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

Mathematical modelling of the sunspot cycle

The sunspot record for the time interval 1749–1977 can be represented conveniently by an harmonic model comprising a relatively large number of lines. Solar activity can otherwise be considered as a sequence of partly overlapping events, triggered periodically at intervals of the order of 11 years. Each individual cycle is approximated by a function of the Maxwell distribution type; the resulting impulse model consists of the superposition of the independent pulses. Application of these two models for the prediction of annual values of the Wolf sunspot numbers leads to controversial results. Mathematical modelling of the sunspot time series does not give an unambiguous result.     

On long-term periodicities in the sunspot cycle

Occurrences of interplanetary shock waves near the Earth after the powerful isolated flares of 1957–1978 are investigated. The close connection between the occurrences of shock waves and the positions of magnetic axes of bipolar groups of sunspots is suggested on the basis of a statistical study. The shock waves are principally observed when the Earth finds itself near the planes that are projected through the flares in parallel to the appropriate magnetic axes of the nearest bipolar groups. This regularity is interpreted as an indirect argument for a three-dimensional geometry for the interplanetary shock waves which, when projected on these flattened to corresponding planes, are traces of large circular arcs. The typical angular scales of isolated interplanetary shock waves are estimated as 150° and 30° parallel and perpendicular, respectively, to the magnetic axes correspondingly.     

Persistent 22-year cycle in sunspot activity: Evidence for a relic solar magnetic field

We use the recently presented group sunspot number series to show that a persistent 22-year cyclicity exists in sunspot activity throughout the entire period of about 400 years of direct sunspot observations. The amplitude of this cyclicity is about 10% of the present sunspot activity level. A 22-year cyclicity in sunspot activity is naturally produced by the 22-year magnetic polarity cycle in the presence of a relic dipole magnetic field. Accordingly, a persistent 22-year cyclicity in sunspot activity gives an evidence for the existence of such a relic magnetic field in the Sun. The stable phase and the roughly constant amplitude of this cyclicity during times of very different sunspot activity level strongly support this interpretation.     

On the average rate of growth in sunspot number and the size of the sunspot cycle

The average rate of growth during the ascending portion of the sunspot cycle, defined here as the difference in smoothed sunspot number values between elapsed time (in months) t and sunspot minimum divided by t, is shown to correlate (r 0.78) with the size of the sunspot cycle, especially for t 18 months. Also, the maximum value of the average rate of growth is shown to highly correlate (r = 0.98) with the size of the cycle. Based on the first 18 months of the cycle, cycle 22 is projected to have an R(M) = 186.0 ± 27.2 (at the ± 1 level), and based on the first 24 months of the cycle, it is projected to have an R(M) = 201.0 ± 20.1 (at the ± 1 level). Presently, the average rate of growth is continuing to rise, having a value of about 4.5 at 24 months into the cycle, a value second only to that of cycle 19 (4.8 at t = 24 and a maximum value of 5.26 at t = 27). Using 4.5 as the maximum value of the average rate of growth for cycle 22, a lower limit can be estimated for R(M); namely R(M) for cycle 22 is estimated to be 164.0 (at the 97.5% level of confidence). Thus, these findings are consistent with the previous single variate predictions that project R(M) for cycle 22 to be one of the greatest on record, probably larger than cycle 21 (164.5) and near that of cycle 19 (201.3).     

Predicting the maximum amplitude for the sunspot cycle from the rate of rise in sunspot number

Examined are associational aspects as they relate the maximum amplitude R _M for the sunspot cycle to the rate of rise R _t during the ascending phase, where R _M is the smoothed sunspot number at cycle maximum and R _t is the sum of the monthly mean sunspot numbers for selected 6-month intervals (t) measured from cycle onset. One finds that, prior to about 2 yr into the cycle, the rate of rise is not a reliable predictor for maximum amplitude. Only during the latter half of the ascent do the fits display strong linearity, having a coefficient of correlation r 0.9 and a standard error S _yx 20. During the first four intervals, the expected R _M and the observed R _M were found to differ by no more than 20 units of smoothed sunspot number only 25, 42, 50, and 58 % of the time; during the latter four intervals, they differed by no more than 20 units 67, 83, 92, and 100% of the time.     

On the maximum rate of change in sunspot number growth and the size of the sunspot cycle

Statistically significant correlations exist between the size (maximum amplitude) of the sunspot cycle and, especially, the maximum value of the rate of rise during the ascending portion of the sunspot cycle, where the rate of rise is computed either as the difference in the month-to-month smoothed sunspot number values or as the average rate of growth in smoothed sunspot number from sunspot minimum. Based on the observed values of these quantities (equal to 10.6 and 4.63, respectively) as of early 1989, one infers that cycle 22's maximum amplitude will be about 175 ± 30 or 185 ± 10, respectively, where the error bars represent approximately twice the average error found during cycles 10–21 from the two fits.     

Solar cycle variation of sunspot intensity

Broad band pinhole photometer intensity observations of 15 large sunspots covering the spectral region 0.387–2.35 m are presented. The data are based on measurements on approximately 500 days during the period June, 1967 to December, 1979.We have found real and significant intensity differences between large sunspots. These differences may be explained by a systematic variation in the umbral temperature throughout the solar cycle. A connection between umbra intensity and heliographic latitude is discussed.No center-limb variation in the umbra/photosphere intensity ratio is detected. We have searched for possible connections between umbra intensity and a number of other sunspot parameters, like the spot size, without detecting any significant correlation. We conclude that the umbra/photosphere intensity ratio seems to be a unique function of epoch for large sunspots.     

A new empirical model of a sunspot umbra

H and K-line spectra of quiescent prominences, taken with the slit placed normal to the limb, commonly reveal a gas streaming (5–50 km/s) that is peculiar to the upper edge of these objects. On the average this streaming is uni-directional and consistent with a hypothetical east-west wind.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

The solar wind cycle,the sunspot cycle,and the corona

Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e. sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion we note that the shape of the corona typical of a maximum eclipse occurs 1.5yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's standard model. Further, we argue that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km s^–1 in the solar wind velocity and 1 in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.     

Coronal holes,solar wind streams,and geomagnetic activity during the new sunspot cycle

We have extended our previous study of coronal holes, solar wind streams, and geomagnetic disturbances from the declining phase (1973–1975) of sunspot cycle 20 through sunspot minimum (1976) into the rising phase (1977) of cycle 21. Using daily He I 10830 Å spectroheliograms and photospheric magnetograms, we found the following results:

1. As the magnetic field patterns changed, the solar atmosphere evolved from a structure having a few, large, long-lived, low-latitude coronal holes to one having numerous small, short-lived, high-latitude holes (in addition to the polar holes which persisted throughout this 5-year interval).
2. The high-latitude holes recurred with a synodic rotation period of 28–29 days instead of the 27-day period already known to be characteristic of low-latitude holes.
3. During 1976–1977 many coronal holes were intrinsically ‘weak’ in the sense that their average intensities did not differ greatly from the intensity of their surroundings. Such low-contrast holes were rare during 1973–1975.

An updated Bartels display of the occurrence of holes, wind speed, and geomagnetic activity summarizes the evolution of their characteristics and interrelations as the sunspot cycle has progressed. Long-lived, low-latitude holes have become rare but remain terrestrially effective. The more common high-latitude holes are effective only when the Earth lies at a relatively high heliographic latitude in the same solar hemisphere.     

Solar cycle variations in the growth and decay of sunspot groups

We analysed the combined Greenwich (1874–1976) and Solar Optical Observatories Network (1977–2011) data on sunspot groups. The daily rate of change of the area of a spot group is computed using the differences between the epochs of the spot group observation on any two consecutive days during its life-time and between the corrected whole spot areas of the spot group at these epochs. Positive/negative value of the daily rate of change of the area of a spot group represents the growth/decay rate of the spot group. We found that the total amounts of growth and decay of spot groups whose life times ≥2 days in a given time interval (say one-year) well correlate to the amount of activity in the same interval. We have also found that there exists a reasonably good correlation and an approximate linear relationship between the logarithmic values of the decay rate and area of the spot group at the first day of the corresponding consecutive days, largely suggesting that a large/small area (magnetic flux) decreases in a faster/slower rate. There exists a long-term variation (about 90-year) in the slope of the linear relationship. The solar cycle variation in the decay of spot groups may have a strong relationship with the corresponding variations in solar energetic phenomena such as solar flare activity. The decay of spot groups may also substantially contribute to the coherence relationship between the total solar irradiance and the solar activity variations.     

Prediction of maximum sunspot number in solar cycle 23

Instantaneous predictions of the maximum monthly smoothed sunspot number in solar cycle 23 have been made with a linear regressive model, which gives the predicted maximum value as a function of the smoothed sunspot numbers corresponding to a given month from the minimum in all preceding cycles. These predictions indicate that the intensity of solar activity in the current cycle will be at an average level.     

The use of solar faculae in studies of the sunspot cycle

Comparison of the long-term variation of photospheric faculae areas with that of sunspots shows that studies of faculae provide both complementary and supplementary information on the behaviour of the solar cycle. Detailed studies of the development of sunspots with respect to faculae show that there is a high degree of order over much of a given cycle, but marked differences from cycle to cycle. Within a cycle the relationship between spot and faculae areas appears to be similar for the N and S solar hemispheres, and over the early stages of a cycle it is directly related to the magnitude of the maximum sunspot number subsequently attained in that cycle.This result may well have predictive applications, and formulae are given relating the peak sunspot number to simple parameters derived from this early developmental stage. Full application to the current cycle 21 is denied due to the cessation of the Greenwich daily photoheliographic measurements, but use of the cruder weekly data suggests a maximum smoothed sunspot number of 150 ± 22.The effects of the incompatibility of the spot and faculae data, in that faculae are unobservable over a large fraction of the solar disc and also do not always develop associated spots, have been examined in a detailed study of two cycles and shown not to vitiate the results.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

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.     

A new look at wolf sunspot numbers in the late 1700's

Long-term homogeneous observations of solar activity or many solar cycles are essential for investigating many problems in solar physics and climatology. The one key parameter used in most long-term studies is the Wolf sunspot number, which is susceptible to observer bias, particularly because it is highly sensitive to the observer's ability to see the smallest sunspots. In this paper we show how the Wolf sunspot number can be derived from the number of sunspot groups alone. We utilize this approach to obtain a Group Wolf number. This technique has advantages over the classical method of determining the Wolf number because corrections for observer differences are reduced and long-term self-consistent time series can be developed. The level of activity can be calculated to an accuracy of ± 5% using this method. Applying the technique to Christian Horrebow's observations of solar cycles 1, 2, and 3 (1761–1777), we find that the standard Wolf numbers are nearly homogeneous with sunspot numbers measured from 1875 to 1976 except the peak of solar cycle 2 is too low by 30%. This result suggests that further analyses of early sunspot observations could lead to significant improvements in the uniformity of the measurements of solar activity. Such improvements could have important impacts upon our understanding of long-term variations in solar activity, such as the Gleissberg cycle, or secular variations in the Earth's climate.