Area of polar coronal holes and sunspot activity: Years 1939–1993

The correlation between the size of polar coronal holes and sunspot numbers has been investigated for the last five solar cycles. The area of polar coronal holes over the period from 1939 to 1993 was derived from ground-based observations of the green coronal line at 530.3 nm (Fe xiv). Correlation analysis revealed that there is no general shift in the maxima of the curves of these two solar indices. The analysis showed the same shift in months in cycles 21 and 22 when the best correlation between the indices is reached; the time shift found in cycle 20 is slightly different from that in cycle 18; in cycle 19, there is found a shift with a value between the values in cycles 18, 20 and 21, 22. The time between succesive peaks of smoothed polar hole size and smoothed sunspot number is different in each cycle.     

Polar coronal holes and solar cycles

The relationship between the geomagnetic activity of the three years preceding a sunspot minimum and the peak of the next sunspot maximum confirms the polar origin of the solar wind during one part of the solar cycle. Pointing out that the polar holes have a very small size or disappear at the time of the polar field reversal, we suggest a low latitude origin of the solar wind at sunspot maximum and we describe the cycle variation of solar wind and geomagnetic activity. In addition we note a close relationship between the maximum level of the geomagnetic activity reached few years before a solar minimum and its level at the next sunspot maximum. Studying separately the effects of both the low latitude holes and the solar activity, we point out the possibility of predicting both the level of geomagnetic activity and the sunspot number at the next sunspot maximum. As a conclusion we specify the different categories of phenomena contributing to a solar cycle.     

Solar cycle dependence of polar coronal holes

A study has been made of the polar coronal holes in relation to solar cycle activity. Important results obtained are: (i) the peak of the frequency distribution of coronal hole size shifts towards lower values as the solar cycle advances towards maximum, this being true for both the north and south polar holes, (ii) coronal hole size decreases with the increase of sunspot number.     

A survey of coronal holes and their solar wind associations throughout sunspot cycle 20

To gain insight into the relationships between solar activity, the occurrence and variability of coronal holes, and the association of such holes with solar wind features such as high-velocity streams, a study of the period 1963–1974 was made. This period corresponds approximately with sunspot cycle 20. The primary data used for this work consisted of X-ray and XUV solar images obtained from rockets. The investigation revealed that:

1. The polar coronal holes prominent at solar minimum, decreased in area as solar activity increased and were small or absent at maximum phase. This evolution exhibited the same phase difference between the two hemispheres that was observed in other indicators of activity.
2. During maximum, coronal holes occurred poleward of the sunspot belts and in the equatorial region between them. The observed equatorial holes were small and persisted for one or two solar rotations only; some high latitude holes had lifetimes exceeding two solar rotations.
3. During 1963–74 whenever XUV or X-ray images were available, nearly all recurrent solar wind streams of speed ?500 km s^?1 were found associated with coronal holes at less than 40° latitude; however some coronal holes appeared to have no associated wind streams at the Earth.

     

THE CORRELATION BETWEEN SUNSPOT AND CORONAL HOLE CYCLES AND A FORECAST OF THE MAXIMUM OF SUNSPOT CYCLE 23

We have shown in previous papers that a close relationship exists between the evolution of polar coronal hole area, estimated from K-coronameter observations, and the Wolf sunspot number, with a time lag of about half a solar cycle. In this paper we study the same relationship, but with the total coronal hole area at the base of the corona as obtained from a potential field model of the coronal magnetic field, which provides a more complete series of about three solar cycles. We confirm the relationship for the two last cycles and find that the forward time shift in the coronal hole area for the best correlation with sunspot number is almost the same for cycles 21 and 22, and this shift is also the time between peaks in both series. We use this result to make an early prediction of the time and size of the sunspot maximum for solar cycle 23, and find that this should occur early in 2001 and have a magnitude of about 190, similar to that of the two previous sunspot cycles.     

Evolution of polar coronal holes and sunspots during cycles 21 and 22

A very good correlation between the evolution of polar coronal hole size and sunspot number half a solar cycle later was found by Bravo and Otaola for solar cycle 21. In this paper we use a more complete set of data to reanalyse the relationship for solar cycle 21 and investigate the same relationship for solar cycle 22. We find that the complete set of data for cycle 21 yields a slightly different time shift for the best correlation between sunspots and holes and that the time shift for cycle 22 is different from that of cycle 21. However, because of limited availability of data of cycle 22, we consider it necessary to wait until the end of this cycle in order to decide if the difference is statistically significant or not. We also found that the time between successive peaks of smoothed polar hole area and smoothed sunspot number is the same in both cycles. This may provide a useful tool for the forecasting of future sunspot maxima. The constant of proportionality between polar coronal hole area and sunspot number can be seen to be different in both cycles. We discuss this difference and interpret it in terms of a different magnitude of the polar field strength in the two cycles.     

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.     

Sunspot groups at high latitude

Data of sunspot groups at high latitude (35°), from the year 1874 to the present (2000 January), are collected to show their evolutional behaviour and to investigate features of the yearly number of sunspot groups at high latitude. Subsequently, an evolutional pattern of sunspot group number at high latitude is given in this paper. Results obtained show that the number of sunspot groups of a solar cycle at high latitude rises to a maximum value about 1 yr earlier than the time of the maximum of sunspot relative numbers of the solar cycle, and then falls to zero more rapidly. The results also show that, at the moment, solar activity described by the sunspot relative numbers has not yet reached its minimum. In general, sunspot groups at high latitude have not appeared on the solar disc during the last 3 yr of a Wolf solar cycle. The asymmetry of the high latitude sunspot group number of a Wolf solar cycle can reflect the asymmetry of solar activity in the Wolf solar cycle, and it is suggested that one could further use the high latitude sunspot group number during the rising time of a Wolf solar cycle, maximum year included, to judge the asymmetry of solar activity over the whole solar cycle.     

Cyclic variations of the polar coronal hole

The extension of the polar coronal holes has been studied for four cycles (1940–1978), using the observations of the corona line 530.3 nm. For about 7 years of each cycle, including sunspot minimum, the polar hole exists permanently and has a diameter of about 40° or even more. For about 3 years around sunspot maximum no polar hole does exist (Figure 5). The boundary of the hole is flanked at a distance of 10° by the polar zone of the corona and at one of 20° by that of the prominences. In the polar caps, so far they are occupied by the holes, polar photospheric faculae and the well-known plumes of the polar corona are found, and the polar crown of prominences, encircling the polar hole, is the belt where the reversal of the magnetic polarity takes place.     

Prediction of the maximum annual mean sunspot number in the coming solar maximum epoch

Using an earlier correlation analysis between the annual sunspot numbers at sunspot maximum epochs and the minimum annual aa index in the immediately preceding years, the minimum annual aa index (21.6) during 1985–86 implies a maximum annual sunspot number of about 190±40 in the coming solar maximum epoch, in about 1988–89.     

Relationship between sunspot numbers during years of sunspot maximum and sunspot minimum

A correlation analysis shows that the sunspot numbers at the peaks of the last eight solar cycles are well-correlated with the sunspot numbers in heliolatitudes 20°–40° (specially in the southern hemisphere) occurring in the solar minimum years immediately preceding the solar maximum years.On leave from Physical Research Laboratory, Ahmedabad, India.     

Prediction for the amplitude of solar cycle 24 from the pattern of activity near the cycle minimum

Correlations are investigated between the pattern of solar activity described by the smoothed monthly relative sunspot numbers (Wolf numbers) near the minimum of a solar cycle and the cycle amplitude. The closest correlation is found between the amplitude of a solar cycle and the sum of the decrease in activity over two years prior to the cycle minimum and the increase in activity over two years after the minimum; the correlation coefficient between these parameters is 0.92. This parameter is used as a precursor to predict the amplitude of solar cycle 24, which is expected to reach its maximum amplitude (85 ± 12) in February 2014. Based on the correlations between the mean parameters of solar cycles, cycle 24 is expected to last for approximately 11.3 years and the minimum of the next cycle 25 is predicted for May 2020.     

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.     

Coronal Holes and Flare Index: A correlation study

The correlation between the presence of coronal holes and flare indices has been investigated for the period from 1976 to 1995. The analysis shows that in the cases of 227 Carrington rotations (CRs) backward time lags yield the highest correlation between the coronal holes and flare indices. The maximum correlations were found at time lags of 222 and 142 CRs for polar and equatorial coronal holes, respectively. The period of study covers the past two solar cycles (21 and 22). Correlation analysis of both solar cycles has also been studied individually. The correlation analysis reveals that there is in general a forward shift in the maximum correlation for polar coronal holes, but it cannot be recommended to use polar coronal hole numbers for forecasting the next solar cycle.     

Observations of the reappearance of polar coronal holes and the reversal of the polar magnetic field

We examine observations relating to the evolution of the polar magnetic field around sunspot maximum, when the net polar flux reverses polarity and coronal holes redevelop around the poles. Coronal hole observations during the last two solar maxima are examined in detail. Long-term averages of the latitudinal dependence of the photospheric magnetic field and the evolutionary pattern of the polar crown filaments are used to trace the poleward motion of the reversal of the large-scale surface field, and are compared to the redevelopment of the polar holes. The polar holes evolve from small, mid-latitude holes of new-cycle polarity which expand poleward until they join and cover the pole. We find that the appearance of these mid-latitude holes, the peak of flux emergence at low latitudes, and the polar polarity reversal all occur within a few solar rotations. Lagging 6 months to 1 1/2 yr after this time, the polar crown disappears and the polar holes redevelop.These results are examined in the context of phenomenological models of the solar cycle. We believe the following results in particular must be accounted for in successful models of the solar cycle: (1) The process of polarity reversal and redevelopment of the polar holes is discontinuous, occurring in 2 or 3 longitude bands, with surges of flux of old-cycle polarity interrupting the poleward migration of new-cycle flux. There is a persistent asymmetry in these processes between the two hemispheres; the polarity reversal in the two hemispheres is offset by 6 months to 1 1/2 yr. (2) Contrary to the Babcock hypothesis, the polar crown disappears months after the magnetic polar reversal. We suggest one possible scenario to explain this effect. (3) Our observations support suggestions of a poleward meridional flow around solar maximum that cannot be accounted for by Leighton-type diffusion.     

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.     

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.     

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.     

Amplitude and period of the dynamo wave and prediction of the solar cycle

The relation of the solar cycle period and its amplitude is a complex problem as there is no direct correlation between these two quantities. Nevertheless, the period of the cycle is of important influence to the Earth's climate, which has been noted by many authors. The present authors make an attempt to analyse the solar indices data taking into account recent developments of the asymptotic theory of the solar dynamo. The use of the WKB method enables us to estimate the amplitude and the period of the cycle versus dynamo wave parameters in the framework of the nonlinear development of the one-dimensional Parker migratory dynamo. These estimates link the period T and the amplitude a with dynamo number D and thickness of the generation layer of the solar convective zone h. As previous authors, we have not revealed any considerable correlation between the above quantities calculated in the usual way. However, we have found some similar dependences with good confidence using running cycle periods. We have noticed statistically significant dependences between the Wolf numbers and the running period of the magnetic cycle, as well as between maximum sunspot number and duration of the phase of growth of each sunspot cycle. The latter one supports asymptotic estimates of the nonlinear dynamo wave suggested earlier. These dependences may be useful for understanding the mechanism of the solar dynamo wave and prediction of the average maximum amplitude of solar cycles. Besides that, we have noted that the maximum amplitude of the cycle and the temporal derivative of the monthly Wolf numbers at the very beginning of the phase of growth of the cycle have high correlation coefficient of order 0.95. The link between Wolf number data and their derivative taken with a time shift enabled us to predict the dynamics of the sunspot activity. For the current cycle 23 this yields Wolf numbers of order 107±7.     

Evolution of the Green Corona in 1996–2002

We analysed the green-line coronal intensities (530.3 nm, Fexiv), both their time- latitudinal distribution as well as the coronal index of solar activity (CI) over the period 1996–2002. Maximum values of the CI (smoothed) were observed in mid-August 2001, even though the `first' peak was observed in the period January–April 2000. The maximum of the Wolf number occurred in 2000, April – July, and the `second peak' occurred in December 2001–March 2002. Both indices have a similar course in the cycle, but their maxima are shifted by 1.5 year. There was high correlation between CI and Wolf number, the 2800 MHz radio flux, the X-ray 0.1–0.8 nm flux and cosmic-ray flux. The CI values in present cycle 23 are lower than those of the two former solar cycles 21 and 22 by about 1/3. Polar branches, which separated from the principal equatorward branch at mid-latitudes in the cycle minimum, 1996, reached the poles around 2000. The new principal branch for cycle 24 split in 2001, turned over around ±60° in 2002.5 and moves to the equator, where it will end in 2019. Minimum between cycles 23 and 24 will occur around 2007.5, cycle maximum 24 around 2012.5. Poleward branches in cycle 24 will reach the solar poles in 2011.