Long-term fluctuations of solar activity during the last thousand years

Long-term variations of solar activity during the last thousand years were derived from historical observations (by the naked eye) of large sunspots and from records of auroras at latitudes < 55°. The results shown in Figure 1 indicate very good agreement as regards the occurrence of maxima and minima of all three indices (sunspots, auroras, ¹⁴C), and even between secondary fluctuations of the ¹⁴C-curve, which were usually neglected in the presentation of the smoothed curve.     

Gleissberg cycle of solar activity over the last 7000 years

Long-term variations of solar activity significantly affect terrestrial phenomena. Studies have shown cyclic components in solar activity and geophysical phenomena (e.g., the Schwabe, Hale, Gleissberg, and Suess cycles, and a cycle of about 2300 years). In this paper, the wavelet technique is employed to investigate the Gleissberg cycle in solar variations during 5000 BC–1995 AD. Analysis shows time-variable characteristics in the Gleissberg solar cycle over the period; no obvious correlation between the Gleissberg and Suess cycles has been found.     

Was the solar activity in the last 100 years abnormally high? On the quality of modern solar paleoreconstructions

A technique for verifying the currently available reconstructions of solar activity in the preinstrumental epoch (prior to 1615 AD), covering time intervals up to 10 000 years, has been developed and tested. The technique is based on investigation of the possibility of predicting the actual sunspot numbers determined by means of telescopic observations using reconstructed solar series. Testing several paleoreconstructions over time intervals as long as 10 000 years has shown that they most likely contain only qualitative information about the behavior of solar activity in the past and are not very suitable for extracting quantitative information. It is shown that the recently suggested hypothesis that the current level of solar activity is highest in the last 8000 years is only an arbitrary assumption that can be neither confirmed nor refuted at the present level of knowledge about the past of our star.     

Long-term persistence of solar activity

We examine the question of whether or not the non-periodic variations in solar activity are caused by a white-noise, random process. The Hurst exponent, which characterizes the persistence of a time series, is evaluated for the series of¹⁴C data for the time interval from about 6000 BC to 1950 AD. We find a constant Hurst exponent, suggesting that solar activity in the frequency range from 100 to 3000 years includes an important continuum component in addition to the well-known periodic variations. The value we calculate,H 0.8, is significantly larger than the value of 0.5 that would correspond to variations produced by a white-noise process. This value is in good agreement with the results for the monthly sunspot data reported elsewhere, indicating that the physics that produces the continuum is a correlated random process and that it is the same type of process over a wide range of time interval lengths.     

Long-term prediction of solar activity

After reviewing the various methods used so far in the long-term prediction of solar activity, we have opted to use methods based on the 80-year period and probability considerations. Our predictions for Cycle No. 21 are:

• 1.Maximum of the annual average Wolf number: 54 – 94
• 2.Minimum of the annual average Wolf number: 0 – 4
• 3.Epoch of maximum: first half of 1981 - first half of 1983
• 4.Epoch of minimum: first half of 1976 - first half of 1977

A comparison of our predictions with others is made.     

Long-term persistence of solar activity

The solar irradiante has been found to change by 0.1% over the recent solar cycle. A change of irradiante of about 0.5% is required to effect the Earth's climate. How frequently can a variation of this size be expected? We examine the question of the persistence of non-periodic variations in solar activity. The Hürst exponent, which characterizes the persistence of a time series (Mandelbrot and Wallis, 1969), is evaluated for the series of¹⁴ C data for the time interval from about 6000 BC to 1950 AD (Stuiver and Pearson, 1986). We find a constant Hürst exponent, suggesting that solar activity in the frequency range of from 100 to 3000 years includes an important continuum component in addition to the well-known periodic variations. The value we calculate,H ≈ 0.8, is significantly larger than the value of 0.5 that would correspond to variations produced by a white-noise process. This value is in good agreement with the results for the monthly sunspot data reported elsewhere, indicating that the physics that produces the continuum is a correlated random process (Ruzmaikin et al., 1992), and that it is the same type of process over a wide range of time interval lengths. We conclude that the time period over which an irradiance change of 0.5% can be expected to occur is significantly shorter than that which would be expected for variations produced by a white-noise process. The full paper has been submitted to Solar Physics. Part of the research decribed here was carried out by JPL, Caltech under a contract with NASA.     

Periodicities of solar irradiance and solar activity indices,I

Using a standard FFT time series analysis, our results show an 8–11 months periodicity in the solar total and UV irradiances, 10.7 cm radio flux, Ca-K plage index, and sunspot blocking function. The physical origin of this period is not known, but the evidence in the results exclude the possibility that the observed period is a harmonic due to the FFT transform or detrending. Periods at 150–157 and 51 days are found in those solar data which are related to strong magnetic fields. The 51-day period is the dominant period in the projected areas of developing complex sunspot groups, but it is missing from the old decaying sunspot areas. This evidence suggests that the 51-day period is related to the emergence of new magnetic fields. A strong 13.5-day period is found in the total irradiance and projected areas of developing complex groups. This confirms those results (e.g., Donnelly et al., 1983, 1984; Bai, 1987, 1989) which show that active centers are located 180 deg apart from each other.Our study also shows that the modulation of various solar data due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion. This arises from that the active regions and their magnetic fields are better organized and more long-lived during the maximum and declining portion of solar cycle than during its rising portion.     

Periodicities of solar irradiance and solar activity indices,II

Using a dynamic power spectral analysis technique, the time-varying nature of solar periodicities is investigated for background X-ray flux, 10.7 cm flux, several indices to UV chromospheric flux, total solar irradiance, projected sunspot areas, and a sunspot blocking function. Many prior studies by a host of authors have differed over a wide range on solar periodicities. This investigation was designed to help resolve the differences by examining how periodicities change over time, and how the power spectra of solar data depend on the layer of the solar atmosphere. Using contour diagrams that show the percent of total power over time for periods ranging from 8 to 400 days, the transitory nature of solar periodicities is demonstrated, including periods at 12–14, 26–28, 51–52, and approximately 154 days. Results indicate that indices related to strong magnetic fields show the greatest variation in the number of periodicities, seldom persist for more than three solar rotations, and are highly variable in their frequency and amplitude. Periodicities found in the chromospheric indices are fewer, persist for up to 8–12 solar rotations, and are more stable in their frequency and amplitude. An additional result, found in all indices to varying degrees and related to the combined effects of solar rotation and active region evolution, is the fashion in which periodicities vary from about 20 to 36 days. I conclude that the solar data examined here are both quasi-periodic and quasistationary, with chromospheric indices showing the longest intervals of stationarity, and data representing strong magnetic fields showing the least stationarity. These results may have important implications to the results of linear statistical analysis techniques that assume stationarity, and in the interpretation of time series studies of solar variability.     

Cosmic-ray intensity related to solar and terrestrial activity indices in solar cycle No. 20

The 11-year modulation of cosmic-ray intensity is studied using the data from nine world-wide neutron monitoring station over the period 1965–1975. From this analysis the following relation among the modulated cosmic-ray intensityI, the relative sunspot numberR, the number of proton eventsN _p and the geomagnetic indexA _p has been derived which describes the long-term modulation of cosmic rays $$I = C - 10^{ - 3} (KR + 4N_P + 12A_P ),$$ whereC is a constant which depends on the rigidity of each station, andK is a coefficient related to the diffusion coefficient of cosmic rays and its transition in space. The standard deviation between the observed and calculated values of cosmic-ray intensity is about 5–9%. This relation has been explained by a generalization of the Simpson solar wind model which has been proved by the spherically symmetric diffusion-convection theory.     

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation co-efficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle ei-ther from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.     

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.     

Solar radio fluxes as indices of solar activity

The daily solar radio flux values at 9400, 3750, 2000 and 1000 MHz and at 2800 MHz observed since 1957 at Toyokawa and Ottawa, respectively, have been used to provide new information on the solar radio fluxes as indices of solar activity. After an examination of the yearly mean values at each frequency, another investigation based on mean ratios during periods of 18 or 6 months indicates that a close connection is observed between the radio fluxes in the cm region and that anomalies related to calibration problems can be detected. The regression analysis of the daily values of the fluxes during at least 25 years and a special test on the sensitivity may provide final information on the stability of the data with respect to time and solar activity. The method is capable of detecting long-term trends corresponding to instrumental drifts. Such information is essential to our understanding of anomalies detected in the observations of u.v. and X-ray irradiances. However, such a method is based on a linear relationship. When a quadratic form, as it is observed in the decimeter region, is adopted, the effect of the various levels of activity in a solar cycle must be considered.     

Long-term modulation of the coronal index of solar activity

Monthly mean values of the coronal index of solar activity and other solar indices are analyzed for the period 1965–1997 covering three solar cycles. The coronal index is based upon the total irradiance of the coronal 530.3 nm green line from observations at five stations. The significant correlation of this index with the sunspot number and the number of the grouped solar flares have led to an analytical expression which can reproduce the coronal index of solar activity as a function of these parameters. This expression well explains the existence of the two maxima during the solar cycles taking into account the evolution of the magnetic field that can be expressed by a sinusoidal term with a 6-year period. The agreement between observed and calculated values of the coronal index on a monthly basis is high enough and reaches the value of 92%. It is concluded that the coronal index can be used as a representative index of solar activity in order to be correlated with different periodic solar–terrestrial phenomena useful for space weather studies.     

Relation of the fluctuations of some of the solar activity indices

In this Letter we obtained the fluctuation curves from the differences of unsmoothed and smoothed values of the different solar activity indices. We compared the pattern of fluctuations of these curves. Also using monthly mean values of each index we studied the degree of correlation between the pairs of indices during the selected time intervals.     

Quiet corona density model for the last maximum of solar activity

We have selected observations of quiet K corona in maximum activity phase (1970 and 1972) and we have computed the corresponding density models. The density is found to be two times smaller than in average maximum coronal models (Newkirk, 1967) and nearly equal to that of minimum coronas (Saïto, 1970). The research of quiet coronas between active periods has been extended to the three past solar cycles thanks to 5303 Å measurements: very low 5303 Å intensities, corresponding to very small densities, are found even in maximum activity phase. A short discussion about the values of average quiet coronal models is given.     

Series of classical solar activity indices: Kislovodsk data

We present data on the series of solar activity indices, Wolf sunspot numbers W and total sunspot areas S, obtained at the Kislovodsk high-altitude station of the Pulkovo Observatory. The problem of properly extending the 133-year-long Zürich series of W and the 102-year-long Greenwich series of S, which were discontinued in 1980 and 1976, respectively, is emphasized. We stress that the Kislovodsk data have retained mutual homogeneity with the classical series until now and that they are preferred for extension. The question under consideration is of fundamental importance in studying the solar activity variations on long time scales and related processes in the Sun-Earth system.     

Background magnetic fields during last three cycles of solar activity

This paper describes our studies of evolution of the solar magnetic field with different sign and field strength in the range from –100 G to 100 G. The structure and evolution of large‐scale magnetic fields on the Sun during the last 3 cycles of solar activity is investigated using magnetograph data from the Kitt Peak Solar Observatory. This analysis reveals two groups of the large‐scale magnetic fields evolving differently during the cycles. The first group is represented by relatively weak background fields, and is best observed in the range of 3–10 Gauss. The second group is represented by stronger fields of 75–100 Gauss. The spatial and temporal properties of these groups are described and compared with the total magnetic flux. It is shown that the anomalous behaviour of the total flux during the last cycle can be found only in the second group. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The asymmetry of solar activity in the years 1959–1969

One of the most outstanding feature of solar activity in the decade 1959–1969 was a very strong asymmetry on the two hemispheres. On the northern hemisphere spots, faculae and prominences were more numerous and the white light corona was brighter than on the southern hemisphere. This happened as well in the main zone as in the polar zone. The green coronal line too was brighter on the northern hemisphere, but the intensity of the red line was asymmetric in the opposite sense. From this behaviour it follows that over the more active hemisphere the corona is denser and hotter. Between density N _e and temperature T holds the relation: N _e = 10^–10 T ³. The real asymmetry was strengthened by a phase difference of the two hemispheres. This phase shift is subject to a long period that contains 8 eleven-year cycles. The intensity of the individual cycles follows the same long period. With low maxima of solar activity the northern hemisphere precedes, with high maxima the southern hemisphere (Figure 3).Astronomische Mitteilungen der Eidgenössischen Sternwarte Zürich, No. 302.     

Study of the distribution of daily fluctuations in observed solar irradiances and other full-disk indices of solar activity

Analyses based on irradiance observations from space within the last one and a half decades have discovered variations in the entire solar spectrum and at UV wavelengths on time scales of minutes to decades. In this paper we analyze the distribution of the measuring uncertainties and daily fluctuations in total solar irradiance measured by the Nimbus-7/ERB and SMM/ACRIM I radiometers as a function of solar cycle. Changes in solar total irradiance and its surrogates shorter than the solar rotation have also been considered as noise and have been removed from the data. Our results show that the noise (both instrumental and solar noise) changes as a function of the solar cycle, being higher during high solar activity conditions. The analysis of the scatter plot diagrams between the data and their standard deviation, the so-called dispersion diagrams, provides a useful tool to estimate and predict the time of solar maximum and minimum activity conditions.Deceased on October 13, 1994.     

Small scale solar magnetic fields and their relation to various solar activity indices

Correlation studies between various solar activity indices and a long time series of annual sums of the maximum value of solar magnetic field intensity, observed for each group of sunspots during each passage of it over the visible solar hemisphere, have pointed out a couple of interesting points. First, the faculae have a significant contribution to the numerical representation of the small scale solar magnetic coefficients and low standard errors of estimation to the above mentioned maximum values of the solar magnetic field. These properties give to the area index an important physical meaning which is a first approximation to the small scale solar magnetic fields expressed by the above-mentioned maximum values of it. Finally, the main point which comes out is that long term studies of the solar magnetic fields, especially extrapolated studies to the past, could be supported by photospheric indices of the solar activity. This paper constitutes the expanded version of a report presented to theIAU Symposium No. 102 ‘Solar and Stellar magnetic fields: Origins and coronal effects’, held in Zürich 2–6 August, 1982.