Short periodicities in solar activity

Several indices of solar activity are subjected to a high pass filter and power spectral analysis to verify the existance of shorter periodicities in solar activity. Though all these indices show the presence of short periodicities, above 95% confidence level, the common indices like sunspot number, fail to show these periodicities when a stringest statistical test is applied based on a percentage of the ²/v distribution that is appropriately higher than the 95% point (Mitchell et al., 1966). The basic parameters given by Kopecký (1967), however, reveal the presence of 5.6- and 3.5-yr periodicities even when this stringent statistical test is applied.     

Periodogram analysis of 240 years of sunspot records

We have analyzed the direct records of sunspot number between 1749 and 1990 with the same technique currently used in the study of stellar activity cycles observed with Mount Wilson Observatory's 60-inch telescope. In order to mimic the stellar time series, which span only two decades, we analyzed twenty- and fifty-year intervals of the sunspot data in comparison to the entire record. We also examined the reliability of the oldest (pre-1850) sunspot records. The mean solar cycle period determined from the entire record (1749–1990) is 11.04 yr with a computed precision of ± 0.01 yr, but an overall accuracy of only ±1.1 yr. The large uncertainty is caused by variation of the cycle period with time and not observational uncertainty.The correct sunspot period is found slightly more often (82%) in 50-year intervals compared to 20-year (74%). The cause is twofold: first, a more precise period results from the longer sample length, and second, other periodicities exist in the sunspot record, so that a more accurate determination of the dominant 11.0-year period results from the longer time series. As a guideline for cycle periodicities in other stars, the solar results indicate that the 50-year intervals would produce more precise and accurate periods than the 20-year time series. On the other hand, useful statistics concerning long-term activity could be obtained from a less-frequently sampled group of stars that is substantially larger than the group of 100 lower Main-Sequence stars currently observed at Mount Wilson, although knowledge of short-term variability would be sacrificed.Pre-doctoral fellow, Harvard-Smithsonian Center for Astrophysics.     

Reconstruction of Wolf Sunspot Numbers on the Basis of Spectral Characteristics and Estimates of Associated Radio Flux and Solar Wind Parameters for the Last Millennium

A reconstruction of sunspot numbers for the last 1000 years was obtained using a sum of sine waves derived from spectral analysis of the time series of sunspot number R _z for the period 1700–1999. The time series was decomposed in frequency levels using the wavelet transform, and an iterative regression model (ARIST) was used to identify the amplitude and phase of the main periodicities. The 1000-year reconstructed sunspot number reproduces well the great maximums and minimums in solar activity, identified in cosmonuclides variation records, and, specifically, the epochs of the Oort, Wolf, Spörer, Maunder, and Dalton Minimums as well the Medieval and Modern Maximums. The average sunspot number activity in each anomalous period was used in linear equations to obtain estimates of the solar radio flux F _10.7, solar wind velocity, and the southward component of the interplanetary magnetic field.     

Periodicities in Irradiance and in other Solar Activity Indices During Cycle 23

Magnetic fields give rise to distinctive features in different solar atmospheric regimes. To study this, time variations of the flare index, sunspot number and sunspot area, each index arising from different physical conditions, were compared with the solar composite irradiance throughout cycle 23. Rieger-type periodicities in these time series were calculated using Fourier and wavelet transforms (WTs). The peaks of the wavelet power of these periodicities appeared between the years 1999 and 2002. We found that the solar irradiance oscillations are less significant than those in the other indices during this cycle. The irradiance shows non-periodic fluctuations during this time interval. The peaks of the flare index, sunspot number and sunspot total area were seen around 2000.4, 1999.9 and 2001.0, respectively. These periodicities appeared intermittently and were not simultaneous in different solar activity indices during the three years of the maximum phase of solar cycle 23.     

Does sunspot activity originate in slow global oscillations of the sun?

We present preliminary results of a spherical-harmonic-Fourier analysis of sunspot activity during the twenty-two years 1933–1954. The results indicate that the sunspot activity might be originating in global solar oscillations with periods of years and decades. However, except for the axisymmetric mode of degree 6, the set of other axisymmetric modes showing ∼ 11 yr periodicities are different from one sunspot cycle to another. A more detailed analysis, preferably with larger data series, will be needed to arrive at a more definite conclusion.     

Solar cycles during the Maunder minimum

We have obtained new consistent versions of the 400-yr time series of the Wolf sunspot number W, the sunspot group number G, and the total sunspot area S (or the total sunspot magnetic flux Φ). We show that the 11-yr cycle did not cease during the Maunder minimum of solar activity. The characteristics of the extrema of individual 11-yr cycles in 1600–2005 have been determined in terms of the total sunspot area index. We provide arguments for using alternating (“magnetic”) time series of indices in investigating the solar cyclicity.     

Periodicities in the solar differential rotation,surface magnetic field and planetary configurations

Using Greenwich data on sunspot groups during 1874–1976, we have studied the temporal variations in the differential rotation parametersA andB by determining their values during moving time intervals of lengths 1–5 yr successively displaced by 1 yr. FFT analysis of the temporal variations ofB (orB/A) shows periodicities 18.3 ± 3 yr, 8.5 ± 1 yr, 3.9 ± 0.5 yr, 3.1 ± 0.2 yr, and 2.6 ± 0.2 yr at levels 2. This analysis also shows five more periodicities at levels 1–2. The maximum entropy method is used to set narrower limits on the values of these periods. The reality of the existence of all these periodicities ofB (orB/A ) except the one at 2.8 yr is confirmed by analyzing the simulated time series ofB andB/A with values ofA andB randomly distributed within the limits of their respective uncertainties. Four of the prominent periods ofB agree, within their uncertainties, with the known periods in the the large-scale photospheric magnetic field. The deviations from the average differential rotation are larger near the sunspot minima. On longer time scales, the variations in the amount of sunspot activity per unit time are well correlated to the variations in the amplitudes of the torsional oscillation represented by the 22-yr periodicity inB. All the periods inB found here are in good agreement with the synodic periods of two or more consecutive planets. The possibility of planetary configurations providing perturbations needed for the Sun's MHD torsional oscillations is speculated upon and briefly discussed.     

A Search for Periodicities in F10.7 Solar Radio Flux Data

The radio frequency emission at 10.7 cm (or 2800 MHz) wavelength (considered as solar flux density) out of different possible wavelengths is usually selected to identify periodicities because of its high correlation with solar extreme ultraviolet radiation as well as its complete and long observational record other than sunspot related indices. The solar radio flux at 10.7 cm wavelength plays a very valuable role for forecasting the space weather because it is originated from lower corona and chromospheres region of the Sun. Also, solar radio flux is a magnificent indicator of major solar activity. Here in the present work the solar radio flux data from 1965 to 2014 observed at the Domimion Radio Astrophysical Observatory in Penticton, British Columbiahas been processed using Date Compensated Discrete Fourier Transform (DCDFT) to identify predominant periods within the data along with their confidence levels. Also, the multi-taper method (MTM) for periodicity analysis is used to validate the observed periods. Present investigation exhibits multiperiodicity of the time series F10.7 solar radio flux data around 27, 57, 78, 127, 157, 4096 days etc. The observed periods are also compared with the periods of MgII Index data using same algorithm as MgII Index data has 99.9% correlation with F10.7 Solar Radio Flux data. It can be observed that the MgII index data exhibits similar periodicities with very high confidence levels.Present investigation also clearly indicates that the computed results are very much confining with the results obtained in different communication for the similar data of 10.7 cm Solar Radio Flux as well as for the other solar activities.

     

Modulation of the Solar Magnetic Cycle

The modulation model of the solar magnetic cycle for the time interval from 1650 to 1996 A.D. describes an harmonic oscillator with a basic (22.13 ± 0.05)-yr period, which is subjected to amplitude and phase variations that can be represented by a sum of trigonometric series. The simulated sunspot data explain 97.9% of cycle peak height variance and the residual standard deviation is 8.6 mean annual sunspots. A peak height of 139 for cycle 23 occurring in 2001 is predicted, whereas cycle 24 would have a maximum around 132 in 2014. Simulation of the sunspot numbers from 1000 until 2400 A.D. shows that the model recreates recurring minima (Maunder and Spörer Minimum). The prediction also expects a high level of amplitude modulation in the interval 1950–2010 with a rapid decrease afterwards. A greatly reduced cycle activity is reproduced by the simulation from about 2065 to 2100 A.D. No direct explanation of the long-term periodicities of the model can be advanced. The high-frequency contribution of the phase modulation, which accounts for the skewness of the solar cycle, shows coincidences with the orbital periods of Jupiter and Saturn, but no physical basis for the matching periodicities can be conceived.     

Solar Magnetic Activity and Total Irradiance Since the Maunder Minimum

We develop a model for estimating solar total irradiance since 1600 AD using the sunspot number record as input, since this is the only intrinsic record of solar activity extending back far enough in time. Sunspot number is strongly correlated, albeit nonlinearly with the 10.7-cm radio flux (F _10.7), which forms a continuous record back to 1947. This enables the nonlinear relationship to be estimated with usable accuracy and shows that relationship to be consistent over multiple solar activity cycles. From the sunspot number record we estimate F _10.7 values back to 1600 AD. F _10.7 is linearly correlated with the total amount of magnetic flux in active regions, and we use it as input to a simple cascade model for the other magnetic flux components. The irradiance record is estimated by using these magnetic flux components plus a very rudimentary model for the modulation of energy flow to the photosphere by the subphotospheric magnetic flux reservoir feeding the photospheric magnetic structures. Including a Monte Carlo analysis of the consequences of measurement and fitting errors, the model indicates the mean irradiance during the Maunder Minimum was about 1 ± 0.4 W m⁻² lower than the mean irradiance over the last solar activity cycle.     

Periodicities of Sunspot Number and Coronal Index Time Series During Solar Cycle 23

We investigate the presence and temporal evolution of short- and intermediate-term periodicities in the daily data of sunspot numbers and coronal index for the time span from May 1996 to December 2008, which covers the entire Solar Cycle 23. The daily sunspot number data have been analyzed for the full disk, and for northern and southern hemispheres of the Sun. Using the wavelet power spectrum technique, we find a number of quasi-periodic oscillations in all the data sets. We also find a prominent period of 22 to 35 days in the high-frequency range, and detect the Rieger period of 150 to 160 days in both data sets during different phases of Cycle 23. We also detect ∼1.3 year oscillation in both sunspot and coronal index time series. In addition, we find a number of other short and mid-term periods. We discuss possible explanations of the observed periodicities in the light of previous results and existing numerical models.     

Short-Term Periodicities in Sunspot Activity and Flare Index Data during Solar Cycle 23

The short-term periodicities in sunspot numbers, sunspot areas, and flare index data are investigated in detail using the Date Compensated Discrete Fourier Transform (DCDFT) for the full disk of the Sun separately over the rising, the maximum, and the declining portions of solar cycle 23 (1996 – 2006). While sunspot numbers and areas show several significant periodicities in a wide range between 23.1 and 36.4 days, the flare index data do not exhibit any significant periodicity. The earlier conclusion of Pap, Tobiska, and Bouwer (1990, Solar Phys. 129, 165) and Kane (2003, J. Atmos. Solar-Terr. Phys. 65, 1169), that the 27-day periodicity is more pronounced in the declining portion of a solar cycle than in the rising and maximum ones, seems to be true for sunspot numbers and sunspot area data analyzed here during solar cycle 23.     

Periodicities in solar activity

The techniques of power spectral analysis are used to determine significant periodicities in the annual mean relative sunspot numbers. The main conclusion is that a period of 10.45 yr is very basic and can be associated with an excitation of new solar cycles. When combined with a period of 11.8 yr, associated here with the free-running length of a solar cycle, the mean cycle length of 11.06 yr and a phase variation of 190 yr are explained. Similarly the amplitude variations with periods 88 and 59 yr (previously described as the 80-yr cycle) are due to an amplitude modulation of the solar cycle by a period of 11.9±0.3 yr. The results dispute several associations of planetary position and solar activity.Radiophysics Publication RPP 1647, January, 1973.     

Minimum of 2008 or the “quantum” Sun-2

The prolonged 2007–2009 minimum is a big surprise for solar physics. In order to reveal the causes, we analyze the variability of the general magnetic field (GMF) of the Sun as a star measured by CrAO and five other observatories since 1968 (more than 19000 daily field strengths B were obtained in 41 years). Sharp yearly mean extrema of the negative (S) field took place in 1969, 1990, and 2008, with the third extremum, in contrast to the two previous ones, having coincided with the sunspot minimum. This explains both the long duration of the minimum and the record (over the last 100 years) increase in the length of the Wolf cycle (no. 23) to 12 or more years. The S-field extrema followed with a period of 19.5 ± 1.1 yr—some mean between the 22.1 ± 0.3-yr sunspot cycle, the 18.6-yr saros, and the 19.9-yr Jupiter-Saturn conjunction period. It is pointed out that, for some unclear reason, the negative polarity dominated on the Sun in 1968–2008: the overall mean B = −0.021 ± 0.015 G. The existence of a second Sun that obeys the laws of quantum mechanics is hypothesized. The “quantum” model of the Sun-2 explains many properties of the “classical” Sun-1, including the coronal heating, cyclic activity, periodic variations in GMF, and its sector structure.     

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.     

On the long-term secular increase in sunspot number

Correlated with the maximum amplitude (R _max) of the sunspot cycle are the sum (R _sum) and the mean (R _mean) of sunspot number over the duration of the cycle, having a correlation coefficient r equal to 0.925 and 0.960, respectively. Runs tests of R _max, R _sum, and R _mean for cycles 0–21 have probabilities of randomness P equal to 6.3, 1.2, and 9.2%, respectively, indicating a tendency for these solar-cycle related parameters to be nonrandomly distributed. The past record of these parameters can be described using a simple two-parameter secular fit, one parameter being an 8-cycle modulation (the so-called Gleissberg cycle or long period) and the other being a long-term general (linear) increase lasting tens of cycles. For each of the solar-cycle related parameters, the secular fit has an r equal to about 0.7–0.8, implying that about 50–60% of the variation in R _max, R _sum, and R _mean can be accounted for by the variation in the secular fit.Extrapolation of the two-parameter secular fit of R _max to cycle 22 suggests that the present cycle will have an R _max = 74.5 ± 49.0, where the error bar equals ± 2 standard errors; hence, the maximum amplitude for cycle 22 should be lower than about 125 when sunspot number is expressed as an annual average or it should be lower than about 130 when sunspot number is expressed as a smoothed (13-month running mean) average. The long-term general increase in sunspot number appears to have begun about the time of the Maunder minimum, implying that the 314-yr periodicity found in ancient varve data may not be a dominant feature of present sunspot cycles.     

Intermediate-term periodicities in solar activity

The presence of intermediate-term periodicities in solar activity, at approximately 323 and 540 days, has been claimed by different authors. In this paper, we have performed a search for them in the historical records of two main indices of solar activity, namely, the daily sunspot areas (cycles 12–21) and the daily Zürich sunspot number (cycles 6–21). Two different methods to compute power spectra have been used, one of them being especially appropriate to deal with gapped time series. The results obtained for the periodicity near 323 days indicate that it has only been present in cycle 21, while in previous cycles no significant evidence for it has been found. On the other hand, a significant periodicity at 350 days is found in sunspot areas and Zürich sunspot number during cycles 12–21 considered all together, also having been detected in some individual cycles. However, this last periodicity must be looked into with care due to the lack of confirmation for it coming from other features of solar activity. The periodicity around 540 days is found in cycles 12, 14, and 17 in sunspot areas, while during cycles 18 and 19 it is present, with a very high significance, in sunspot areas and Zürich sunspot number. It also appears at 528 days in sunspot areas during cycles 12–21. On the other hand, it is important to note the coincidence between the asymmetry, favouring the northern hemisphere, of sunspot areas and solar flares during cycle 19, and the fact that the periodicity at 540 days was only present, with high significance, in that hemisphere during that solar cycle.     

大行星运动对太阳黑子活动的可能影响

本文计算了由太阳系大行星轨道运动引起的日心相对于太阳系质心的轨道运动角动量变化率j_⊙,在理论上对j_⊙作展开,表明它存在多项短周期变化,与太阳黑子资料的分析结果相比较,两者结果是符合的,它们具有一致的谱结构。因此,行星的轨道运动对太阳黑子活动存在动力作用的可能性又进一步得到了验证。     

The thermoluminescence profile of a recent sea sediment core and the solar variability

The analysis of the thermoluminescence (TL) profile of the GT14 recent sea sedimentary core shows the existence of four main periodicities of 137.7, 59,12.06, and 10.8 years. Here we discuss the affinity of these waves to the known cycles of solar variability. The beats of the two high frequency components produce a modulated wavetrain with a carrier wave of 11.4 years and an amplitude modulation with period 206 years. The minima of this squared amplitude modulation fall in 1810 and 1913 A.D. and closely correspond to the periods of lowest solar activity as indicated by the sunspot series. The sum of the two low frequency waves can in turn be rewritten as a component with period 82.6 years which is amplitude modulated by a second component with period of 206 years. The 82.6-yr wave has the period commonly attributed to the Gleissberg cycle of solar activity. The maxima of the 82.6-yr wave occur in agreement with the dates of maximum solar radius as suggested by Gilliland (1981).