On the Fractal Structure of Solar Supergranulation

We employ fractal analysis to study the complexity of supergranulation structure using the Solar and Heliospheric Observatory (SOHO) dopplergrams. Our data consists of 200 visually selected supergranular cells, for which we find a broad, slightly asymmetric dispersion in the size distribution, with the most probable size around 31.9 Mm. From the area–perimeter relation, we deduce a fractal dimension D of about 1.25. This is consistent with that for isobars, and suggests a possible turbulent origin of supergranulation. By relating this to the variances of kinetic energy, temperature and pressure, it is concluded that the supergranular network is close to being isobaric and that it has a possible turbulent origin.     

An Analysis of Solar Global Activity

This article proposes a unified observational model of solar activity based on sunspot number and the solar global activity in the rotation of the structures, both per 11-year cycle. The rotation rates show a variation of a half-century period and the same period is also associated to the sunspot amplitude variation. The global solar rotation interweaves with the observed global organisation of solar activity. An important role for this assembly is played by the Grand Cycle formed by the merging of five sunspot cycles: a forgotten discovery by R. Wolf. On the basis of these elements, the nature of the Dalton Minimum, the Maunder Minimum, the Gleissberg Cycle, and the Grand Minima are presented.     

Systematic Time Delay of Hemispheric Solar Activity

Five solar-activity indices – the monthly-mean sunspot numbers from January 1945 to March 2008, the monthly-mean sunspot areas during the period of May 1874 to March 2008, the monthly numbers of sunspot groups from May 1874 to May 2008, the monthly-mean flare indices from January 1966 to December 2006, and the numbers of solar filaments per Carrington rotation in the time interval of solar rotations 876 to 1823 – have been used to show a systematic time delay between northern and southern hemispheric solar activities in a cycle. It is found that solar activity does not occur synchronously in the northern and southern hemispheres, and there is a systematic time lag or lead (phase shift) between northern and southern hemispheric solar activity in a cycle. About an eight-cycle period is inferred to exist in such phase shifts. The activity on the Sun may be governed by two different and coupled processes, not by a single process.     

Short-Term Periodicities in the Time Series of Solar Radio Emissions at Different Solar Altitudes

A spectral analysis of the time series of daily values of 12 parameters, namely, ten solar radio emissions in the range 275–1755 MHz, 2800 MHz solar radio flux, and sunspot numbers for six continuous intervals of 132 values each during June 1997–July 1999 showed considerable differences from one interval to the next, indicating a nonstationary nature. A 27-day periodicity was noticed in Interval 2 (26.8 days), 3 (27.0 days), 5 (25.5 days), 6 (27.0 days). Other periodicities were near 11.4, 12.3, 13.3, 14.5, 15.5, 16.5, 35, 40, 50–70 days. Periodicities were very similar in a large vertical span of the coronal region corresponding to 670–1755 MHz. Above this region, the homogeneity disappeared. Below this region, there were complications and distortions due to localized solar surface phenomena.     

Detection of Quasi-Periodic Pulsations in Solar EUV Time Series

Quasi-periodic pulsations (QPPs) are intrinsically connected to the mechanism of solar flares. They are regularly observed in the impulsive phase of flares since the 1970s. In the past years, the studies of QPPs regained interest with the advent of a new generation of soft X-ray/extreme ultraviolet radiometers that pave the way for statistical surveys. Since the amplitude of QPPs in these wavelengths is rather small, detecting them implies that the overall trend of the time series needs to be removed before applying any Fourier or wavelet transform. This detrending process is known to produce artificial detection of periods that must then be distinguished from real ones. In this paper, we propose a set of criteria to help identify real periods and discard artifacts. We apply these criteria to data taken by the Extreme Ultraviolet Variability Experiment (EVE)/ESP onboard the Solar Dynamics Observatory (SDO) and the Large Yield Radiometer (LYRA) onboard the PRoject for On-Board Autonomy 2 (PROBA2) to search for QPPs in flares stronger than M5.0 that occurred during Solar Cycle 24.     

Applications of the DFT/CLEAN Technique to Solar Time Series

A new technique of Fourier analysis, DFT/CLEAN, has been adapted for the study of solar time series. The technique was developed by Roberts and his collaborators (1987, 1994) to address the limitations of other techniques of Fourier analysis and the shortcomings of many astronomical time series. The utility of the technique is illustrated with several applications to solar time series.     

Cosmic Rays and Solar Coronal Emissions: Cross-Correlations of the Time Series

The cosmic-ray (CR) time series were compared with the green 530.3 nm coronal emission line intensity over the period 1951–2003. There is a clear asymmetry in the cross-correlation between the cosmic rays and green emission corona for the even- and odd-numbered solar cycles, where a time lag is ranging between 0 and 380 days. While over the period 1954–1964 and 1978–1985 the time lag is above 200 days, over the period 1965–1976 and 1986–1995 the time lag is below 130 days. A possible reason for the lag asymmetry is discussed. The cross-correlations between the cosmic rays and Wolf sunspot number over the period 1951–2003 is also presented.     

Influence of the Solar Global Magnetic-Field Structure Evolution on CMEs

We consider the influence of the solar global magnetic-field structure (GMFS) cycle evolution on the occurrence rate and parameters of coronal mass ejections (CMEs) in Solar Cycles 23?–?24. It has been shown that, over solar cycles, CMEs are not distributed randomly, but they are regulated by evolutionary changes in the GMFS. It is proposed that the generation of magnetic Rossby waves in the solar tachocline results in the GMFS cycle changes. Each Rossby wave period favors a particular GMFS. It is proposed that the changes in wave periods result in GMFS reorganization and consequently in CME location, occurrence rate, and parameter changes. The CME rate and parameters depend on the sharpness of the GMFS changes, the strength of the global magnetic field, and the phase of a cycle.     

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.     

The Global Context of Solar Activity During the Whole Heliosphere Interval Campaign

The Whole Heliosphere Interval (WHI) was an international observing and modeling effort to characterize the 3-D interconnected ??heliophysical?? system during this solar minimum, centered on Carrington Rotation 2068, March 20??C?April 16, 2008. During the latter half of the WHI period, the Sun presented a sunspot-free, deep solar minimum type face. But during the first half of CR 2068 three solar active regions flanked by two opposite-polarity, low-latitude coronal holes were present. These departures from the quiet Sun led to both eruptive activity and solar wind structure. Most of the eruptive activity, i.e., flares, filament eruptions and coronal mass ejections (CMEs), occurred during this first, active half of the interval. We determined the source locations of the CMEs and the type of associated region, such as active region, or quiet sun or active region prominence. To analyze the evolution of the events in the context of the global solar magnetic field and its evolution during the three rotations centered on CR 2068, we plotted the CME source locations onto synoptic maps of the photospheric magnetic field, of the magnetic and chromospheric structure, of the white light corona, and of helioseismological subsurface flows. Most of the CME sources were associated with the three dominant active regions on CR 2068, particularly AR 10989. Most of the other sources on all three CRs appear to have been associated with either isolated filaments or filaments in the north polar crown filament channel. Although calculations of the flux balance and helicity of the surface magnetic features did not clearly identify a dominance of one region over the others, helioseismological subsurface flows beneath these active regions did reveal a pronounced difference among them. These preliminary results suggest that the ??twistedness?? (i.e., vorticity and helicity) of subsurface flows and its temporal variation might be related to the CME productivity of active regions, similar to the relationship between flares and subsurface flows.     

Correlation of Solar Indices with Solar euv Fluxes

The paper presents a more extensive comparison of Extreme Ultraviolet (EUV) irradiances during AE-E (1977–1980), Pioneer Venus (1979–1992) and SEM/SOHO (1996 onwards) with other solar indices than has been discussed previously. For long-term changes (solar cycle), all indices had similar trends and inter-correlations were high, so that any one could serve as a proxy for the other. For intermediate time-scales (monthly means), only L, F10 (2800 MHz) and Mgii had reasonably high correlations with EUV. The 2695 MHz radio emission also had a high correlation. For daily values, data for many indices are intermittant and these cannot serve as proxies. Again, only L, F10 (and 2695 MHz), Mgii stand out as possible proxies for EUV, particularly during intervals of strong 27-day sequences.     

The Relationship Between the Amplitude and Descending Time of a Solar Activity Cycle

The amplitude of a solar-activity cycle is found to be well correlated (r = −0.811) with the descending time three cycles earlier, in smoothed monthly-mean sunspot numbers for Cycles 8 – 23. The descending time therefore can be used as one of the indicators to predict the amplitudes. As a result, the amplitudes of Cycles 24 – 25 are estimated to be 114.8 ± 17.4, 111.6 ± 17.4, respectively, where the error bar equals ± standard error.     

Periodicities in the Time Series of Solar Coronal Radio Emissions and Chromospheric uv Emission Lines

A spectral analysis of the time series of daily values of ten solar coronal radio emissions in the range 275–1755 MHz, the 2800 MHz radio flux, several UV emission lines in the chromosphere and in the transition region, and sunspot number, for six successive intervals of 132 days each, during June 1997–July 1999 (26 months) showed that the spectral characteristics were not the same for all intervals. Details are presented for Interval 1, where there was no 27-day oscillation, and Interval 2, where there was a strong 27-day oscillation. In every interval, periodicities were remarkably similar in most of these indices, indicating that the solar atmosphere (chromosphere and corona) rotated as one block, up to a height of 150000 km. Above this height, the periodicities became obscure. Near the solar surface, sunspots showed extra or different periodicities, some of which vanished at low altitudes. For the 27-day feature as also for the long-term rise during 1996–1998, the maximum percentage changes were for radio emissions near 1350–1620 MHz.     

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.     

A Correlative Study of Green Coronal Intensity with Other Solar Indices

Lomnický tít data of 5303 Ú coronal green-line index (CI) are analysed for the years 1965–1994. The yearly quiet-Sun component (Q_ci) of CI estimated through the linear regression analysis of CI with sunspot numbers (SS) and CI with Ca plage index (CA) are found to vary with the 11-year solar activity cycle. Comparison of Q_ci with the quiet-Sun component of 10.7 cm flux (Q_10.7) revealed that the Q_ci contributes principally to the entire CI, while Q_10.7 assumes much smaller values compared to its yearly averages. The slowly varying component of 5303 Ú emission associated with sunspots and plages seems to be nearly absent in CI. This aspect is also confirmed through the multiple-linear regression analysis of CI with sunspots and plages. The delayed response of green corona to both sunspots and plages also revealed similar results.     

Quasi-Biennial Oscillations of Global Solar-Activity Indices

Quasi-biennial oscillations of solar activity are investigated using several global indices. The Singular Spectrum Analysis is used to separate out and study quasi-biennial oscillations; this method is one of the modifications of the main components method. The principal components of the solar cycle are stable 11-year, secular, and quasi-biennial variations. The periods and shapes of individual variations in each quasi-biennial train depend on the length and power of the particular 11-year cycle.     

The Transitional Time Scale from Stochastic to Chaotic Behavior for Solar Activity

Following the progression of nonlinear dynamical system theory, many authors have used varied methods to calculate the fractal dimension and the largest Lyapunov exponent ₁ of the sunspot numbers and to evaluate the character of the chaotic attractor governing solar activity. These include the Grassberger–Procaccia algorithm, the technique provided by Wolf et al., and the nonlinear forecasting approach based on the method of distinguishing between chaos and measurement errors in time series described by Sugihara and May. In this paper, we use the Grassberger–Procaccia algorithm to estimate the other character of the chaotic attractor. This character is time scale of a transition from high-dimensional or stochastic at shorter times to a low-dimensional chaotic behavior at longer times. We find that the transitional time scale in the monthly mean sunspot numbers is about 8 yr; the low-dimensional chaotic behavior operates at time scales longer than about 8 yr and a high-dimensional or stochastic process operates at time scales shorter than about 8 yr.     

Fourier Analysis of Gapped Time Series: Improved Estimates of Solar and Stellar Oscillation Parameters

Quantitative helioseismology and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. The precision of these measurements depends on the total length (T), quality, and completeness of the observations. Except in a few simple cases, the effect of gaps in the data on measurement precision is poorly understood, in particular in Fourier space where the convolution of the observable with the observation window introduces correlations between different frequencies. Here we describe and implement a rather general method to retrieve maximum likelihood estimates of the oscillation parameters, taking into account the proper statistics of the observations. Our fitting method applies in complex Fourier space and exploits the phase information. We consider both solar-like stochastic oscillations and long-lived harmonic oscillations, plus random noise. Using numerical simulations, we demonstrate the existence of cases for which our improved fitting method is less biased and has a greater precision than when the frequency correlations are ignored. This is especially true of low signal-to-noise solar-like oscillations. For example, we discuss a case where the precision of the mode frequency estimate is increased by a factor of five, for a duty cycle of 15%. In the case of long-lived sinusoidal oscillations, a proper treatment of the frequency correlations does not provide any significant improvement; nevertheless, we confirm that the mode frequency can be measured from gapped data with a much better precision than the 1/T Rayleigh resolution.     

Solar Cycle Phase Dependence of Supergranular Fractal Dimension

We study the complexity of supergranular cells using the intensity patterns obtained from the Kodaikanal Solar Observatory during the 23rd solar cycle. Our data consists of visually identified supergranular cells, from which a fractal dimension D for supergranulation is obtained according to the relation P?∝?A ^D/2, where A is the area and P is the perimeter of the supergranular cells. We find a difference in the fractal dimension between active and quiet region cells in the ascending phase, during the peak and in the descending phase which is conjectured to be due to the magnetic activity level.