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.     

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.     

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.     

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.     

Comparison of three solar activity indices based on sunspot observations

The following sunspot formation indices are analyzed: the relative sunspot number R _z, the normalized sunspot group number R _g, and the total sunspot area A. Six empirical formulas are derived to describe the relations among these indices after 1908. The earlier data exhibit systematic deviations from these formulas, which can be attributed to systematic errors of the indices. The Greenwich data on the sunspot total area A and the sunspot group number in 1874–1880 are found to be doubtful. Erroneous data at the beginning of the Greenwich series must spoil the values of the index R _g in the XVII–XIX centuries. The Hoyt-Schatten series of R _g may be less reliable than the well-known Wolf number series R _z.     

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.     

Long-term trends in solar activity. Variations of solar indices in the last 40 years

We analyze long-term variations of several solar activity indices(AIs) that have been measured over the last 40 years. With this goal, we study the AIs that characterize the fluxes from different areas in the solar atmosphere. Our consideration of mutual correlations between the solar indices is based on the study of relationships between them in the period from 1950 to 1990. This period of time, covering activity cycles 19–22, is characterized by relatively stable relations between the indices. We investigate the normalized variations of these indices in recent time in relation to their values which were calculated by considering radiation from the Sun in the radio range at a wavelength of 10.7 cm(F10.7) in 1950–1990.The analysis of time series, representing variations of the normalized AI(AIFF) in solar cycles 23–24,shows different trends exist for different indices in terms of their long-term behavior. We assume that variations of normalized International Sunspot Number(SSN), F530.3 and Flare Index, which have shown sharp decreases in the last 40 years, are possibly associated with a decrease in the intensity of large-scale magnetic fields in the photosphere(SSN) and in the corona(the coronal index and the Flare Index).     

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.     

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.     

Rieger quasi-periodicity in solar indices

Using wavelet analysis and Fourier analysis, the temporal behavior of ??156-day quasi-periodicity (Rieger quasi-periodicity, RQ) is investigated for series of daily solar indices: Wolf numbers W for 161 years (from 1849), the flux F_10.7 of the Sun??s radio emission at a frequency of 2800 MHz for 63 years (from 1947), the number of X-ray flares N _X for 29 years (from 1981), and the number of optical flares N _?? for 11 years in cycle 21. The N _?? series are studied for four quadrants of the solar disk. It is found for the W series that there is no stable dependence of the amplitude RQ on the cycle phase and the W value. It is associated with the fact that, corresponding to a period of around eight years, in the power spectrum changes in the amplitude of the Rieger quasiperiodicity of the index W are dominated by the peak. Moreover, the peaks corresponding to the 11-year cyclicity are also significant. The comparative study of the temporal behavior of the Rieger quasi-periodicity amplitude of the indices W, F_10.7, and N _X has shown that the quasi-periodicity covers the processes, occurring in active regions on the Sun at different altitudes, almost simultaneously. It is found that for N _??, the lag of variations of the Rieger quasi-periodicity amplitude for series of the Sun??s western hemisphere, relative to those for series of the eastern hemisphere, is on average less than for the flare series. Thus, if the flare occurrence is modulated by the Rieger quasi-periodicity process as a wave propagating over the Sun??s disc, then the wave is not a retrograde one. Different interpretations of the nature of the Rieger quasi-periodicity are discussed including the hypothesis of Rossby waves.     

Solar neutrino data and the 11-year solar activity cycle

Recent data on solar neutrino flux have been analysed and it is shown that there is a statistically significant variation of solar neutrino flux data with the solar activity cycle. Thus the observation suggests that the solar activity cycle is due to the pulsating characters of the nuclear energy generation in the interior of the Sun.     

Forecast daily indices of solar activity, F10.7, using support vector regression method

The 10.7 cm solar radio flux （F10.7）, the value of the solar radio emission flux density at a wavelength of 10.7 cm, is a useful index of solar activity as a proxy for solar extreme ultraviolet radiation. It is meaningful and important to predict F10.7 values accurately for both long-term （months-years） and short-term （days） forecasting, which are often used as inputs in space weather models. This study applies a novel neural network technique, support vector regression （SVR）, to forecasting daily values of F10.7. The aim of this study is to examine the feasibility of SVR in short-term F10.7 forecasting. The approach, based on SVR, reduces the dimension of feature space in the training process by using a kernel-based learning algorithm. Thus, the complexity of the calculation becomes lower and a small amount of training data will be sufficient. The time series of F10.7 from 2002 to 2006 are employed as the data sets. The performance of the approach is estimated by calculating the norm mean square error and mean absolute percentage error. It is shown that our approach can perform well by using fewer training data points than the traditional neural network.     

Forecast daily indices of solar activity, F10.7, using support vector regression method

The 10.7cm solar radio flux (F10.7), the value of the solar radio emission flux density at a wavelength of 10.7cm, is a useful index of solar activity as a proxy for solar extreme ultraviolet radiation. It is meaningful and important to predict F10.7 values accurately for both long-term (months-years) and short-term (days) forecasting, which are often used as inputs in space weather models. This study applies a novel neural network technique, support vector regression (SVR), to forecasting daily values of F10.7. The aim of this study is to examine the feasibility of SVR in short-term F10.7 forecasting. The approach, based on SVR, reduces the dimension of feature space in the training process by using a kernel-based learning algorithm. Thus, the complexity of the calculation becomes lower and a small amount of training data will be sufficient. The time series of F10.7 from 2002 to 2006 are employed as the data sets. The performance of the approach is estimated by calculating the norm mean square error and mean absolute percentage error. It is shown that our approach can perform well by using fewer training data points than the traditional neural network.     

On a relation between the indices of solar activity in the photosphere and the corona

In the first part a new index of solar activity in the photosphere is introduced i.e. the areas index I _a defined with the help of the relation, where A and f are the total areas of the sunspots and faculae respectively corrected for foreshortening.In the second part a relation of the form: is proposed, where S represents the intensity of solar radio-emission in the frequency range 1000 f < 10000 MHz, i _f is the index of solar flares, S ₀o is the corresponding value of s for I _a = 0 and K is a constant.In the third part a relation of the form: is proposed, where I 5303 is the mean intensity of the coronal line 5303 Å for each quarter of the years 1954–1964, n _pf is the corresponding number of proton flares, I ₀ is the value of I ₅₃₀₃ corresponding to I = 0 and K is a constant.     

The 156-day quasi-periodicity in solar indices

This paper investigates a series of daily solar indices: the sunspot number W (1900–2008), solar flux at 2800 MHz F _10.7 (1947–2008), and a number of X-ray flares N _x (1981–2008). The methods of Fourier and wavelet analysis are used to reveal the so-called 156-day Rieger-type periodicity (RTP). The W index is observed to have a statistically significant RTP amplitude in the neighborhood of the solar maxima in most of the solar cycles under study, except for cycles 14, 15, and 23. The 156-day peak is observed to have its largest power during the declining phase of cycle 16, at the maximum of cycle 21, and during the increasing phase of cycles 20 and 23. Statistically significant RTPs are also observed at the minima of cycles 17, 18 and 19. We conclude that there is no stable dependence between RTP and the solar cycle. The wavelet analysis shows that the pattern of the RTP time dependence for the F _10.7 index is almost identical to that of the W index. The correlation coefficient between the RTP curves is 0.95. The correlation coefficients for the pairs of indices W-N _x and F _10.7-N _x are 0.36 and 0.32, respectively. No time lags are found between the RTP starting points for different indices. Thus, the 156-day quasi-periodicity involves, almost simultaneously, events that occur in active regions of the solar atmosphere at different heights. This paper discusses the possible nature of RTP.     

Thermal characteristics of a classical solar telescope primary mirror

We present a detailed thermal and structural analysis of a 2 m class solar telescope mirror which is subjected to a varying heat load at an observatory site. A 3-dimensional heat transfer model of the mirror takes into account the heating caused by a smooth and gradual increase of the solar flux during the day-time observations and cooling resulting from the exponentially decaying ambient temperature at night. The thermal and structural response of two competing materials for optical telescopes, namely Silicon Carbide – best known for excellent heat conductivity and Zerodur – preferred for its extremely low coefficient of thermal expansion, is investigated in detail. The insight gained from these simulations will provide a valuable input for devising an efficient and stable thermal control system for the primary mirror.     

Soft solar X-rays and solar activity

Soft solar X-rays in the wavelength interval 8–12 Å were observed from OSO III. The totality of the observations that were made between 9 March, 1967, and 18 May, 1968, is summarized graphically and compared to the course of solar activity as observed at other wavelengths, with particular emphasis upon visible activity.     

Soft solar X-rays and solar activity

Soft X-radiation between 8–12 Å was found to be emitted from the Sun at the time of four optically-identified major systems of loop prominences. The peak emission rates and time-integrated X-ray energies are very similar for three of the events while the fourth appeared to emit X-rays only weakly. The data are not consistent with a compression-condensation model for the loops, and support the fast-proton injection model. Proton injection may take place on a long time scale.     

Delay times between geoeffective solar disturbances and geomagnetic indices

We have examined delay times between solar disturbances (X-ray flares and DSFs) and storm sudden commencements(SSC) as well as between SSC and major geomagnetic storms. To carry out cross-correlation analysis of these point series data, we have introduced a new correlation measure which is defined by the ratio of the median value of the absolute residual differences between two sets of time series data to the one determined from hypothetical target series. We have confirmed from the correlation analyses that (1) the most probable traveling time of a solar disturbance from the Sun to the Earth is estimated to be about 2 days for a disturbance associated with major (X and M class) solar flares, and about 3 days for a disturbance associated with DSFs, (2) long-duration flares are better correlated with SSCs than short-duration flares, (3) travelling times of solar disturbances strongly depend on the heliolongitude where they originate, and (4) solar disturbances associated with flares and DSFs at the western limb can hardly reach the Earth. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solar indices and solar u.v.-irradiances

Solar radio fluxes, Zurich relative sunspot number R_z, and Solar Call plage indexes daily values for the period 1957–1980 are analyzed in order to test the stability of the series with respect to time and solar activity. It is found that between the series of the 3,8 and 10 cm radio fluxes and the series of R_z no significant trend with time, solar activity or solar cycle exists when mean values for periods of the order of one year are considered.Then, the daily solar u.v.-irradiances measured since 1969 for H-Lyman-alpha and-beta, the Hel-resonance line and HeII-Lyman-alpha are compared with the 10.7 cm radio fluxes and adjusted. After adjustment, the behaviour of the four series of irradiances with respect to the 10.7 cm flux shows a similar structure as the behaviour typical for the series of the 3 cm or the 8 cm fluxes.This adjustment allows the determination of the slope of the mean variation of the u.v.-irradiances with solar activity. The increases from solar minimum to solar maximum related to the minimum values are respectively : 60% for H-Lyman-alpha, 80% for H-Lyman-beta and 90% for Hel and Hell.