Wavelet Analysis of the New Solar Neutrino Capture Rate Data for the Homestake Experiment

Wavelet analysis offers an alternative to Fourier based time- series analysis and is particularly useful when spectral features are time dependent. We analyze the solar neutrino capture rate of the radiochemical Homestake chlorine experiment with abbreviated Morlet wavelets, using Foster's (AJ, 111,1709(1996)) rescaled wavelet technique. We emphasize the complementarity of wavelet analysis to Fourier analysis. Wavelet analysis confirms the results of previously undertaken Fourier analysis. The Homestake data seem to contain a harmonic content with periodicities of 4.76 yr, 1.89 yr, 0.85 yr, and 0.51 yr. Wavelet analysis reveals that the 4.76 yr and 1.89 yr periods show an almost constant behavior over the 25 yr Homestake data record, while the 0.85 yr and 0.51 yr periods exhibit a transient phenomenon. The analysis does not show strong evidence for a period of the solar 11 yr cycle. This revised version was published online in July 2006 with corrections to the Cover Date.     

The search for possible time variations in Davis' measurements of the argon production rate in the solar neutrino experiment

With the gradual accumulation of experimental data in the solar neutrino experiment of DAVIS and collaborators (runs 18–74 for 1970–1982), the question, whether there are time variations of the solar neutrino flux, is of renewed interest. We discuss the mathematical-numerical methods applied to the statistical analysis of DAVIS ' argon-37 production rate up till now known in the literature. These methods are characterized by the arbitrary arrangement of the DAVIS data in a time series. We perform a certain Fourier transformation for unequally-spaced time series of the measuring data of the argon-37 production rate, discuss the discovered periods and give significance criteria with respect to each period. We find that all periods discussed in the literature are contained in our series of periods. Pointing out the more mathematical character of the time series analysis we emphasize the predominant significance of the detected periods.     

Kinematics and evolution of local features of the large-scale magnetic field – II. Relation to Active Regions

Relationships have been studied between the background magnetic field and the distribution of active regions over the solar surface and time. A series of magnetic-field synoptic maps covering a 20-year period has been cross-correlated with spatio-temporal distributions of three types of active formations (sunspots, calcium plages, and solar flares) used as indicators of the active regions. To make the data analysis more effective, we expanded both the magnetic-field and the active-region distributions in terms of Fourier series in longitude, and then cross-correlated the latitude-dependent Fourier harmonics. Cross-correlation functions calculated from the lower-order Fourier harmonics exhibit prolonged maxima of the amplitude. For the first-order harmonic, the maxima can be tracked throughout a long time interval of at least 13 Carrington rotations, but the time of cross-correlation decreases down to 2 rotations, as the harmonic order increases up to 8. The maxima of the cross-correlation functions indicate moreover a poleward directed drift of the magnetic features that occurred with a velocity of 10–15 m s^–1. The cross-correlation functions calculated separately by using the three types of active formations as indicators of the active regions are similar to each other, although they differ in some details of minor significance. The results of the data analysis make it possible to conclude that the cross-correlation between the magnetic-field and the active-region distributions displays long-term evolution of the magnetic features emerged in the photosphere in the form of the active regions, and that the evolution occurs in accordance with Leighton's (1964) concept known at present as the flux transport model. In order to verify this conclusion, we applied the cross-correlation technique to analyze a magnetic field distribution simulated by means of the flux transport equation by using an ensemble of local-scale magnetic bipoles as a source of magnetic flux. Results of the simulated magnetic field analysis exhibit a substantial qualitative agreement with those obtained by examining the observational data.     

Intermediate‐term variations in solar radius during solar cycle 23

In this study, we look for the mid‐term variations in the daily average data of solar radius measurements made at the Solar Astrolabe Station of TUBITAK National Observatory (TUG) during solar cycle 23 for a time interval from 2000 February 26 to 2006 November 15. Due to the weather conditions and seasonal effect dependent on the latitude, the data series has the temporal gaps. For spectral analysis of the data series, thus, we use the Date Compensated Discrete Fourier Transform (DCDFT) and the CLEANest algorithm, which are powerful methods for irregularly spaced data. The CLEANest spectra of the solar radius data exhibit several significant mid‐term periodicities at 393.2, 338.9, 206.5, 195.2, 172.3 and 125.4 days which are consistent with periods detected in several solar time series by several authors during different solar cycles. The knowledge relating to the origin of solar radius variations is not yet present. To see whether these variations will repeat in next cycles and to understand how the amplitudes of such variations change with different phases of the solar cycles, we need more systematic efforts and the long‐term homogeneous data. Since most of the periodicities detected in the present study are frequently seen in solar activity indicators, it is thought that the physical mechanisms driving the periodicities of solar activity may also be effective in solar radius variations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating Long-Term Solar Irradiance Variability: A New Approach

The detection of solar irradiance variations (both bolometric and at various wavelengths) by satellite-based experiments during the last one-and-a-half decades stimulated modeling efforts to help identify their causes and to provide estimates of irradiance data for those time intervals when no satellite observations exist. In this paper we present estimates of the long-term irradiance changes developed with Fourier and wavelet transforms. The month-to-month irradiance variations, after removing the solar cycle related long-term changes, are studied with the cross-correlation technique. Results of the analysis reveal a significant phase shift at 3 months between the full-disk magnetic field strength and total solar and UV irradiance, with irradiance leading the magnetic field variability. In addition to this time delay between the changes in solar irradiance and the magnetic field, a 10-month phase shift has been found between the UV flux at 280 nm and total solar irradiance corrected for sunspot darkening. The existence of these phase shifts suggests the possibility of a coupling between the physical processes taking place below, in, and above the photosphere.     

The 27-Day Signal in Sunspot Number Series and the Solar Dynamo

We analyze the Wolf number daily series WN (1849 to present) as well as two other related series characterizing solar activity. Our analysis consists in computing the amplitude of a given Fourier component in a sliding time window and examining its long-term evolution. We start with the well-known 27.03- and 27.6-day periods and observe strong decadal variations of this amplitude as well as a sharp increase of the average value starting around 1905. We then consider a packet of 31 lines with periods from 25.743 to 28.453 days, which is shown to be a better representation of the synodic solar rotation. We first examine the temporal evolution of individual lines, then the energy of the packet. The energy of the packet increases sharply at the beginning of the 20th century, leading by more than two decades the well-known increase of the Wolf number. The nonaxisymmetry of sunspots increases before the total increase of activity and may be considered as a precursor. We discuss briefly and tentatively this observation in terms of solar dynamo theory.     

Evaluation of the short-term periodicities in the flare index between the years 1966–2002

The short-term periodicities of the flare index are investigated in detail using Fourier and wavelet transforms for the full disc and for the northern and the southern hemispheres of the Sun separately over the epoch of almost 4 cycles (1966–2002). The most pronounced power peaks were found by the Fourier transform to be present at 25.6, 27.0, 30.2, and 33.8 days. The wavelet transform results show that the occurrence of periodicities of flare index power is highly intermittent in time. A comparison of the results of the Fourier transform and the time-period wavelet transform of the flare index time series has clarified the importance of different periodicities, whether they are or are not the harmonics of the basic ones, as well as the temporal location of their occurrence. We found that the modulation of the flare index due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion.     

Correlation Between the Sunspot Number,the Total Solar Irradiance,and the Terrestrial Insolation

Our study deals with the correlations between the solar activity on the one hand and the solar irradiance above the Earth’s atmosphere and at ground level on the other. We analyzed the combined ACRIM I+II time series of the total solar irradiance (TSI), the Mauna Loa time series of terrestrial insolation data, and data of terrestrial cosmic ray fluxes. We find that the correlation between the TSI and the sunspot number is strongly non-linear. We interpret this as the net balance between brightening by faculae and darkening by sunspots where faculae dominate at low activity and sunspots dominate at high activity. Such a behavior is hitherto known from stellar analogs of the Sun in a statistical manner. We perform the same analysis for the Mauna Loa data of terrestrial insolation. Here we find that the linear relation between sunspot number and insolation shows more than 1% rise in insolation by sunspot number variations which is much stronger than for the TSI. Our conclusion is that the Earth atmosphere acts as an amplifier between space and ground, and that the amplification is probably controlled by solar activity. We suspect the cosmic rays intensity as the link between solar activity and atmospheric transparency. A Fourier analysis of the time series of insolation shows three dominant peaks: 10.5, 20.4, and 14.0 years. As a matter of fact, the cosmic rays data show the same pattern of significant peaks: 10.7, 22.4, and 14.9 years. This analogy supports our idea that the cosmic rays variation has influence on the transparency of the Earth atmosphere.     

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.     

Short-term variations of cosmic-ray intensity and flare related data in 1981–1983

A statistical analysis of the cosmic-ray intensity (CR) daily means, registered at three Neutron Monitor stations with different cut-off rigidities (Deep River, Climax and Alma-Ata), as well as, of the solar hard X-ray flares fluence recorded by Venera-13, -14 space-probes, has been performed for the time interval 1981–1983. Various methods of time series spectrum analysis, such as Fast Fourier Analysis (FFT) and Maximum Entropy (MESA), accompanied by appropriate statistical tests, have been employed to detect periodicities, while the method of Successive Approximations (SA) is used independently in order to define the amplitude and the phase of each fluctuation. New short-term periodicities of 100, 70, 50 and 32 days, in addition to the known ones of 152, 27 and 14 days, appeared in cosmic ray data. During this particular time interval, similar spectral behaviour has been reported in the solar hard X-ray flares data. The influence of the solar hard X-ray flares variability in the energy range 50–500 keV, expressed by their fluence values, upon the cosmic-ray modulation, is discussed.     

Sixty six day periodicity of polar coronal holes

Fourier analysis of the coronal hole size distribution shows sixty six day periodicity in respect of the time of advancement of solar cycle which is presumed to be due to the differential rotation of solar envelope.     

A 14-day periodicity in the mean solar magnetic field

In the present paper we look for periodicities in the mean solar magnetic field observed at Stanford Observatory, using Fourier transform and autocorrelation techniques. Apart from the periodicity equal to that of the synodic rotational modulation of the Sun, other periods were also found by examining the time series formed at different epochs of the solar cycle. From the aforesaid analyses a 14-day periodicity has been confirmed, which is found to occur in all the cases taken under consideration.     

Solar radiation and solar differential rotation

Areas of sunspots and their positions taken from the Greenwich Photoheliographic Results (1874–1976) and typical intensities of the umbrae and penumbrae are used to calculate daily values of the solar flux at a wavelength of about 500 nm. Using overlapping time series of 512 days each solar rotation periods are determined by Fourier transformation. The periods found depend on the phase of the solar activity cycle, as expected from the solar differential rotation. This method may be used for solar type stars to determine relations between activity and rotation too. The problems of errors - e.g. by faculae or the variation of the umbral intensity within the activity cycle - are explained.Mitteilungen aus dem Kiepenheuer-Institut Nr. 284     

On the fourier spectrum analysis of the solar neutrino capture rate

Periodic variations in Davis' experimental data concerning the solar neutrino capture rate are derived on the basis of a Fourier spectrum analysis. Variations in the ³⁷Ar production rate are obtained for a series of randomly spaced observations in the period 1970–1985 (runs 18–89). The harmonic analysis of runs 18–89 has determined solar neutrino capture rate variations with periods of 8.33, 5.00, 2.13, 1.61, 0.83, 0.61, 0.54, and 0.51 yr, thereby confirming earlier calculations performed for the set of runs 18–69 (1983), 18–74 (1985a), and 18–80 (1985b). The results also confirm those of Sakurai (1979) who showed that there is strong evidence that the observed solar neutrino flux has a tendency to vary with quasi-biennial periodicity. We show that the results of the Fourier spectrum analysis do not depend upon certain high or low values in Davis' experimental data.     

Timescale Analysis of Spectral Lags

A technique for timescale analysis of spectral lags performed directly in the time domain is developed. Simulation studies are made to compare the time domain technique with the Fourier frequency analysis for spectral time lags. The time domain technique is applied to studying rapid variabilities of X-ray binaries and γ-ray bursts. The results indicate that in comparison with the Fourier analysis the timescale analysis technique is more powerful for the study of spectral lags in rapid variabilities on short time scales and short duration flaring phenomena.     

The wavelet analysis of the period of solar activity

Using the wavelet technique, we analyzed the time series of solar radio fluxes at 2800 MHz as well as sunspot numbers and areas. The results are as follows: (1) These three data sets demonstrate that the most prominent period is 10.69 years and that all other periods are not obvious. (2) The wavelet power spectrum displays the changes of the power spectrum over the entire time-period range and shows the variations in the local power of a given period in a given time interval. Our analysis shows that periods shorter than one year are distinct only around solar activity maximum. (3) The time curves of the wavelet power at three periods (10.69 years, 5.11 years and 155.5 days) for the three times series are rather alike, with the same times of peaks and similar undulations. The shorter the period, the more frequent the fluctuations.     

78-Day periodicity in the solar 1–8 Å X-ray index during the ascending branch of cycle 21

In the present paper, the time series of 1–8 Å X-ray index for the time interval between January 1977 to September 1981 has been analyzed by carrying out power spectrum using Discrete Fourier Transform. The 78-day periodicity which is one-half of the period found from various solar parameters of cycles 20 and 21 by various authors, was found. This periodicity is thought to be related to the 152-day periodicity.     

太阳硬X射线成像望远镜模拟研究

调制准直器型太阳硬X射线成像望远镜是目前较为通用的太阳观测设备.空间调制望远镜是基于中心轴不旋转的望远镜,适用于3轴稳定的卫星.针对我国可能的太阳观测计划,给出并比较了两组空间调制望远镜的配置方案,然后利用GEANT4高能物理通用软件模拟实际光子的计数情况,使用MATLAB实现图像重建.比较模拟光子计数得到的重建图与几...     

LSTM neural network for solar radio spectrum classification

A solar radio spectrometer records solar radio radiation in the radio waveband. Such solar radio radiation spanning multiple frequency channels and over a short time period could provide a solar radio spectrum which is a two dimensional image. The vertical axis of a spectrum represents frequency channel and the horizontal axis signifies time. Intrinsically, time dependence exists between neighboring columns of a spectrum since solar radio radiation varies continuously over time. Thus, a spectrum can be treated as a time series consisting of all columns of a spectrum, while treating it as a general image would lose its time series property. A recurrent neural network(RNN) is designed for time series analysis. It can explore the correlation and interaction between neighboring inputs of a time series by augmenting a loop in a network.This paper makes the first attempt to utilize an RNN, specifically long short-term memory(LSTM), for solar radio spectrum classification. LSTM can mine well the context of a time series to acquire more information beyond a non-time series model. As such, as demonstrated by our experimental results, LSTM can learn a better representation of a spectrum, and thus contribute better classification.