Identification of Gleissberg Cycles and a Rising Trend in a 315-Year-Long Series of Sunspot Numbers

We show in this short note that the method of singular spectrum analysis (SSA) is able to clearly extract a strong, clean, and clear component from the longest available sunspot (International Sunspot Number, ISN) time series (1700?–?2015) that cannot be an artifact of the method and that can be safely identified as the Gleissberg cycle. This is not a small component, as it accounts for 13% of the total variance of the total original signal. Almost three and a half clear Gleissberg cycles are identified in the sunspot number series. Four extended solar minima (XSM) are determined by SSA, the latest around 2000 (Cycle 23/24 minimum). Several authors have argued in favor of a double-peaked structure for the Gleissberg cycle, with one peak between 55 and 59 years and another between 88 and 97 years. We find no evidence of the former: solar activity contains an important component that has undergone clear oscillations of \(\approx90\) years over the past three centuries, with some small but systematic longer-term evolution of “instantaneous” period and amplitude. Half of the variance of solar activity on these time scales can be satisfactorily reproduced as the sum of a monotonous multi-secular increase, a \(\approx90\)-year Gleissberg cycle, and a double-peaked (\(\approx10.0\) and 11.0 years) Schwabe cycle (the sum amounts to 46% of the total variance of the signal). The Gleissberg-cycle component definitely needs to be addressed when attempting to build dynamo models of solar activity. The first SSA component offers evidence of an increasing long-term trend in sunspot numbers, which is compatible with the existence of the modern grand maximum.     

An investigation on the relationship between solar irradiance signal from ERBS and 8B solar neutrino flux signals from SNO

In the present work an attempt has been made to investigate statistical association between solar neutrino flux data (both D₂O and Salt data) collected from Sudbury Neutrino Observatory and solar irradiance data detected by Earth Radiation Budget Satellite. To serve the present purpose we have used the Multifractal Detrended Cross Correlation Analysis (MF-DCCA) based on Detrended Fluctuation Analysis (MF-X-DFA) method and the Detrending Moving Average Analysis (MF-X-DMA) which explores the long term power-law cross correlations between above two pairs of data sets. Investigation also has been made to find the frequency and time dependent local phase relationship in each pair of data sets using continuous wavelet transform (CWT) based Semblance Analysis. The Semblance Analysis reveals that there exists positive phase correlation as well as negative phase correlation between solar irradiance and D₂O data at different time sub-intervals. This type of mixed phase correlation is also experienced between solar irradiance and Salt data at different time sub-intervals. The causal relationship between the D₂O and the solar irradiance time series and that between Salt and solar irradiance time series have been revealed using Singular Spectral Analysis (SSA). Calculations indicate that possibly the present solar neutrino flux data (both D₂O and Salt data) is supportive to predict the solar irradiance data but may not the vice versa which in turn suggests that the variability of nuclear energy generation process inside the Sun may influence the solar activity.     

Separation of periodic, chaotic, and random components in solar activity

Two new techniques were applied to search for chaotic behavior in solar activity. A mixture of periodic and chaotic components in a time series makes it difficult to find chaotic behavior. The singular spectrum analysis (SSA) method (Broomhead and King, 1986) was used to separate periodic and irregular components in solar activity (e.g., sunspot number and 10.7 cm flux). The nonlinear prediction method (Sugihara and May, 1990) was applied for each component to examine whether it has a chaotic characteristic. The result suggests that are are dominant periodic components and highly irregular (random) components in solar activity.     

Changes of solar magnetic asymmetry

The results of an analysis of the north–south asymmetry in solar activity and solar magnetic fields are reported. The analysis is based on solar mean magnetic field and solar polar magnetic field time series, 1975–2015 (http://wso.stanford.edu), and the Greenwich sunspot data, 1875–2015 (http://solarscience.msfc.nasa.gov/greenwch.shtml). A long-term cycle (small-scale magnetic fields, toroidal component) of ~140 years is identified in the north–south asymmetry in solar activity by analyzing the cumulative sum of the time series for the north–south asymmetry in the area of sunspots. A comparative analysis of the variations in the cumulative sums of the time series composed of the daily values of the sun’s global magnetic field and in the asymmetry of the daily sunspot data over the time interval 1975–2015 shows that the photospheric large-scale magnetic fields may also have a similar long-term cycle. The variations in the asymmetry of large-scale and small-scale solar magnetic fields (sunspot area) are in sync until 2005.5 and in antiphase since then.     

Short-Period Fluctuations in Coronal Mass Ejection Activity during Solar Cycle 23

We have constructed a time series of the number of coronal mass ejections (CMEs) observed by SOHO/LASCO during solar cycle 23. Using spectral analysis techniques (the maximum entropy method and wavelet analysis) we found short-period (< one year) semiperiodic activity. Among others, we found interesting periodicities at 193, 36, 28, and 25 days. We discuss the implications of such short-period activity in terms of the emergence and escape of magnetic flux from the convection zone, through the low solar atmosphere (where these periodicities have been found for numerous activity parameters), toward interplanetary space. This analysis shows that CMEs remove the magnetic flux in a quasiperiodic process in a way similar to that of magnetic flux emergence and other solar eruptive activity.     

Generalization of the cross-wavelet function

We introduce the method of multiple cross-wavelet algorithm, hereafter also as Einstein’s cross functions, for the time-frequency study of solar activity records or any astronomical and geophysical time series in general. The main purpose of this algorithm is to allow the simultaneous examination of the time-frequency information contents in n > 2 time series available. Previous cross-wavelet algorithm only permit the study of two time series at a time and was not extended to the generalized n > 2 problems until now. Furthermore, our new work lifted the restriction from the original formulation that are valid only for stationary processes. We applied our new algorithm to several of the solar activity proxies available in order to demonstrate the broad and powerful utility of this technique. We have used solar activity proxy records that are obtained under different geophysical archives and time periods which are, in turn, suitable for studying both the statistical and physical properties for solar variations valid on timescales of multi-century, millennium to several millennia. We focus on documenting the methodology in this paper rather than any elaborate interpretation of the results.     

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.     

New Approach to Study Extended Evolution of Supergranular Flows and Their Advection of Magnetic Elements

Using velocity and magnetogram data extracted from the full-disk field of view of MDI during the 1999 Dynamics Program, we have studied the dynamics of small-scale magnetic elements (3–7 Mm in size) over time periods as long as six days while they are readily visible on the solar disk. By exploiting concurrent time series of magnetograms and Doppler images, we have compared the motion of magnetic flux elements with the supergranular velocity field inferred from the correlation tracking of mesogranular motions. Using this new method (which combines the results from correlation tracking of mesogranules with detailed analysis of simultaneous magnetograms), it is now possible to correlate the motions of the velocity field and magnetic flux for long periods of time and at high temporal resolution. This technique can be utilized to examine the long-term evolution of supergranulation and associated magnetic fields, for it can be applied to data that span far longer time durations than has been possible previously. As tests of its efficacy, we are able to use this method to verify many results of earlier investigations. We confirm that magnetic elements travel at approximately 350 m s ^–1 throughout the duration of their lifetime as they are transported by supergranular outflows. We also find that the positions of the magnetic flux elements coincide with the supergranular network boundaries and adjust as the supergranular network itself evolves over the six days of this data set. Thus we conclude that this new method permits us to study the extended evolution of the supergranular flow field and its advection of magnetic elements. Since small-scale magnetic elements are strongly advected by turbulent convection, their dynamics can give important insight into the properties of the subsurface convection.     

Short-term periodicity in proton fluences during solar cycle 22

The data of proton fluences measured in three ranges of energy values (1 MeV, 10MeV, and 100 MeV) in the current solar cycle 22 have been analysed to detect periodicities. Power spectral analysis of the time series of the data of proton fluences shows a periodicity of 74 days, which conforms to that of other kinds of solar activity as reported by earlier authors, thus indicating the intimate relationship of proton emission with solar activity.     

SoFAST: Automated Flare Detection with the PROBA2/SWAP EUV Imager

The Sun Watcher with Active Pixels and Image Processing (SWAP) EUV imager onboard PROBA2 provides a non-stop stream of coronal extreme-ultraviolet (EUV) images at a cadence of typically 130 seconds. These images show the solar drivers of space-weather, such as flares and erupting filaments. We have developed a software tool that automatically processes the images and localises and identifies flares. On one hand, the output of this software tool is intended as a service to the Space Weather Segment of ESA’s Space Situational Awareness (SSA) program. On the other hand, we consider the PROBA2/SWAP images as a model for the data from the Extreme Ultraviolet Imager (EUI) instrument prepared for the future Solar Orbiter mission, where onboard intelligence is required for prioritising data within the challenging telemetry quota. In this article we present the concept of the software, the first statistics on its effectiveness and the online display in real time of its results. Our results indicate that it is not only possible to detect EUV flares automatically in an acquired dataset, but that quantifying a range of EUV dynamics is also possible. The method is based on thresholding of macropixelled image sequences. The robustness and simplicity of the algorithm is a clear advantage for future onboard use.     

Solar Variability Induced in a Dynamo Code by Realistic Meridional Circulation Variations

In this work we use an already-published method to infer a variation profile for the solar meridional circulation over the last 250 years. We feed this variation profile into a numerical dynamo code, and we reconstruct a sunspot time series that acts as a proxy for solar cycle activity. We perform three simulations with slightly different parameters, and the results are compared with the observational data. The medium and large correlation coefficients between reconstructed and observational time series seem to indicate that variations in meridional circulation play an important role in the modulation of solar activity.     

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.     

The influence of solar system oscillation on the variability of the total solar irradiance

Total solar irradiance (TSI) is the primary quantity of energy that is provided to the Earth. The properties of the TSI variability are critical for understanding the cause of the irradiation variability and its expected influence on climate variations. A deterministic property of TSI variability can provide information about future irradiation variability and expected long-term climate variation, whereas a non-deterministic variability can only explain the past.This study of solar variability is based on an analysis of two TSI data series, one since 1700 A.D. and one since 1000 A.D.; a sunspot data series since 1610 A.D.; and a solar orbit data series from 1000 A.D. The study is based on a wavelet spectrum analysis. First, the TSI data series are transformed into a wavelet spectrum. Then, the wavelet spectrum is transformed into an autocorrelation spectrum to identify stationary, subharmonic and coincidence periods in the TSI variability.The results indicate that the TSI and sunspot data series have periodic cycles that are correlated with the oscillations of the solar position relative to the barycenter of the solar system, which is controlled by gravity force variations from the large planets Jupiter, Saturn, Uranus and Neptune. A possible explanation for solar activity variations is forced oscillations between the large planets and the solar dynamo.We find that a stationary component of the solar variability is controlled by the 12-year Jupiter period and the 84-year Uranus period with subharmonics. For TSI and sunspot variations, we find stationary periods related to the 84-year Uranus period. Deterministic models based on the stationary periods confirm the results through a close relation to known long solar minima since 1000 A.D. and suggest a modern maximum period from 1940 to 2015. The model computes a new Dalton-type sunspot minimum from approximately 2025 to 2050 and a new Dalton-type period TSI minimum from approximately 2040 to 2065.     

Application of diffusion — Convection model to diurnal anisotropy data

The diurnal anisotropy of cosmic-ray intensity observed over the period 1970–1977 has been analysed using neutron-monitor data of the Athens and Deep River stations. Our results indicate that the time of the maximum of diurnal variation shows a remarkable systematic shift towards earlier hours than normally beginning in 1971. This phase shift continued until 1976, the solar activity minimum, except for a sudden shift to a later hour for one year, in 1974, the secondary maximum of solar activity.This behavior of the diurnal time of maximum has been shown to be consistent with the convective- diffusive mechanism which relates the solar diurnal anisotropy of cosmic-rays to the dynamics of the solar wind and of the interplanetary magnetic field. Once again we have confirmed the field-aligned direction of the diffusive vector independently of the interplanetary magnetic field polarity. It is also noteworthy that the diurnal phase may follow in time the variations of the size of the polar coronal holes. All these are in agreement with the drift motions of cosmic-ray particles in the interplanetarty magnetic field during this time period.     

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.

     

A phenomenological study of the timing of solar activity minima of the last millennium through a physical modeling of the Sun–Planets Interaction

We numerically integrate the Sun’s orbital movement around the barycenter of the solar system under the persistent perturbation of the planets from the epoch J2000.0, backward for about one millennium, and forward for another millennium to 3000 AD. Under the Sun–Planets Interaction (SPI) framework and interpretation of Wolff and Patrone (2010), we calculated the corresponding variations of the most important storage of the specific potential energy (PE) within the Sun that could be released by the exchanges between two rotating, fluid-mass elements that conserve its angular momentum. This energy comes about as a result of the roto-translational dynamics of the cell around the solar system barycenter. We find that the maximum variations of this PE storage correspond remarkably well with the occurrences of well-documented Grand Minima (GM) solar events throughout the available proxy solar magnetic activity records for the past 1000 yr. It is also clear that the maximum changes in PE precede the GM events in that we can identify precursor warnings to the imminent weakening of solar activity for an extended period. The dynamical explanation of these PE minima is connected to the minima of the Sun’s position relative to the barycenter as well as the significant amount of time the Sun’s inertial motion revolving near and close to the barycenter. We presented our calculation of PE forward by another 1000 yr until 3000 AD. If the assumption of the solar activity minima corresponding to PE minima is correct, then we can identify quite a few significant future solar activity GM events with a clustering of PE minima pulses starting at around 2150 AD, 2310 AD, 2500 AD, 2700 AD and 2850 AD.     

Solar and geomagnetic activity on a long time scale: Reconstructions and possibilities for predictions

Using two mathematical methods based on the wavelet transform and nonlinear dynamics, we reconstructed the behavior of the aa-index of geomagnetic activity in the past. Two versions of the series are provided: for the last 400 years and on an almost 1000-year time scale. We consider typical values of the aa-index at grandiose extrema of solar activity. The same high level of geomagnetic activity as that observed in the last 50 years is shown to have also taken place in the early 12th and late 14th centuries. We suggest an extended time series of A-indices of the large-scale solar magnetic field. On the 400-year time scale, we confirmed that the large-scale magnetic field develops earlier than the magnetic fields of active regions. Ohl’s prediction method was verified on the same time scale.     

The fuzzy forecast of the activity of solar active regions

In this paper, the theory and method of fuzzy mathematics are applied to forecast the activity of solar active regions. According to the correlation between flares and several solar activity indices of active regions, the membership functions are constructed to comprehensively evaluate and predict the activity of solar active regions. By means of data reduction and analysis, some comparatively accurate results of prediction have been obtained. The accuracy of predicting the activity grades of active regions is higher than 97%. This implies that the method of fuzzy forecast is a good one for solar activity prediction. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.