Long-Term Modulation of Cosmic-Ray Intensity and Correlation Analysis Using Solar and Heliospheric Parameters

Based on the monthly sunspot numbers (SSNs), the solar-flare index (SFI), grouped solar flares (GSFs), the tilt angle of heliospheric current sheet (HCS), and cosmic-ray intensity (CRI) for Solar Cycles 21?–?24, a detailed correlation study has been performed using the cycle-wise average correlation (with and without time lag) method as well as by the “running cross-correlation” method. It is found that the slope of regression lines between SSN and SFI, as well as between SSN and GSF, is continuously decreasing from Solar Cycle 21 to 24. The length of regression lines has significantly decreased during Cycles 23 and 24 in comparison to Cycles 21 and 22. The cross-correlation coefficient (without time lag) between SSN–CRI, SFI–CRI, and GSF–CRI has been found to be almost the same during Cycles 21 and 22, while during Cycles 23 and 24 it is significantly higher between SSN–CRI and HCS–CRI than for SFI–CRI and GSF–CRI. Considering time lags of 1 to 20 months, the maximum correlation coefficient (negative) amongst all of the sets of solar parameters is observed with almost the same time lags during Cycles 21?–?23, whereas exceptional behaviour of the time lag has been observed during Cycle 24, as the correlation coefficient attains its maximum value with two time lags (four and ten months) in the case of the SSN–CRI relationship. A remarkably large time lag (22 months) between HCS and CRI has been observed during the odd-numbered Cycle 21, whereas during another odd cycle, Cycle 23, the lag is small (nine months) in comparison to that for other solar/flare parameters (13?–?15 months). On the other hand, the time lag between SSN–CRI and HCS–CRI has been found to be almost the same during even-numbered Solar Cycles 22 and 24. A similar analysis has been performed between SFI and CRI, and it is found that the correlation coefficient is maximum at zero time lag during the present solar cycle. The GSFs have shown better maximum correlation with CRI as compared to SFI during Cycles 21 to 23, indicating that GSF could also be used as a significant solar parameter to study the cosmic-ray modulation. Furthermore, the running cross-correlation coefficient between SSN–CRI and HCS–CRI, as well as between solar-flare activity parameters (SFI and GSF) and CRI is observed to be strong during the ascending and descending phases of solar cycles. The level of cosmic-ray modulation during the period of investigation shows the appropriateness of different parameters in different cycles, and even during the different phases of a particular solar cycle. We have also studied the galactic cosmic-ray modulation in relation to combined solar and heliospheric parameters using the empirical model suggested by Paouris et al. (Solar Phys.280, 255, 2012). The proposed model for the calculation of the modulated cosmic-ray intensity obtained from the combination of solar and heliospheric parameter gives a very satisfactory value of standard deviation as well as \(R^{2}\) (the coefficient of determination) for Solar Cycles 21?–?24.     

Sunspot Time Series: Passive and Active Intervals

Solar activity slowly and irregularly decreases from the first spotless day (FSD) in the declining phase of the old sunspot cycle and systematically, but also in an irregular way, increases to the new cycle maximum after the last spotless day (LSD). The time interval between the first and the last spotless day can be called the passive interval (PI), while the time interval from the last spotless day to the first one after the new cycle maximum is the related active interval (AI). Minima of solar cycles are inside PIs, while maxima are inside AIs. In this article, we study the properties of passive and active intervals to determine the relation between them. We have found that some properties of PIs, and related AIs, differ significantly between two group of solar cycles; this has allowed us to classify Cycles 8?–?15 as passive cycles, and Cycles 17?–?23 as active ones. We conclude that the solar activity in the PI declining phase (a descending phase of the previous cycle) determines the strength of the approaching maximum in the case of active cycles, while the activity of the PI rising phase (a phase of the ongoing cycle early growth) determines the strength of passive cycles. This can have implications for solar dynamo models. Our approach indicates the important role of solar activity during the declining and the rising phases of the solar-cycle minimum.     

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.     

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.     

Cosmic-ray intensity versus solar soft X-ray background in cross-correlation analysis

The relationship between the galactic cosmic ray modulation (CR) and the non-flare coronal level, as given by the solar soft X-ray background (XBG), is investigated from 1 July 1968 to 30 June 1980 on a daily basis. The stationarity problem of a multivariate time series, as well as the role of the short- and medium-term corona variability are faced. From them it is found that the CR/XBG relation is variable during the considered heliomagnetic semicycle, while CR and XBG are highly anticorrelated on a long-time scale (12-month averages). The CR/XBG relationship during the declining phase of solar activity shows a moderately strong anticorrelation, on short- and medium-term time scales (coefficient up to –0.77 for 27-day running averages), went towards insignificant values in the minimum phase and is only partially reconstructed during the rise of the following solar cycle. During the solar activity maximum of cycle 20 the cosmic-ray modulation is only related to the short-term coronal fluctuations (no other time scales are significant, supporting the reliability of the so-called `Gnevyshev gap' in solar parameters).     

Geoeffectiveness of magnetic cloud, shock/sheath, interaction region, high-speed stream and their combined occurrence

A subset of CMEs, called interplanetary magnetic clouds (MCs), are observed to have systematic rotation [northward to southward (NS) or southward to northward (SN)] in their field structures. These MCs identified in the heliospheric plasma and field data at 1 AU may have different features associated with them. These structures (NS/SN) may be isolated MC moving with the ambient solar wind. MCs (NS/SN) may also be associated with shock/sheath region, formed due to compression of the ambient plasma/field ahead of them. A fraction from each of these four types of MCs have additional features, being ‘pushed’ by fast solar wind streams from coronal holes, forming interaction region (IR) between MCs and high-speed solar wind streams (HSS). Using these different sets of MCs, we have done a detailed study of the geoeffectiveness of NS and SN turning MCs and their associated features (shock/sheath, IR and HSS). To study the process that produces the geomagnetic disturbances and influences its amplitude/duration, we have utilized the interplanetary plasma and field parameters, namely, plasma velocity, density, temperature, pressure, field strength and its north-south component, during the passage of these structures with different associated properties. Differences in the geoeffectiveness of MCs with different structural and dynamical properties have been identified. The possible role of high-speed stream in influencing the recovery time (and hence duration) of geomagnetic disturbance has also been investigated. A best-fit equation representing the relation between level of the geomagnetic activity (due to MCs) and interplanetary plasma/field parameter has been obtained.     

The Relative Phase Asynchronization between Sunspot Numbers and Polar Faculae

The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astronomical Observatory of Japan, for the interval of March 1954 to March 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar disk and for both hemispheres in solar cycles 19, 20, 21 and 22. We found that (1) the polar faculae begin earlier than sunspot activity, and the phase difference exhibits a consistent behaviour for different hemispheres in each of the solar cycles, implying that this phenomenon should not be regarded as a stochastic fluctuation; (2) the inverse correlation between polar faculae and sunspot numbers is not only a long-term behaviour, but also exists in short time range; (3) the polar faculae show leads of about 50–71 months relative to sunspot numbers, and the phase difference between them varies with solar cycle; (4) the phase difference value in the northern hemisphere differs from that in the southern hemisphere in a solar cycle, which means that phase difference also existed between the two hemispheres. Moreover, the phase difference between the two hemispheres exhibits a periodical behaviour. Our results seem to support the finding of Hiremath (2010).     

Study of Multiple Coronal Mass Ejections at Solar Minimum Conditions

Solar activity alternates between active and quiet phases with an average period of 11?years, and this is known as the Schwabe cycle. Additionally, solar activity occasionally falls into a prolonged quiet phase (grand solar minimum), as represented by the Maunder Minimum in the 17th century, when sunspots were almost absent for 70?years and the length of the Schwabe cycle increased to 14?years. To examine the consistency of the cycle length characteristics during the grand solar minima, the carbon-14 contents in single-year tree rings were measured using an accelerator mass spectrometer as an index of the solar variability during the grand solar minimum of the 4th century BC. The signal of the Schwabe cycle was detected with a statistical confidence level of higher than 95?% by wavelet analysis. This is the oldest evidence for the Schwabe cycle at the present time, and the cycle length is considered to have increased to approximately 16?years during the grand solar minimum of the 4th century BC. This result confirms the association between the increase of the Schwabe cycle length and the weakening of solar activity, and indicates the possible prolonged absence of sunspots in the 4th century BC as during the Maunder Minimum. Theoretical implications from solar dynamo theory are discussed in order to identify the trigger of prolonged sunspot absence. A possible association between the long-term solar variation around the 4th century BC and terrestrial cooling in this period is also discussed.     

Evidence for the effect of sunspot activity on the El Niño/Southern Oscillation

The El Niño No. 3 area index (5°S∼ 5°N, 150°W∼ 90°W) and yearly sunspot number (SSN) from 1408 to 1978 are used to investigate the influence of solar activity on the El Niño/Southern Oscillation (ENSO), through periodicity analysis, cross wavelet transform (XWT), cross correlation and ensemble empirical mode decomposition (EEMD) analyses. The solar activity period, the Hale period, and the Gleissberg period are determined in the El Niño index time series, but of weak statistical significance. Cross correlation analysis of the index with SSN, and that of its low-frequency components decomposed by EEMD clearly indicate that solar activity may take effect on the ENSO, and such an impact should undergo an accumulation procedure (phase delay). XWT also indicates the existence of the impact. It is found that the index is negatively correlated with SSN when SSN is large during a certain long-term interval, and positively when SSN is small. Strong El Niño is inferred to be taken place in decade(s) to come.     

Reconstruction of the Heliospheric Current Sheet Tilts Using Sunspot Numbers

We have investigated the correlation between the relative sunspot number and tilt of the heliospheric current sheet (HCS) in solar cycles 21–23. Strong and highly significant positive correlation (r > 0.8, P < 0.001) was found for corresponding data in the time interval from May 1976 through December 2004. Cross-correlation analysis does not reveal any time shift between the data sets. Reconstructed values of the HCS tilt, for the time interval before 1976, are found using sunspot numbers. To take different amplitude of solar cycles into account they were then normalized to zero in the minima of the solar activity and to average in solar cycles 21–23 maximal calculated HCS tilt in the maxima. These normalized reconstructed HCS data are compared with the angular positions of the brightest coronal streamers observed during total solar eclipses in 1870–2002, and their agreement is better for the minima of the solar activity than for the maxima.     

North-south distribution of solar flares during cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemispheres of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of the descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to the previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997–2000). The dominance of northern hemisphere shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.     

Wavelet Analysis of the Schwabe Cycle Properties in Solar Activity

Properties of the Schwabe cycles in solar activity are investigated by using wavelet transform. We study the main range of the Schwabe cycles of the solar activity recorded by relative sunspot numbers, and find that the main range of the Schwabe cycles is the periodic span from 8-year to 14-year. We make the comparison of 11-year‘s phase between relative sunspot numbers and sunspot group numbers. The results show that there is some difference between two phases for the interval from 1710 to 1810, while the two phases are almost the same for the interval from 1810 to 1990.     

Study of high and low amplitude wave trains of cosmic ray diurnal variation during solar cycle 23

A detailed study has been conducted on the long-term changes in the diurnal variation of cosmic rays in terms of high and low amplitude wave trains event (HAEs/LAEs) during the period 1996–2008 (solar cycle 23), using the neutron monitor data from Kiel neutron monitoring station. As such, 17 HAE and 48 LAE cases have been detected and analyzed. These HAEs appear quite dominantly during the declining phase as well as near the maximum of the solar activity cycle 23. In contrast, the low amplitude events (LAEs) are inversely correlated with solar activity cycle. In fact, LAEs appear quite dominantly during the minimum phase of the solar activity. When we compare our results for diurnal phase with that observed on an annual average basis, we notice no significant diurnal phase shift for HAEs as well as for LAEs. Moreover, we find that the high-speed solar wind streams (HSSWS) do not play any significant role in causing these variations. These results are discussed on the basis of that observed in earlier cycles.     

Ten cycles of solar and geomagnetic activity

Series of 110 years of sunspot numbers and indices of geomagnetic activity are used with 17 years of solar wind data in order to study through solar cycles both stream and shock event solar activity. According to their patterns on Bartels diagrams of geomagnetic indices, stable wind streams and transient solar activities are separated from each other. Two classes of stable streams are identified: equatorial streams occurring sporadically, for several months, during the main phase of sunspot cycles and both polar streams established, for several years, at each cycle, before sunspot minimum. Polar streams are the first activity of solar cycles. For study of the relationship between transient geomagnetic phenomena and sunspot activity, we raise the importance of the contribution, at high spot number, of severe storms and, at low spot number, of short lived and unstable streams. Solar wind data are used to check and complete the above results. As a conclusion, we suggest a unified scheme of solar activity evolution with a starting point every eleventh year, a total duration of 17 years and an overlapping of 6 years between the first and the last phase of both successive series of phenomena: first, from polar field reversal to sunspot minimum, a phase of polar wind activity of the beginning cycle is superimposed on the weak contribution of shock events of the ending cycle; secondly, an equatorial phase mostly of shock events is superimposed on a variable contribution of short lived and sporadic stable equatorial stream activities; and thirdly a phase of low latitude shock events is superimposed on the polar stream interval of the following cycle.     

Phase asynchrony of hemispheric flare activity revisited: empirical mode decomposition and wavelet transform analyses

The phase relation of flare index in the northern and southern hemispheres in the time interval of January 1966 to December 2008 is investigated. It is found that, (1) the flare index in the northern hemisphere begin six months earlier than that in the southern one, which should lead to phase asynchrony between them but with a slight effect; (2) the main periods of the flare activity in the two hemispheres slightly differ from each other, which should also lead to phase asynchrony between them; (3) the low-frequency modes of the flare activity can be used to study the varying relationship of long-term solar activities and the high-frequency modes can be considered as the stochastic component that is amplitude modulated.     

Statistical Study of the CME-Solar Flares Associated Events

The aim of this paper is studying the relation between the coronal mass ejections (CMEs), and their associated solar flares. I used the CMEs data (obtained from CME catalogue) which observed by SOHO/LASCO, during the Solar Cycle 23rd (1996–2006), during this period I selected 12,433 CME records. Also I used the X-ray flares data which provided geostationary operational environmental satellite (GOES), during the same interval in the 1–8 Å GOES channel, the recorded flare events are 22,688. I filtered these CMEs and solar flare events to select 529 CME-Flare events. I found that there is a moderate relation between the solar flare fluxes and their associated CME energies, where R = 58 %. In addition I found that 61 % of the CME-Flare associated events ejected from the solar surface after the occurrence of the associated flare. Furthermore I found that the CME-Flare relation improved during the period of high solar activity. Finally, I examined the CME association rate as a function of flare longitude and I found that the CME association rate of the total 529 selected CME-Flare events are mostly disk-Flare events.     

Determination of precipitation cycle in Beijing area and comparison with solar activity cycle

We examine the annual precipitation in Beijing area response to solar activity changes during the period 1749–2001. A hierarchy of changing complex periods of precipitation is carefully detected and related cycles compared with results from SN analysis. Our findings support the suggestion that solar activity influence precipitation, at least in part in Beijing.     

Contribution of chromospheric features to UV irradiance variability from spatially-resolved Ca II K spectroheliograms

We have digitized the Ca ii K spectroheliograms, observed at the National Solar Observatory at Sacramento Peak, for the period 1980 (maximum of solar cycle 21), 1985 (minimum of solar cycle 21), 1987 (beginning of the ascending phase of solar cycle 22), 1988 and 1989 (ascending phase and maximum of solar cycle 22), and 1992 (declining phase of solar cycle 22). A new method for analyzing the K spectroheliograms has been developed and applied to the K images for the time interval of 1992. Using histograms of intensity, we have segregated and measured the cumulative intensity and area of various chromospheric features like the plages, magnetic network and intranetwork elements. Also, the full width at half maximum (FWHM) derived from the histograms has been introduced as a new index for describing the chromospheric activity in the K-line. The full-disk intensity (spatial K index) has been derived from spatially-resolved K images and compared to the spectral K index derived from the line profiles for the full disk. Both the spatial K index and FWHM have been compared to the UV irradiance measured in the Mg ii h and k lines by the NOAA9 satellite and found that they are highly correlated with the Mg ii h and k c/w ratio.NRC Resident Research Associate, on leave from Indian Institute of Astrophysics, Bangalore 560034, India.     

Solar UV Activity at Solar Cycle 21 and 22 Minimum from NOAA-9 SBUV/2 Data

Although solar ultraviolet (UV) irradiance measurements have been made regularly from satellite instruments for almost 20 years, only one complete solar cycle minimum has been observed during this period. Solar activity is currently moving through the minimum phase between cycles 22 and 23, so it is of interest to compare recent data taken from the NOAA-9 SBUV/2 instrument with data taken by the same instrument during the previous solar minimum in 1985–1986. NOAA-9 SBUV/2 is the first instrument to make continuous solar UV measurements for a complete solar cycle. Direct irradiance measurements (e.g., 205 nm) from NOAA-9 are currently useful for examining short-term variations, but have not been corrected for long-term instrument sensitivity changes. We use the Mgii proxy index to illustrate variability on solar cycle time scales, and to provide complementary information on short-term variability. Comparisons with contemporaneous data from Nimbus-7 SBUV (1985–1986) and UARS SUSIM (1994–1995) are used to validate the results obtained from the NOAA-9 data. Current short-term UV activity differs from the cycle 21–22 minimum. Continuous 13-day periodicity was observed from September 1994 to March 1995, a condition which has only been seen previously for shorter intervals during rising or maximum activity levels. The 205 nm irradiance and Mgii index are expected to track very closely on short time scales, but show differences in behavior during the minimum between cycles 22 and 23.     

Different Periodicities in the Sunspot Area and the Occurrence of Solar Flares and Coronal Mass Ejections in Solar Cycle 23 – 24

In order to investigate the relationship between magnetic-flux emergence, solar flares, and coronal mass ejections (CMEs), we study the periodicity in the time series of these quantities. It has been known that solar flares, sunspot area, and photospheric magnetic flux have a dominant periodicity of about 155 days, which is confined to a part of the phase of the solar cycle. These periodicities occur at different phases of the solar cycle during successive phases. We present a time-series analysis of sunspot area, flare and CME occurrence during Cycle 23 and the rising phase of Cycle 24 from 1996 to 2011. We find that the flux emergence, represented by sunspot area, has multiple periodicities. Flares and CMEs, however, do not occur with the same period as the flux emergence. Using the results of this study, we discuss the possible activity sources producing emerging flux.