Comparison of long-term trend of solar radius with sunspot activity and flare index

Results are presented from a study of solar radius measurements taken with the solar astrolabe at the TUBITAK National Observatory (TUG) over seven years, 2001–2007. The data series with standard deviation of 0.35 arcsec shows the long-term variational trend with 0.04 arcsec/year. On the other hand, the data series of solar radius are compared with the data of sunspot activity and H-α flare index for the same period. Over the seven year trend, we have found significant linear anti-correlations between the solar radius and other indicators such as sunspot numbers, sunspot areas, and H-α flare index. While the solar radius displays the strongest anti-correlation (−0.7676) with sunspot numbers, it shows a significant anti-correlation of −0.6365 with sunspot areas. But, the anti-correlation between the solar radius and H-α flare index is found to be −0.4975, slightly lower than others. In addition, we computed Hurst exponent of the data sets ranging between 0.7214 and 0.7996, exhibiting the persistent behavior for the long term trend. In the light of the strong correlations with high significance, we may suggest that there are a causal relationship between the solar radius and solar time series such as sunspot activity and H-α flare index.     

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 Correlation of Solar Activity and Sunspot: Evidence of Lifetime Increase

We perform a nonlinear study of the short-term correlation properties of the solar activity (daily range) in order to reveal their long-life variations. We estimate the lifetime of the high-frequency component of a Markov-type signal when the high-frequency component is modulated by a slowly varying multiplicative factor. This treatment is applied to different series of solar activity: Wolf Sunspot numbers (WSN), Sunspot Group numbers (SGN), and Royal Greenwich Observatory (RGO) sunspot group series. We obtain that all the lifetime estimates exhibit similar temporal variations that agree with the variations of the sunspot lifetimes directly measured from the RGO data and those of the sunspot areas. An increase of lifetimes by a factor 1.4 is observed from 1915 to 1940. At the same time, a stable ratio is observed between the sunspot group’s maximal area and the lifetime, confirming the Gnevyshev–Waldmeier-type relationship. The analysis identifies also time intervals where the homogeneity of the different time series may be questioned.     

Evolution of Solar and Geomagnetic Activity Indices, and Their Relationship: 1960?�C?2001

We employ annually averaged solar and geomagnetic activity indices for the period 1960??C?2001 to analyze the relationship between different measures of solar activity as well as the relationship between solar activity and various aspects of geomagnetic activity. In particular, to quantify the solar activity we use the sunspot number R _s, group sunspot number R _g, cumulative sunspot area Cum, solar radio flux F10.7, and interplanetary magnetic field strength IMF. For the geomagnetic activity we employ global indices Ap, Dst and Dcx, as well as the regional geomagnetic index RES, specifically estimated for the European region. In the paper we present the relative evolution of these indices and quantify the correlations between them. Variations have been found in: i) time lag between the solar and geomagnetic indices; ii) relative amplitude of the geomagnetic and solar activity peaks; iii) dual-peak distribution in some of solar and geomagnetic indices. The behavior of geomagnetic indices is correlated the best with IMF variations. Interestingly, among geomagnetic indices, RES shows the highest degree of correlation with solar indices.     

Comparison of the Variations of CMEs and ICMEs with those of other Solar and Interplanetary Parameters During Solar Cycle 23

This paper examines the variations of coronal mass ejections (CMEs) and interplanetary CMEs (ICMEs) during solar cycle 23 and compares these with those of several other indices. During cycle 23, solar and interplanetary parameters had an increase from 1996 (sunspot minimum) to ∼2000, but the interval 1998–2002 had short-term fluctuations. Sunspot numbers had peaks in 1998, 1999, 2000 (largest), 2001 (second largest), and 2002. Other solar indices had matching peaks, but the peak in 2000 was larger than the peak in 2001 only for a few indices, and smaller or equal for other solar indices. The solar open magnetic flux had very different characteristics for different solar latitudes. The high solar latitudes (45^∘–90^∘) in both N and S hemispheres had flux evolutions anti-parallel to sunspot activity. Fluxes in low solar latitudes (0^∘–45^∘) evolved roughly parallel to sunspot activity, but the finer structures (peaks etc. during sunspot maximum years) did not match with sunspot peaks. Also, the low latitude fluxes had considerable N–S asymmetry. For CMEs and ICMEs, there were increases similar to sunspots during 1996–2000, and during 2000–2002, there was good matching of peaks. But the peaks in 2000 and 2001 for CMEs and ICMEs had similar sizes, in contrast to the 2000 peak being greater than the 2001 peak for sunspots. Whereas ICMEs started decreasing from 2001 onwards, CMEs continued to remain high in 2002, probably due to extra contribution from high-latitude prominences, which had no equivalent interplanetary ICMEs or shocks. Cosmic ray intensity had features matching with those of sunspots during 2000–2001, with the 2000 peak (on a reverse scale, actually a cosmic ray decrease or trough) larger than the 2001 peak. However, cosmic ray decreases started with a delay and ended with a delay with respect to sunspot activity.     

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.     

Wavelet entropy and the multi-peaked structure of solar cycle maximum

Wavelet analysis of different solar activity indices—sunspot numbers, sunspot areas and flare index—allows us to investigate the time evolution of some frequency dependent functionals, like wavelet entropy, which gives useful information about the complexity level of the related signals. The main aim of this work is the analysis of the time behavior of wavelet entropy near the maximum phases of solar cycles 21–22–23 in order to further contribute to the characterization of the multi-peaked structure of solar cycle maxima and to support the current interpretation of the so-called Gnevyshev gap.     

Fluctuations of Solar Activity during the Declining Phase of the 11-Year Sunspot Cycle

The number of coronal mass ejections (CMEs) erupting from the Sun follows a trend similar to that of sunspot numbers during the rising and maximum phase of the solar cycle. In the declining phase, the CME number has large fluctuations, dissimilar to those of sunspot numbers. In several studies of solar – interplanetary and solar – terrestrial relationships, the sunspot numbers and the 2800-MHz flux (F10) are used as representative of solar activity. In the rising phase, this may be adequate, but in the declining phase, solar parameters such as CMEs may have a different behaviour. Cosmic-ray Forbush decreases may occur even when sunspot activity is low. Therefore, when studying the solar influence on the Earth, one has to consider that although geomagnetic conditions at solar maximum will be disturbed, conditions at solar minimum may not be necessarily quiet.     

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 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).     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

Periodicities in Global Mean TEC from GNSS Observations

As an important measurement parameter, global total electron content (TEC) is appropriate for the study of the Sun–Earth connection. In this paper, the wavelet technique is employed to investigate the periodicities in global mean TEC during 1995–2008. Analysis results show several remarkable components (including 27-day, semiannual and annual cycles) existing in global mean TEC with obvious time-variable characteristics, besides 11-year cycle. After analyzing sunspot numbers and solar extreme ultra-violet (EUV) radiation variations during this time period, except for semiannual variations, close correlation between global mean TEC and solar variations is found, especially, a strong resemblance of the 27-day fluctuation exists in global mean TEC, sunspot and solar EUV radiation variations.     

Erratum to: Width of Sunspot Generating Zone and Reconstruction of Butterfly Diagram

Based on the extended Greenwich – NOAA/USAF catalogue of sunspot groups, it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of the SGZ. The ratio of the sunspot number to the width of the SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of the SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (Solar Phys. 179, 189, 1998), the latitude distribution of sunspot groups (“the Maunder butterfly diagram”) for the eighteenth and the first half of the nineteenth centuries is reconstructed and compared with historical sunspot observations.     

A forecast of solar activity for the 21st solar cycle

Predicted values of some main indices of solar activity for the 21st solar cycle are given. The epoch of maximum of solar activity has been placed in 1980.8±0.1. The predicted peak values of the relative sunspot numbers published by other authors are also given.     

A new look at wolf sunspot numbers in the late 1700's

Long-term homogeneous observations of solar activity or many solar cycles are essential for investigating many problems in solar physics and climatology. The one key parameter used in most long-term studies is the Wolf sunspot number, which is susceptible to observer bias, particularly because it is highly sensitive to the observer's ability to see the smallest sunspots. In this paper we show how the Wolf sunspot number can be derived from the number of sunspot groups alone. We utilize this approach to obtain a Group Wolf number. This technique has advantages over the classical method of determining the Wolf number because corrections for observer differences are reduced and long-term self-consistent time series can be developed. The level of activity can be calculated to an accuracy of ± 5% using this method. Applying the technique to Christian Horrebow's observations of solar cycles 1, 2, and 3 (1761–1777), we find that the standard Wolf numbers are nearly homogeneous with sunspot numbers measured from 1875 to 1976 except the peak of solar cycle 2 is too low by 30%. This result suggests that further analyses of early sunspot observations could lead to significant improvements in the uniformity of the measurements of solar activity. Such improvements could have important impacts upon our understanding of long-term variations in solar activity, such as the Gleissberg cycle, or secular variations in the Earth's climate.     

A Detailed Comparison of Cosmic Ray Gaps with solar Gnevyshev Gaps

After increasing almost monotonically from sunspot minimum, sunspot activity near maximum falters and remains in a narrow grove for several tens of months. During the 2–3 years of turmoil near sunspot maximum, sunspots depict several peaks (Gnevyshev peaks). The spaces between successive peaks are termed as Gnevyshev Gaps (GG). An examination showed that the depths of the troughs varied considerably from one GG to the next in the same cycle, with magnitudes varying in a wide range (<1% to ∼20%). In any cycle, the sunspot patterns were dissimilar to those of other solar parameters, qualitatively as well as quantitatively, indicating a general turbulence, affecting different solar parameters differently. The solar polar magnetic field reversal does not occur at the beginning of the general turmoil; it occurs much later. For cosmic ray (CR) modulation which occurs deep in the heliosphere, one would have thought that the solar open magnetic field flux would play a crucial role, but observations show that the sunspot GGs are not reflected well in the solar open magnetic flux, where sometimes only one peak occurred (hence no GG at all), not matching with any sunspot peak and with different peaks in the northern and southern hemispheres (north – south asymmetry). Gaps are seen in interplanetary parameters but these do not match exactly with sunspot GGs. For CR data available only for five cycles (19 – 23), there are CR gaps in some cycles, but the CR gaps do not match perfectly with gaps in the solar open magnetic field flux or in interplanetary parameters or with sunspot GGs. Durations are different and/or there are variable delays, and magnitudes of the sunspot GGs and CR gaps are not proportional. Solar polar magnetic field reversal intervals do not coincide with either sunspot GGs or CR gaps, and some CR gaps start before magnetic field reversals, which should not happen if the magnetic field reversals are the cause of the CR gaps.     

Possible Influence of the 11-year Solar Cycle on Precipitation in Huashan Mountain of China over the Last 300 Years

Taking into account reconstructed precipitation time series in Huashan mountain area of China on the one hand and sunspot numbers observations on the other hand, the authors used here continuous wavelet transform and cross wavelet transform to investigate possible connection between the two sets of indicators. The analysis was performed over the last 300 years: it is found that solar activity influences precipitation in that geographical area of China to some extent, with an excess of 5% statistical significance level red noise over the 11-year solar activity cycle.     

On Short-Term Periodicity of the Solar Radius Measurements

The aim of the present study is to investigate the short-term periodicity in the solar radius measurements and to compare with the short periods in sunspot numbers, sunspot areas and flare index data. The spectral analysis of data sets covering a time interval from 26 February 2000 to 26 October 2007 during Solar Cycle 23 were made by using the Date Compensated Discrete Fourier Transform (DCDFT). The power spectrum of solar radius data corrected for the seeing effect gives an evident peak at 25.7 days with the amplitude of 0.034 arcsec, which is slightly different from the peaks of 26.2 and 26.7 days produced by sunspot numbers and sunspot areas data, respectively. Besides, the main peak of 25.7 days detected in the power spectrum of solar radius data is in agreement with the period of 25.5 days, suggested to be the fundamental period of the Sun by Bai and Sturrock (in Nature 350, 141, 1991).     

One Possible Reason for Double-Peaked Maxima in Solar Cycles: Is a Second Maximum of Solar Cycle 24 Expected?

We investigate solar activity by focusing on double maxima in solar cycles and try to estimate the shape of the current solar cycle (Cycle 24) during its maximum. We analyzed data for Solar Cycle 24 by using Learmonth Solar Observatory sunspot-group data collected since 2008. All sunspot groups (SGs) recorded during this time interval were separated into two groups: The first group includes small SGs [A, B, C, and H classes according to the Zurich classification], the second group consists of large SGs [D, E, and F]. We then calculated how many small and large sunspot groups occurred, their sunspot numbers [SSN], and the Zurich numbers [Rz] from their daily mean numbers as observed on the solar disk during a given month. We found that the temporal variations for these three different separations behave similarly. We also analyzed the general shape of solar cycles from Cycle 1 to 23 by using monthly International Sunspot Number [ISSN] data and found that the durations of maxima were about 2.9 years. Finally, we used the ascending time and SSN relationship and found that the maximum of Solar Cycle 24 is expected to occur later than 2011. Thus, we conclude that i) one possible reason for a double maximum in solar cycles is the different behavior of large and small sunspot groups, and ii) a double maximum is expected for Solar Cycle 24.     

To the description of long-term variations in the solar magnetic flux: The sunspot area index

We show that the Wolf sunspot numbers W and the group sunspot numbers GSN are physically different indices of solar activity and that it is improper to compare them. Based on the approach of the so-called “primary” indices from the observational series of W(t) and GSN(t), we suggest series of yearly mean sunspot areas beginning in 1610 and monthly mean sunspot areas beginning in 1749.