Search for relationship between duration of the extended solar cycles and amplitude of sunspot cycle

Duration of the extended solar cycles is taken into the consideration. The beginning of cycles is counted from the moment of polarity reversal of large-scale magnetic field in high latitudes, occurring in the sunspot cycle n till the minimum of the cycle n + 2. The connection between cycle duration and its amplitude is established. Duration of the “latent” period of evolution of extended cycle between reversals and a minimum of the current sunspot cycle is entered. It is shown, that the latent period of cycles evolution is connected with the next sunspot cycle amplitude and can be used for the prognosis of a level and time of a sunspot maximum. The 24th activity cycle prognosis is made. The found dependences correspond to transport dynamo model of generation of solar cyclicity, it is possible with various speed of meridional circulation. Long-term behavior of extended cycle's lengths and connection with change of a climate of the Earth is considered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solar Modulation of Cosmic Rays during the Declining and Minimum Phases of Solar Cycle 23: Comparison with Past Three Solar Cycles

We study solar modulation of galactic cosmic rays (GCRs) during the deep solar minimum, including the declining phase, of solar cycle 23 and compare the results of this unusual period with the results obtained during similar phases of the previous solar cycles 20, 21, and 22. These periods consist of two epochs each of negative and positive polarities of the heliospheric magnetic field from the north polar region of the Sun. In addition to cosmic-ray data, we utilize simultaneous solar and interplanetary plasma/field data including the tilt angle of the heliospheric current sheet. We study the relation between simultaneous variations in cosmic ray intensity and solar/interplanetary parameters during the declining and the minimum phases of cycle 23. We compare these relations with those obtained for the same phases in the three previous solar cycles. We observe certain peculiar features in cosmic ray modulation during the minimum of solar cycle 23 including the record high GCR intensity. We find, during this unusual minimum, that the correlation of GCR intensity is poor with sunspot number (correlation coefficient R=?0.41), better with interplanetary magnetic field (R=?0.66), still better with solar wind velocity (R=?0.80) and much better with the tilt angle of the heliospheric current sheet (R=?0.92). In our view, it is not the diffusion or the drift alone, but the solar wind convection that is the most likely additional effect responsible for the record high GCR intensity observed during the deep minimum of solar cycle 23.     

Multi-parametric effect of solar activity on cosmic rays

The long-term modulation of cosmic ray intensity (CRI) by different solar activity (SA) parameters and an inverse correlation between individual SA parameter and CRI is well known. Earlier, it has been suggested that the concept of multi-parametric modulation of CRI may play an important role in the study of long-term modulation of CRI. In the present study, we have tried to investigate the combined effect of a set of two SA parameters in the long-term modulation of CRI. For this purpose, we have used a new statistical technique called “Running multiple correlation method”, based on the “Running cross correlation method”. The running multiple correlation functions among different sets of two SA parameters (e.g., sunspot numbers and solar flux, sunspot numbers and coronal index, sunspot numbers and grouped solar flares, etc.) and CRI have been correlated separately. It is found that the strength of multiple correlation (among two SA parameters and CRI) and cross correlation (between individual SA parameter and CRI) is almost similar throughout the period of investigation (1955–2005). It is also found that the multiple correlations among various SA parameters and CRI is stronger during ascending and descending phases of the solar cycles and it becomes weaker during maxima and minima of the solar cycles, which is in accordance with the linear relationship between SA parameters and CRI. The values of multiple correlation functions among different sets of SA parameters and CRI fall well within the 95% confidence interval. In the view of odd-even hypothesis of solar cycles, the strange behaviour of present cycle 23 (odd cycle), as this is characterized by many peculiarities with double peaks and many quiet periods (Gnevyshev gaps) interrupted the solar activity (for example April 2001, October–November 2003 and January 2005), leads us to speculate that the solar cycle 24 (even cycle) might be of exceptional nature.     

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.     

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.     

Galactic Cosmic Ray Modulation and the Last Solar Minimum

In this work the galactic cosmic ray modulation in relation to solar activity indices and heliospheric parameters during the years 1996??C?2010 covering solar cycle 23 and the solar minimum between cycles 23 and 24 is studied. A new perspective of this contribution is that cosmic ray data with a rigidity of 10 GV at the top of the atmosphere obtained from many ground-based neutron monitors were used. The proposed empirical relation gave much better results than those in previous works concerning the hysteresis effect. The proposed models obtained from a combination of solar activity indices and heliospheric parameters give a standard deviation <?10?% for all the cases. The correlation coefficient between the cosmic ray variations of 10?GV and the sunspot number reached a value of r=?0.89 with a time lag of 13.6±0.4 months. The best reproduction of the cosmic ray intensity is obtained by taking into account solar and interplanetary indices such as sunspot number, interplanetary magnetic field, CME index, and heliospheric current sheet tilt. The standard deviation between the observed and calculated values is about 7.15?% for all of solar cycle 23; it also works very well during the different phases of the cycle. Moreover, the use of the cosmic ray intensity of 10?GV during the long minimum period between cycles 23 and 24 is of special interest and is discussed in terms of cosmic ray intensity modulation.     

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.     

Solar-cycle evolution of the coronal general magnetic field of 1959–1974 and the synchronous variation of high-speed solar wind streams and galactic cosmic rays

The simultaneous enhancement or subsidence of both the high-speed solar wind streams and the galactic cosmic rays in the minimum or the maximum phase of the solar cycle are interpreted in a unified manner by the concept of geometrical evolution of the general magnetic field of the corona-heliomagnetosphere system. The coronal general magnetic field evolves from an open dipole-like configuration in the minimum phase to a closed configuration with many loop-like formations in the maximum phase of the solar cycle. This concept, developed in a theoretical solar-cycle model driven by the dynamo action of the global convection, is examined and found to be valid by studying the evolution of the coronal general magnetic field calculated from the observed surface general magnetic field of 1959–1974. It is also found that the energy density of the poloidal component of the general surface field, from which the coronal field originates, attained a maximum in the maximum phase and showed a evolution with virtually no phase delay with respect to that of the toroidal component of the field, to which the sunspot activity is related. The subsidence of the high-speed solar wind in the maximum phase is understood as a braking of the solar wind streams by the tightly closed and strong coronal field lines in the lower corona in the maximum phase. The field lines of the heliomagnetosphere, which originate from the coronal field lines drawn by the solar wind, are inferred to be also more tightly closed at the heliopause in the maximum phase than in the minimum phase. The decrease of the galactic cosmic rays in the maximum phase (known as the Forbush's negative correlation between the galactic cosmic ray intensity and the solar activity or the Forbush solar-cycle modulation of the galactic cosmic rays) is interpreted as a braking of the cosmic rays by the closed magnetic field lines at the heliopause. The observed phase lag (approximately one year) of the galactic cosmic ray modulation with respect to the evolution of the solar cycle, and the observed absence of the gradient of the total cosmic ray intensity between 1 AU and 8 AU, are discussed to support this view of the cosmic ray modulation at the remote heliopause, and reject other hypotheses to explain the phenomenon in terms of the magnetic irregularities of various kinds carried by the solar wind: The short-term Forbush decrease at a time of a flare shows that the magnetic irregularities can react on the cosmic rays relatively near the Sun if they even played a dominant role in the long-term modulation. The concept of the general magnetic field of the corona and the surface is also used to understand the basic nature of the surface field itself, by comparing the geometry of the calculated coronal field lines with the eclipse photographs of the corona, and by discussing, in the context of the coronal general magnetic field associated with the solar cycle, the process of the emergence of the coronal field lines from the interior and the formation of the transequatorial arches and loops connecting the two hemispheres in the corona.     

PREDICTIONS OF THE FEATURES FOR SUNSPOT CYCLE 23

Smoothed monthly mean Ap indices are decomposed into two components (Ap) _c and (Ap) _n. The former is directly correlated with the current sunspot numbers, while the latter is shown to achieve its maximum correlation with the sunspot numbers after some time lag. This latter property is used to develop a method for predicting the sunspot maximum based on the observed value of (Ap) _n maximum which occurs during the preceding cycle. The value of R _M for cycle 23 predicted by this method is 149.3 ± 19.9. A method to estimate the rise time (from solar minimum to maximum) has been developed (based on analyses of Hathaway, Wilson, and Reichmann, 1994) and yields a value of 4.2 years. Using an estimate that the minimum between cycles 22 and 23 occurred in May 1996, it is predicted that the sunspot maximum for cycle 23 will occur in July 2000.     

High Flare Activity in the Late Declining Phase of Cycle 23

In the declining phase of the current solar cycle (23), a large number of major flares were produced. In this cycle, the monthly sunspot number continuously remained below 100 since October 2002. However, during four epochs since then, flare activity became very high. Compared to this, each of cycles 21 and 22 produced only one epoch of high activity in the declining phase. In the declining phase of cycle 20, similarly to this cycle, there were four epochs of high flare activity. During 2003 and 2004, the distribution of flare sizes measured in GOES classes was much harder (i.e., proportionately more energetic flares) than during the maximum years. Such pronounced hardening of the size distribution was not observed in the previous cycles. It is of theoretical interest to understand why some cycles are very active in the declining phase, and the high level of activity in the declining phase has practical implications for planning solar observations and forecasting space weather.     

A new pattern for the north–south asymmetry of sunspots

We study the solar cycle evolution during the last 8 solar cycles using a vectorial sunspot area called the LA (longitudinal asymmetry) parameter. This is a useful measure of solar activity in which the stochastic, longitudinally evenly distributed sunspot activity is reduced and which therefore emphasizes the more systematic, longitudinally asymmetric sunspot activity. Interesting differences are found between the LA parameter and the more conventional sunspot activity indices like the (scalar) sunspot area and the sunspot number. E.g., cycle 19 is not the highest cycle according to LA. We have calculated the separate LA parameters for the northern and southern hemisphere and found a systematic dipolar-type oscillation in the dominating hemisphere during high solar activity times which is reproduced from cycle to cycle. We have analyzed this oscillation during cycles 16–22 by a superposed epoch method using the date of magnetic reversal in the southern hemisphere as the zero epoch time. According to our analysis, the oscillation starts by an excess of the northern LA value in the ascending phase of the solar cycle which lasts for about 2.3 years. Soon after the maximum northern dominance, the southern hemisphere starts dominating, reaching its minimum some 1.2–1.7 years later. The period of southern dominance lasts for about 1.6 years and ends, on an average, slightly before the end of magnetic reversal.     

Longterm Prediction of Solar Activity Using the Combined Method

The Combined Method is a non-parametric regression technique for long-term prediction of smoothed monthly sunspot numbers. Starting from a solar minimum, a prediction of the succeeding maximum is obtained by using a dynamo-based relation between the geomagnetic aa index and succeeding solar maxima. Then a series of predictions is calculated by computing the weighted average of past cycles of similar level. This technique leads to a good prediction performance, particularly in the ascending phase of the solar cycle where purely statistical methods tend to be inaccurate. For cycle 23 the combined method predicts a maximum of 160 (in terms of smoothed sunspot number) early in the year 2000.     

The 10-year time delay of the solar cycle luminosity modulation of the Sun behind the solar cycle magnetic oscillation

We found an evidence that the solar cycle luminosity modulation of the Sun deduced from the total irradiance modulation which was measured by the Earth Radiation Budget (ERB) experiment on board of Nimbus 7 from November 16, 1978 to December 13, 1993 was not in phase with the solar cycle magnetic oscillation when we used the sunspot relative number as its index. The modulation was delayed in time behind the solar cycle magnetic oscillation by an amount of about 10.3 years on the order of length of one solar cycle. In order to quantitatively evaluate the correlation between the two quantities, we devised a method to extract characteristics which were proper to a particular solar cycle by defining a new index of the correlation called multiplied correlation index (MCI). We found that the characteristics of the ERB data time profile between solar cycles 21 and 22 were more similar to those of the solar cycle magnetic oscillation between solar cycles 20 and 21 than those between solar cycles 21 and 22 and thus the time profile of the luminosity modulation from the maximum phase of solar cycle 21 to the declining phase of the solar cycle 22 corresponded to the solar cycle magnetic oscillation from the maximum phase of solar cycle 20 to the declining phase of solar cycle 21. We interpret this phenomenon as an evidence that main features of the modulation is not caused by dark sunspots and bright faculae and plages on the surface of the Sun that should instantaneously affect the luminosity modulation but is caused by time-delayed modulation of global convection by the Lorentz force of the magnetic field of the solar cycle. The delay time of about 10.3 years is the time needed for the force to modify the flows of the convection and to modulate heat flow. Thus the delay time is a function of the strength of the magnetic field oscillation of the solar cycle which is represented by amplitude of the solar cycle. Accordingly, the delay time for other time intervals of the solar cycle magnetic oscillation with different amplitudes can be different from 10.3 years for the interval of the present analysis.     

Recurrent magnetic activity,sunspot number and its rate of decline

Power spectral densities computed from low-latitude horizontal intensity of the Earth's magnetic field over two-year periods of declining phases of solar cycles 16 to 19 show a close relationship with the maximum relative sunspot number of the following solar cycles. The maximum sunspot number shows an exponential rise with the power density near 1/27 cd^?1; maximum R _z,however, increases linearly with power density near 1/14 cd^?1. It is also shown that the rate of decline of sunspot number in a solar cycle is almost exactly related, linearly, to power spectral density for the preceding solar cycle. Power densities near 1/27 and 1/14 cd^?1 in declining phase of solar cycle appear to be satisfactory indices for the maximum relative sunspot number of the following cycle and its rate of decline thereafter.     

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.     

Prediction of maximum sunspot number in solar cycle 23

Instantaneous predictions of the maximum monthly smoothed sunspot number in solar cycle 23 have been made with a linear regressive model, which gives the predicted maximum value as a function of the smoothed sunspot numbers corresponding to a given month from the minimum in all preceding cycles. These predictions indicate that the intensity of solar activity in the current cycle will be at an average level.     

A Transfer Function Model for the Sunspot Cycle

The mean annual sunspot record for the time interval 1700–2002 can be considered as a sequence of independent, partly overlapping events, triggered quasi-periodically at intervals of the order of 11 years. The individual cycles are approximated by the step response of a band-pass dynamical system and the resulting model consists of the superposition of the response to the independent pulses. The simulated sunspot data explain 98.4% of the cycle peak height variance and the residual standard deviation is 8.2 mean annual sunspots. An empirical linear relationship is found between the amplitude of the transfer function model for each cycle and the pulse interval of the preceding cycle that can be used as a tool of short-term forecasting of solar activity. A peak height of 112 for the solar cycle 23 occurring in 2000 is predicted, whereas the next cycle would start at about 2007 and will have a maximum around 110 in 2011. Cycle 24 is expected to have an annual mean peak value in the range 95 to 125. The model reproduces the high level of amplitude modulation in the interval 1950–2000 with a decrease afterwards, but the peak values for the cycles 18, 19, 21, and 22 are fairly underestimated. The semi-empirical model also recreates recurring sunspot minima and is linked to the phenomenon of the reversal of the solar magnetic field.     

Cosmic-Ray Variations During the Two Greatest Bursts of Solar Activity in the 23rd Solar Cycle

During two extreme bursts of solar activity in March–April 2001 and October–November 2003, the ground-based neutron monitor network recorded a series of outstanding events distinguished by their magnitude and unusual peculiarities. The important changes that lead to increased activity initiated not with the sunspot appearance, but with the large-scale solar magnetic field reconfiguration. A series of strong and moderate magnetic storms and powerful proton events (including ground-level enhancements, GLE) were registered during these periods. The largest and most productive in the 23rd solar cycle, active region 486, generated a significant series of solar flares among which the 4 November 2003 flare (X28/3B) was the most powerful X-ray solar event ever observed. The fastest arrival of the interplanetary disturbance from the Sun (after August 1972) and the highest solar wind velocity and IMF intensity were recorded during these events. Within 1 week, three GLEs of solar cosmic rays were registered by the neutron monitor network (28 and 29 October and 2 November 2003). In this work, we perform a tentative analysis of a number of the effects seen in cosmic rays during these two periods, using the neutron monitor network and other relevant data.     

第22和23太阳周太阳活动预测

本文首先分析指出第22太阳周前半周的太阳活动所具有的特点:(1)有最高的起始极小值;(2)上升速度快;(3)升段时间最短;(4)峰期长,可能有双峰;(5)个别时段活动水平极高.然后对第22周后半周的活动情况做了预计:在后半周将可能观测到大约2800个活动区,28000个耀斑,210个X级X射线爆发和大约80次太阳质子事件.最后,应用本文给出的太阳周参量关系式.预报第23周太阳黑子数月均平滑值的峰值为119,位于2001.6年.     

Diurnal anisotropy of cosmic rays during intensive solar activity for the period 2001–2014

The diurnal variation of cosmic ray intensity, based on the records of two neutron monitor stations at Athens (Greece) and Oulu (Finland) for the time period 2001 to 2014, is studied. This period covers the maximum and the descending phase of the solar cycle 23, the minimum of the solar cycles 23/24 and the ascending phase of the solar cycle 24.These two stations differ in their geographic latitude and magnetic threshold rigidity. The amplitude and phase of the diurnal anisotropy vectors have been calculated on annual and monthly basis.From our analysis it is resulted that there is a different behaviour in the characteristics of the diurnal anisotropy during the different phases of the solar cycle, depended on the solar magnetic field polarity, but also during extreme events of solar activity, such as Ground Level Enhancements and cosmic ray events, such as Forbush decreases and magnetospheric events. These results may be useful to Space Weather forecasting and especially to Biomagnetic studies.