Solar Polarity Dependence of Cosmic Ray Power Spectra Observed with Mawson Underground Muon Telescopes

Power spectral density (PSD) of cosmic rays has been calculated from hourly averaged counts observed by underground muon telescopes located at Mawson over the low-frequency range 2.7×10⁻⁷ – 1.4×10⁻⁴ Hz. The first two harmonics of the solar daily variation are well defined for even cycles (20 and 22) whereas only the first harmonic is defined in cycle 21. The amplitude of the diurnal variation is lower for even cycles than for the odd cycle. The spectral power of the odd cycle exceeds those of the even cycles. The spectra are flatter and have lower power when the interplanetary magnetic field (IMF) is directed away from the Sun above the current sheet (A>0) than when the IMF is directed toward the Sun above the current sheet (A<0). The spectra imply that heliospheric magnetic turbulence may be more variable on time scales of several years than previously suspected.     

Long-Term Changes of Polar Activity of the Sun

We discuss long-time changes of polar activity of the Sun using the new observational data sets in the optical range during 1872–2001. A study of the secular and cycle variations of the magnetic activity at the high-latitude regions is the main goal that includes polar magnetic field reversals during 1872–2001 and secular changes of the duration of polar activity cycles. The secular increase of the area of polar zones during the minimum activity in the last 120 years and as consequence a decrease of coronal temperature of the Sun in the high-latitude zones during the last 50 years. Correlation between the polar cycles of Caii-K bright points with the Wolf sunspot numbers cycles, W(t), and the 22-year polar magnetic cycles of Caii-K bright points at the high latitudes during 1905–1995 is discussed.     

The Sun’s Large-Scale Magnetic Field and Its Long-Term Evolution

The Sun’s large-scale external field is formed through the emergence of magnetic flux in active regions and its subsequent dispersal over the solar surface by differential rotation, supergranular convection, and meridional flow. The observed evolution of the polar fields and open flux (or interplanetary field) during recent solar cycles can be reproduced by assuming a supergranular diffusion rate of 500 – 600 km² s⁻¹ and a poleward flow speed of 10 –20 m s⁻¹. The nonaxisymmetric component of the large-scale field decays on the flow timescale of ∼1 yr and must be continually regenerated by new sunspot activity. Stochastic fluctuations in the longitudinal distribution of active regions can produce large peaks in the Sun’s equatorial dipole moment and in the interplanetary field strength during the declining phase of the cycle; by the same token, they can lead to sudden weakenings of the large-scale field near sunspot maximum (Gnevyshev gaps). Flux transport simulations over many solar cycles suggest that the meridional flow speed is correlated with cycle amplitude, with the flow being slower during less active cycles.     

Hale-cycle effects in cosmic-ray intensity during the last four cycles

Monthly cosmic-ray data from Inuvik (0.16 GV) and Climax (2.96 GV) Neutron Monitor stations has been studied with the aid of solar activity parameters for the time period 1947–1995. Systematic differences in the overall shape of successive 11-year modulation cycles and similarities in the alternate 11-year cycles seem to be related to the polarity reversals of the polar magnetic field of the Sun. This suggests a possible effectiveness of the Hale cycle during even and odd solar activity cycles. Our results can be understood in terms of open and closed models of the heliosphere. Positive north pole of the Sun leads to open heliosphere where particles reach the Earth more easily when their access route is by the heliospheric oolar regions (even cycles) than when they gain access along the current sheet (odd cycles). In this case as the route of access becomes longer due to the waviness of the neutral sheet, the hysteresis effect of cosmic-rays is also longer. This interpretation is explained in terms of different contributions of convection, diffusion and drift mechanisms to the whole modulation process influencing cosmic-ray transport in the heliosphere.     

Photospheric Magnetic Field of the Sun: Two Patterns of the Longitudinal Distribution

Longitudinal distributions of the photospheric magnetic field studied on the basis of National Solar Observatory (Kitt Peak) data (1976 – 2003) displayed two opposite patterns during different parts of the 11-year solar cycle. Helio-longitudinal distributions differed for the ascending phase and the maximum of the solar cycle on the one hand and for the descending phase and the minimum on the other, depicting maxima around two diametrically opposite Carrington longitudes (180° and 0°/360°). Thus the maximum of the distribution shifted its position by 180° with the transition from one characteristic period to the other. Two characteristic periods correspond to different situations occurring in the 22-year magnetic cycle of the Sun, in the course of which both global magnetic field and the magnetic field of the leading sunspot in a group change their sign. During the ascending phase and the maximum (active longitude 180°) polarities of the global magnetic field and those of the leading sunspots coincide, whereas for the descending phase and the minimum (active longitude 0°/360°) the polarities are opposite. Thus the observed change of active longitudes may be connected with the polarity changes of Sun’s magnetic field in the course of 22-year magnetic cycle.     

Study of the Diurnal Variation of Cosmic Rays during Different Phases of Solar Activity

The pressure-corrected hourly counting rate data of ground-based super neutron monitor stations, situated in different latitudes, have been employed to study the characteristics of the long-term variation of cosmic-ray diurnal anisotropy for a long (44-year) period (1965?–?2008). Some of these super neutron monitors are situated in low latitudes with high cutoff rigidity. Annual averages of the diurnal amplitudes and phases have been obtained for each station. It is found that the amplitude of the diurnal anisotropy varies with a period of one solar activity cycle (11 years), whereas the diurnal phase varies with a period of 22 years (one solar magnetic cycle). The average diurnal amplitudes and phases have also been calculated by grouping the days on the basis of ascending and descending periods of each solar cycle (Cycles 20, 21, 22, and 23). Systematic and significant differences are observed in the characteristics of the diurnal variation between the descending periods of the odd and even solar cycles. The overall vector averages of the descending periods of the even solar cycles (20 and 22) show significantly smaller diurnal amplitudes compared to the vector averages of the descending periods of the odd solar cycles (21 and 23). In contrast, we find a large diurnal phase shift to earlier hours only during the descending periods of even solar cycles (20 and 22), as compared to almost no shift in the diurnal phase during the descending periods of odd solar cycles. Further, the overall vector average diurnal amplitudes of the ascending period of odd and even solar cycles remain invariant from one ascending period to the other, or even between the even and odd solar cycles. However, we do find a significant diurnal phase shift to earlier hours during the ascending periods of odd solar cycles (21 and 23) in comparison to the diurnal phase in the ascending periods of even solar cycles (20 and 22).     

Long-term modulation of cosmic ray intensity in relation to sunspot numbers and tilt angle

A detailed correlative analysis between sunspot numbers (SSN) and tilt angle (TA) with cosmic ray intensity (CRI) in the neutron monitor energy range has been performed for the solar cycles 21, 22 and 23. It is found that solar activity parameters (SSN and TA) are highly (positive) correlated with each other and have inverse correlation with cosmic ray intensity (CRI). The ‘running cross correlation coefficient’ between cosmic ray intensity and tilt angle has also been calculated and it is found that the correlation is positive during the maxima of odd cycles 21 and 23. Moreover, the time lag analysis between CRI and SSN, and between CRI and TA has also been performed and is supported by hysteresis curves, which are wide for odd cycles and narrow for even cycles.     

Duration of Polar Activity Cycles and Their Relation to Sunspot Activity

We have defined the duration of polar magnetic activity as the time interval between two successive polar reversals. The epochs of the polarity reversals of the magnetic field at the poles of the Sun have been determined (1) by the time of the final disappearance of the polar crown filaments and (2) by the time between the two neighbouring reversals of the magnetic dipole configuration (l=1) from the H synoptic charts covering the period 1870–2001. It is shown that the reversals for the magnetic dipole configuration (l=1) occur on an average 3.3±0.5 years after the sunspot minimum according to the H synoptic charts (Table I) and the Stanford magnetograms (Table III). If we set the time of the final disappearance of the polar crown filaments (determined from the latitude migration of filaments) as the criterion for deciding the epoch of the polarity reversal of the polar fields, then the reversal occurs on an average 5.8±0.6 years from sunspot minimum (last column of Table I). We consider this as the most reliable diagnostic for fixing the epoch of reversals, as the final disappearance of the polar crown filaments can be observed without ambiguity. We show that shorter the duration of the polar activity cycle (i.e., the shorter the duration between two neighbouring reversals), the more intense is the next sunspot cycle. We also notice that the duration of polar activity is always more in even solar cycles than in odd cycles whereas the maximum Wolf numbers W _\max is always higher for odd solar cycles than for even cycles. Furthermore, we assume there is a secular change in the duration of the polar cycle. It has decreased by 1.2 times during the last 120 years.     

The basic cycle of solar activity and the global magnetic field and active phenomena distribution

We have compared the latitudinal distributions of polar faculae, green coronal emission maxima, prominences and of a new index of enhanced geomagnetic recurrence with the distribution of magnetic fields during the cycles Nos. 20 and 21.We did not find a distinct high-latitude initial stage of an extended cycle in the corona, prominences and polar faculae distribution. On the contrary, it seems that the polar faculae and their following polarity magnetic fields represent the last evolutionary phase of a magnetic activity cycle lasting 15–17 years. The enhanced recurrent geomagnetic activity seems to be related to the old cycle fields.All studied phenomena clearly display two types of latitudinal distribution: the polar belts, into which the old following polarity fields have been transported from the equatorial belt where both the polarities developin situ simultaneously, but in which the leading polarity fields only remain, crossing the equator during the minimum of activity, to play the same role on the opposite hemispheres in the new cycle.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Rotation cycles of the sector structure of the solar magnetic field and its activity

We study the rotation of the sector structure of the solar magnetic field by using Stanford magnetographic observations from 1975 until 2000 and magnetic synoptic Hα-maps obtained from 1904 until 2000. The two independent series of observations yielded the same rotation periods of the two-sector (26.86 days) and four-sector (13.64 days) structures. We introduce a new index of the solar rotation, SSPM(t). The spectral power density of the sector structure of the magnetic field is shown to exhibit a 22-year cyclicity. The two-and four-sector structures of the magnetic field rotate faster at the maxima of even 11-year sunspot cycles. This phenomenon may be called the Gnevyshev-Ohl rule for the solar rotation. The 11-year sector-structure activity cycles are shown to lead the 11-year sunspot cycles (Wolf numbers) by 5.5 years. A 55-year component with the slowest rotation in the 18th cycle (1945–1955) was distinguished in the sector-structure rotation.     

Height stratification of solar magnetic fields in cycle 23

The radial component Br of magnetic field was calculated in the potential approximation and the synoptic maps of Br for several heights in the Solar atmosphere were constructed based on observations of the photospheric magnetic field made on the old magnetograph at the US Kitt Peak National Observatory and on the new SOLIS magnetograph at the US National Solar Observatory for cycle 23 (the years 1997–2009). Parameters of large-scale structures of magnetic field with positive and negative polarities were determined at seven heights in the Sun’s atmosphere—from the photosphere (H = Ro) to H = 2.5 Ro (Ro is the Solar radius). The processes of polar reversal for polar fields and changing of the sector structure of the field at middle latitudes were observed. Characteristic lifespans and rotations were ascertained. The general picture of variations of the large-scale solar magnetic field during cycle 23 was put forward. Two types of boundaries of large magnetic structures at various heights were identified.     

Study of the Cosmic Ray Diurnal Anisotropy During Different Solar and Magnetic Conditions

The pressure-corrected hourly counting rate data of four neutron monitor stations have been employed to study the variation of cosmic ray diurnal anisotropy for a period of about 50 years (1955–2003). These neutron monitors, at Oulu ( R _c = 0.78 GV), Deep River ( R _c = 1.07 GV), Climax ( R _c = 2.99 GV), and Huancayo ( R _c = 12.91 GV) are well distributed on the earth over different latitudes and their data have been analyzed. The amplitude of the diurnal anisotropy varies with a period of one solar cycle (∼11 years), while the phase varies with a period of two solar cycles (∼22 years). In addition to its variation on year-to-year basis, the average diurnal amplitude and phase has also been calculated by grouping the days for each solar cycle, viz. 19, 20, 21, 22, and 23. As a result of these groupings over solar cycles, no significant change in the diurnal vectors (amplitude as well as phase) from one cycle to other has been observed. Data were analyzed by arranging them into groups on the basis of the polarity of the solar polar magnetic field and consequently on the basis of polarity states of the heliosphere ( A > 0 and A < 0). Difference in time of maximum of diurnal anisotropy (shift to earlier hours) is observed during A < 0 (1970s, 1990s) polarity states as compared to anisotropy observed during A > 0 (1960s, 1980s). This shift in phase of diurnal anisotropy appears to be related to change in preferential entry of cosmic ray particles (via the helioequatorial plane or via solar poles) into the heliosphere due to switch of the heliosphere from one physical/magnetic state to another following the solar polar field reversal.     

Modeling the Relationship Between Neutron Counting Rates and Sunspot Numbers Using the Hysteresis Effect

Several studies show that temporal variations in the Galactic cosmic ray (GCR) intensity display a distinct 11-year periodicity due to solar modulation of the galactic cosmic rays in the heliosphere. The 11-year periodicity of GCRs is inversely proportional to, but out of phase with, the 11-year solar cycle, implying that there is a time lag between actual solar cycle and the GCR intensity, which is known as the hysteresis effect. In this study, we use the hysteresis effect to model the relationship between neutron counting rates (NCRs), an indicator of the GCR intensity, and sunspot numbers (SSNs) over the period that covers the last four solar cycles (20, 21, 22, and 23). Both linear and ellipse models were applied to SSNs during odd and even cycles in order to calculate temporal variations of NCRs. We find that ellipse modeling provides higher correlation coefficients for odd cycles compared to linear models, e.g. 0.97, 0.97, 0.92, and 0.97 compared to 0.69, 0.72, 0.53, and 0.68 for data from McMurdo, Swarthmore, South Pole, and Thule neutron monitors, respectively, during solar cycle 21 with overall improvement of 31 % for odd cycles. When combined to a continuous model, the better correlation observed for the odd cycles increases the overall correlation between observed and modeled NCRs. The new empirical model therefore provides a better representation of the relationship between NCRs and SSNs. A major goal of the ongoing research is to use the new non-linear empirical model to reconstruct SSNs on annual time scales prior to 1610, where we do not have observational records of SSNs, based on changes in NCRs reconstructed from ¹⁰Be in ice cores.     

Solar magnetic fields and convection

Solar meridional drift motions are vitally important in connection with the origin of magnetic fields, the source of differential rotation, and perhaps convection. A large body of observational evidence is collated with the following conclusions. (i) Sunspot motions reveal latitudinal drifts (Figures 2 and 3) of a few metres per second which vary with latitude and have a strong 11-yr periodicity. There may also be a 22-yr component polewards during even cycles and equatorwards during odd. (ii) Various other tracers, all basically magnetic structures, show the 11-yr drifts at mid- and high latitudes up to the polar caps, motion being polewards during the three years starting just before minimum activity (Figure 4). (iii) The earlier evidence for giant cells or Rossby-type waves is shown to be merely misinterpretation of the hydromagnetic motions of tracers. Evidence against such giant eddies is found in the great stability of other tracer structures. (iv) From the various tracer motions a four cell axisymmetric meridional drift system is determined (Figure 5 (b)) with an 11-yr period of oscillation and amplitude a few metres per second. (v) These meridional oscillations must be a basic component of the activity cycle. They add to the difficulties of the dynamo theory, but may explain the emergence of stitches of flux ropes to form relatively small bipolar magnetic regions. (vi) The two cells also throw light on thetwo sunspot zones in each hemisphere, discussed earlier by Becker and by Antalová and Gnevyshev.     

Solar Polar Fields During Cycles 21 – 23: Correlation with Meridional Flows

We have examined polar magnetic fields for the last three solar cycles, viz. Cycles 21, 22, and 23 using NSO/Kitt Peak synoptic magnetograms. In addition, we have used SOHO/MDI magnetograms to derive the polar fields during Cycle 23. Both Kitt Peak and MDI data at high latitudes (78° – 90°) in both solar hemispheres show a significant drop in the absolute value of polar fields from the late declining phase of the Solar Cycle 22 to the maximum of the Solar Cycle 23. We find that long-term changes in the absolute value of the polar field, in Cycle 23, are well correlated with changes in meridional-flow speeds that have been reported recently. We discuss the implication of this in influencing the extremely prolonged minimum experienced at the start of the current Cycle 24 and in forecasting the behavior of future solar cycles.     

Statistical characteristics of large sunspots in solar activity cycles 17–23

Integral and differential distributions of sunspot diameters are studied for the last seven 11-year cycles of solar activity. Data of the Greenwich catalogue, Pulkovo’s database, and the “Solniechnyie Dannyie” bulletin are used. We found that the average index of integral distribution α is 6.0 for the diameters from 50 to 90 Mm and independent of the Wolf’s numbers, but it depends on a cycle phase in the majority of cycles (four of seven), i.e., it is higher during the ascending phase, of intermediate value during the maximum phase and minimum during the declining phase. Cycles 17, 18, and 22 behave differently: the index α is either invariable with phase or the variations differ from the above ones. It turned out that cycles 17 and 18 are peculiar by sunspot diameters, i.e., sunspots of up to 140–180 Mm in diameter, the largest over the last 80 years, have been observed. Three assumptions concerning the nature of these gigantic sunspots have been proposed: (a) these sunspots occur due to changes in differential rotation of the sun, (b) these sunspots are a certain independent statistical assembly formed in a sporadic discrete region of the convective zone, and (c) these sunspots are surface “fragments” of the relict magnetic field of the solar nucleus.     

Do polar faculae on the sun predict a sunspot cycle?

The paper reports the results of the analysis of the data on polar faculae for three solar cycles (1960–1986) at the Kislovodsk Station of the Pulkovo Observatory and on polar bright points in Ca ii K line for two solar cycles (1940–1957) at the Kodaikanal Station of the Indian Institute of Astrophysics. We have noticed that the monthly numbers of polar faculae and polar bright points in Ca ii K line and monthly sunspot areas in each hemisphere of the following solar cycle have a correlation with each other. A new cycle of polar faculae and polar bright points in the Ca ii K line begins after the polar magnetic field reversal. We find that the smaller the period between the ending of the polar field reversal and the beginning of a new sunspot cycle is, the more intense is the cycle itself. The intensity of the forthcoming solar cycle (cycle 22) and the periods of strong fluctuations in activity expected in this cycle are also discussed.     

22-year variations of the solar rotation and solar activity cycles

We have performed a comparative analysis of the results of our study of the 22-year rotation variations obtained from data on large-scale magnetic fields in the Hα line, magnetographic observations, and spectral-corona observations. All these types of data suggest that the rotation rate at low latitudes slows down at an epoch close to the maximum of odd activity cycles. The 22-year waves of rotation-rate deviation from the mean values drift from high latitudes toward the equator in a time comparable to the magnetic-cycle duration. We discuss the possibility of the generation of a solar magnetic cycle by the interaction of 22-year torsional oscillations with the slowly changing or relic magnetic field. We consider the generation mechanisms of the high-latitude magnetic field through a superposition of the magnetic fields produced by the decay and dissipation of bipolar groups and the relic or slowly changing magnetic field and a superposition of the activity wave from the next activity cycle at high latitudes.     

Coronal Activity During the 22-Year Solar Magnetic Cycle

The existence of a 22-year heliomagnetic cycle was inferred long ago not only from direct measurements of the solar magnetic field but also from a cyclic variability of a number of the solar activity phenomena. In particular, it was stated (a rule derived after Gnevyshev and Ohl (1948) findings and referenced as the G–O rule in the following) that if sunspot number Rz cycles are organized in pairs of even–odd numbered cycles, then the height of the peak in the curve of the yearly-averaged sunspot numbers Rz-y is always lower for a given even cycle in comparison with the corresponding height of the following odd cycle. Exceptions to this rule are only cycles 4 and 8 which, at the same time, are the nearest even cycles to the limits of the so-called Dalton minimum of solar activity (i.e., the 1795–1823 time interval). In the present paper, we are looking for traces of the mentioned G–O rule in green corona brightness (measured in terms of the Fexiv 530.3 nm emission line intensity), using data covering almost five solar cycles (1943–1994). It was found that the G–O rule seems to work within the green-line corona brightness, namely, when coronal intensity measured in an extended solar middle-latitude zone is considered separately from the rest of the solar surface. On the other hand, the same G–O rule is valid at the photospheric level, as the heliographic latitudinal dependence of sunspot numbers (1947–1984) shows.     

Predicting the Amplitude of a Solar Cycle Using the North – South Asymmetry in the Previous Cycle: II. An Improved Prediction for Solar Cycle 24

Recently, using Greenwich and Solar Optical Observing Network sunspot group data during the period 1874 – 2006, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007: Paper I), has found that: (1) the sum of the areas of the sunspot groups in 0° – 10° latitude interval of the Sun’s northern hemisphere and in the time-interval of −1.35 year to +2.15 year from the time of the preceding minimum of a solar cycle n correlates well (corr. coeff. r=0.947) with the amplitude (maximum of the smoothed monthly sunspot number) of the next cycle n+1. (2) The sum of the areas of the spot groups in 0° – 10° latitude interval of the southern hemisphere and in the time-interval of 1.0 year to 1.75 year just after the time of the maximum of the cycle n correlates very well (r=0.966) with the amplitude of cycle n+1. Using these relations, (1) and (2), the values 112±13 and 74±10, respectively, were predicted in Paper I for the amplitude of the upcoming cycle 24. Here we found that the north – south asymmetries in the aforementioned area sums have a strong ≈44-year periodicity and from this we can infer that the upcoming cycle 24 will be weaker than cycle 23. In case of (1), the north – south asymmetry in the area sum of a cycle n also has a relationship, say (3), with the amplitude of cycle n+1, which is similar to (1) but more statistically significant (r=0.968) like (2). By using (3) it is possible to predict the amplitude of a cycle with a better accuracy by about 13 years in advance, and we get 103±10 for the amplitude of the upcoming cycle 24. However, we found a similar but a more statistically significant (r=0.983) relationship, say (4), by using the sum of the area sum used in (2) and the north – south difference used in (3). By using (4) it is possible to predict the amplitude of a cycle by about 9 years in advance with a high accuracy and we get 87±7 for the amplitude of cycle 24, which is about 28% less than the amplitude of cycle 23. Our results also indicate that cycle 25 will be stronger than cycle 24. The variations in the mean meridional motions of the spot groups during odd and even numbered cycles suggest that the solar meridional flows may transport magnetic flux across the solar equator and potentially responsible for all the above relationships. The author did a major part of this work at the Department of Physics and Astronomy, UCLA, 430 Portola Plaza, Los Angeles, CA 90095-1547, USA.