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.     

Gnevyshev Peaks and Gaps for Coronal Mass Ejections of Different Widths Originating in Different Solar Position Angles

The sunspot number series at the peak of sunspot activity often has two or three peaks (Gnevyshev peaks; Gnevyshev, Solar Phys. 1, 107, 1967; Solar Phys. 51, 175, 1977). The sunspot group number (SGN) data were examined for 1997 – 2003 (part of cycle 23) and compared with data for coronal mass ejection (CME) events. It was noticed that they exhibited mostly two Gnevyshev peaks in each of the four latitude belts 0° – 10°, 10° – 20°, 20 ° – 30°, and > 30°, in both N (northern) and S (southern) solar hemispheres. The SGN were confined to within latitudes ± 50° around the Equator, mostly around ± 35°, and seemed to occur later in lower latitudes, indicating possible latitudinal migration as in the Maunder butterfly diagrams. In CMEs, less energetic CMEs (of widths < 71°) showed prominent Gnevyshev peaks during sunspot maximum years in almost all latitude belts, including near the poles. The CME activity lasted longer than the SGN activity. However, the CME peaks did not match the SGN peaks and were almost simultaneous at different latitudes, indicating no latitudinal migration. In energetic CMEs including halo CMEs, the Gnevyshev peaks were obscure and ill-defined. The solar polar magnetic fields show polarity reversal during sunspot maximum years, first at the North Pole and, a few months later, at the South Pole. However, the CME peaks and gaps did not match with the magnetic field reversal times, preceding them by several months, rendering any cause – effect relationship doubtful.     

Which One is the ‘GNEVYSHEV’ GAP?

Gnevyshev [Solar Phys. 1, 107, 1967] showed that in solar cycle 19 (1954 –1965), the coronal line half-yearly average intensity at 5303 Å (green line) had actually two maxima, the first one in 1957 and the second in 1959–1960. In the present communication, the structures at solar maxima were reexamined in detail. It was noted that the two-peak structure of solar indices near sunspot (Rz) maxima was only a crude approximation. On a finer time scale (monthly values), there were generally more than three peaks, with irregular peak separations in a wide range of ～12± 6 months. The sequences were seen simultaneously (within a month or two) at many solar indices (notably the 2800 MHz radio flux) at and above the photosphere, and these can be legitimately termed ‘Gnevyshev peaks’ and ‘Gnevyshev gaps’. The open magnetic flux emanating from the Sun showed this sequence partially, some peaks matching, others not. In interplanetary space, the interplanetary parameters N (number density), V (solar wind speed), B (magnetic field) showed short-time peak structures but mostly not matching with the Rz peaks. Geomagnetic indices (aa, Dst) had peaked structures, which did not match with Rz peaks but were very well related to V and B, particularly to the product VB. The cosmic ray (CR) modulation also showed peaks and troughs near sunspot maximum, but the matching with Rz peaks was poor. Hence, none of these can be termed Gnevyshev peaks and gaps, particularly the gap between aa peaks, one near sunspot maximum and another in the declining phase, as this gap is qualitatively different from the Gnevyshev gap in solar indices.     

Latitude Dependence of the “Gnevyshev” Peaks and Gaps

The occurrence of double peaks near the maximum of sunspot activity was first emphasized by Gnevyshev (Solar Phys. 1, 107, 1967) for the peak years of solar cycle 19 (1954 – 1964). In the present analysis, it is shown that double peaks in sunspot numbers were clearly visible in solar latitudes 10 – 30° N but almost absent in the southern latitudes, where some single peaks were observed out of phase by several months from any of the peaks in the northern latitudes. The spacing between the double peaks increased from higher to lower northern latitudes, hinting at latitudinal migration. In the next cycle 20 (1965 – 1976), which was of about half the strength of cycle 19, no clear-cut double peaks were seen, and the prominent peak in the early part of 1967 in the northern latitudes was seen a few months later in the southern latitudes. A direct relationship of Gnevyshev peaks with changes in the solar polar magnetic fields seems to be dubious. The commencements do not match.     

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.     

Solar-Cycle Characteristics Examined in Separate Hemispheres: Phase,Gnevyshev Gap,and Length of Minimum

According to research results from solar-dynamo models, the northern and southern hemispheres may evolve separately throughout the solar cycle. The observed phase lag between the northern and southern hemispheres provides information regarding how strongly the hemispheres are coupled. Using hemispheric sunspot-area and sunspot-number data from Cycles 12 – 23, we determine how out of phase the separate hemispheres are during the rising, maximum, and declining period of each solar cycle. Hemispheric phase differences range from 0 – 11, 0 – 14, and 2 – 19 months for the rising, maximum, and declining periods, respectively. The phases appear randomly distributed between zero months (in phase) and half of the rise (or decline) time of the solar cycle. An analysis of the sunspot cycle double peak, or Gnevyshev gap, is conducted to determine if the double-peak is caused by the averaging of two hemispheres that are out of phase. We confirm previous findings that the Gnevyshev gap is a phenomenon that occurs in the separate hemispheres and is not due to a superposition of sunspot indices from hemispheres slightly out of phase. Cross hemispheric coupling could be strongest at solar minimum, when there are large quantities of magnetic flux at the Equator. We search for a correlation between the hemispheric phase difference near the end of the solar cycle and the length of solar-cycle minimum, but found none. Because magnetic flux diffusion across the Equator is a mechanism by which the hemispheres couple, we measured the magnetic flux crossing the Equator by examining Kitt Peak Vacuum Telescope and SOLIS magnetograms for Solar Cycles 21 – 23. We find, on average, a surplus of northern hemisphere magnetic flux crossing during the mid-declining phase of each solar cycle. However, we find no correlation between magnitude of magnetic flux crossing the Equator, length of solar minima, and phase lag between the hemispheres.     

Similarities and Dissimilarities between the Variations of CME and Other Solar Parameters at Different Heliographic Latitudes and Time Scales

From the LASCO CME (Coronal Mass Ejection) catalog, the occurrence frequencies of all CMEs (all strong and weak CMEs, irrespective of their widths) were calculated for 3-month intervals and their 12-month running means determined for cycle 23 (1996 – 2007) and were compared with those of other solar parameters. The annual values of all-CME frequency were very well correlated (+ 0.97) with sunspot numbers, but several other parameters also had similarly high correlations. Comparisons of 12-month running means indicated that the sunspot numbers were very well correlated with solar electromagnetic radiations (Lyman-α, 2800-MHz flux, coronal green line index, solar flare indices, and X-ray background); but for corpuscular radiations [proton fluxes, solar energetic particles (SEP), CMEs, interplanetary CMEs (ICMEs), and stream interaction regions (SIR)] and solar open magnetic fields, the correlations were lower. A notable feature was the appearance of two peaks during 2000 – 2002, and those double peaks in different parameters matched approximately except for proton fluxes and SEP and SIR frequencies. When hemispheric intensities were considered, north – south asymmetries appeared, more in some parameters than in others. When intensities in smaller latitude belts (10°) were compared, sunspot group numbers (SGN) were found to be confined mostly to latitudes within ± 30° of the solar equator, showing two peaks in all latitude belts, and during the course of the 11-year cycle, the double peaks shifted from middle to equatorial solar latitudes, just as seen in the Maunder butterfly diagrams. In contrast, CME frequency was comparable at all latitude belts (including high, near-polar latitudes), having more than two peaks in almost all latitude belts, and the peaks were almost simultaneous in all latitude belts. Thus, the matching of SGN peaks with those of CME peaks was poor. Incidentally, the CME frequency data for all events (all widths) after 2003 are not comparable to earlier data, owing to inclusion of very weak (narrow) CMEs in later years. The frequencies are comparable with earlier data only for widths exceeding about 70°.     

Gnevyshev peaks in geomagnetic indices

Sunspots have a major 11-year cycle, but the years near the maximum show two or more peaks called Gnevyshev peaks. It was noticed that in cycle 23, the double peaks in sunspot numbers are reflected in the electromagnetic radiations and coronal mass ejections (CMEs) in the solar atmosphere. But, in the interplanetary space, the ICMEs (interplanetary CMEs) show peaks not all coinciding with the peaks of sunspot numbers. Also, there are stream interaction regions (SIR), including co-rotating interaction regions (CIR), which evolve quite differently from sunspot numbers. In the geomagnetic indices, the peaks are related mainly to the peaks in SIRs, indicating that geomagnetic indices have no direct relationship with most of the phenomena at the Sun but are responding only to the interplanetary blobs due to SIRs, which are more predominant in the declining phase of sunspot activity.     

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.     

The “Floor” in the Interplanetary Magnetic Field: Estimation on the Basis of Relative Duration of ICME Observations in Solar Wind During 1976 – 2000

Measurement of the floor in the interplanetary magnetic field and estimation of the time-invariant open magnetic flux of the Sun require knowledge of closed magnetic flux carried away by coronal mass ejections (CMEs). In contrast with previous papers, we do not use global solar parameters to estimate such values: instead we identify different large-scale types of solar wind for the 1976 – 2000 interval to obtain the fraction of interplanetary CMEs (ICMEs). By calculating the magnitude of the interplanetary magnetic field B averaged over two Carrington rotations, the floor of the magnetic field can be estimated from the B value at a solar cycle minimum when the number of ICMEs is minimal. We find a value of 4.65±0.6 nT, in good agreement with previous results.     

Short-Term Periodicities in Solar Indices

The purpose of the present communication is to identify the short-term (few tens of months) periodicities of several solar indices (sunspot number, Caii area and K index, Lyman , 2800 MHz radio emission, coronal green-line index, solar magnetic field). The procedure used was: from the 3-month running means (3m) the 37-month running means (37m) were subtracted, and the factor (3m – 37m) was examined for several parameters. For solar indices, considerable fluctuations were seen during the ± 4 years around sunspot maxima of cycles 18–23, and virtually no fluctuations were seen in the ± 2 years around sunspot minima. The spacings between successive peaks were irregular but common for various solar indices. Assuming that there are stationary periodicities, a spectral analysis was carried out which indicated periodicities of months: 5.1–5.7, 6.2–7.0, 7.6–7.9, 8.9–9.6, 10.4–12.0, 12.8–13.4, 14.5–17.5, 22–25, 28 (QBO), 31–36 (QBO), 41–47 (QTO). The periodicities of 1.3 year (15.6 months) and 1.7 years (20.4 months) often mentioned in the literature were seen neither often nor prominently. Other periodicities occurred more often and more prominently. For the open magnetic flux estimated by Wang, Lean, and Sheeley (2000) and Wang and Sheeley (2002), it was noticed that the variations were radically different at different solar latitudes. The open flux for < 45 solar latitudes had variations very similar (parallel) to the sunspot cycle, while open flux for > 45 solar latitudes had variations anti-parallel to the sunspot cycle. The open fluxes, interplanetary magnetic field and cosmic rays, all showed periodicities similar to those of solar indices. Many peaks (but not all) matched, indicating that the open flux for < 45 solar latitudes was at least partially an adequate carrier of the solar characteristics to the interplanetary space and thence for galactic cosmic ray modulation.     

Sharp Changes of Solar Wind Ion Flux and Density Within and Outside Current Sheets

Analysis of the Interball-1 spacecraft data (1995 – 2000) has shown that the solar wind ion flux sometimes increases or decreases abruptly by more than 20% over a time period of several seconds or minutes. Typically, the amplitude of such sharp changes in the solar wind ion flux (SCIFs) is larger than 0.5×10⁸ cm⁻² s⁻¹. These sudden changes of the ion flux were also observed by the Solar Wind Experiment (SWE), on board the Wind spacecraft, as the solar wind density increases and decreases with negligible changes in the solar wind velocity. SCIFs occur irregularly at 1 AU, when plasma flows with specific properties come to the Earth’s orbit. SCIFs are usually observed in slow, turbulent solar wind with increased density and interplanetary magnetic field strength. The number of times SCIFs occur during a day is simulated using the solar wind density, magnetic field, and their standard deviations as input parameters for a period of five years. A correlation coefficient of ∼0.7 is obtained between the modelled and the experimental data. It is found that SCIFs are not associated with coronal mass ejections (CMEs), corotating interaction regions (CIRs), or interplanetary shocks; however, 85% of the sector boundaries are surrounded by SCIFs. The properties of the solar wind plasma for days with five or more SCIF observations are the same as those of the solar wind plasma at the sector boundaries. One possible explanation for the occurrence of SCIFs (near sector boundaries) is magnetic reconnection at the heliospheric current sheet or local current sheets. Other probable causes of SCIFs (inside sectors) are turbulent processes in the slow solar wind and at the crossings of flux tubes.     

North-south asymmetry in solar, interplanetary, and geomagnetic indices

Data of hourly interplanetary plasma (field magnitude, solar wind speed, and ion density), solar (sunspot number, solar radio flux), and geomagnetic indices (Kp, Ap) over the period 1970-2010, have been used to examine the asymmetry between the solar field north and south of the heliospheric current sheet (HCS). A persistent yearly north-south asymmetry of the field magnitude is clear over the considered period, and there is no magnetic solar cycle dependence. There is a weak N-S asymmetry in the averaged solar wind speed, exhibited well at times of maximum solar activities. The solar plasma is more dense north of the current sheet than south of it during the second negative solar polarity epoch (qA < 0). Moreover, the N - S asymmetry in solar activity (Rz) can be statistically highly significant. The sign of the average N - S asymmetry depends upon the solar magnetic polarity. The annual magnitudes of N - S asymmetry depend positively on the solar magnetic cycle. Most of the solar radio flux asymmetries occurred during the period of positive IMF polarity.     

Geoeffectiveness of interplanetary shocks during solar minimum (1995–1996) and solar maximum (2000)

Plasma and magnetic field parameter variations across fast forward interplanetary shocks are analyzed during the last solar cycle minimum (1995–1996, 15 shocks), and maximum year 2000 (50 shocks). It was observed that the solar wind velocity and magnetic field strength variation across the shocks were the parameters better correlated with Dst. Superposed epoch analysis centered on the shock showed that, during solar minimum, B _z profiles had a southward, long-duration variation superposed with fluctuations, whereas in solar maximum the B _z profile presented 2 peaks. The first peak occurred 4 hr after the shock, and seems to be associated with the magnetic field disturbed by the shock in the sheath region. The second peak occurred 19 hr after the shock, and seems to be associated with the ejecta fields. The difference in shape and peak in solar maximum (Dst peak =−50 nT, moderate activity) and minimum (Dst peak =−30 nT, weak activity) in average Dst profiles after shocks are, probably, a consequence of the energy injection in the magnetosphere being driven by different interplanetary southward magnetic structures. A statistical distribution of geomagnetic activity levels following interplanetary shocks was also obtained. It was observed that during solar maximum, 36% of interplanetary shocks were followed by intense (Dst≤−100 nT) and 28% by moderate (−50≤Dst <−100 nT) geomagnetic activity. During solar minimum, 13% and 33% of the shocks were followed by intense and moderate geomagnetic activity, respectively. Thus, during solar maximum a higher relative number of interplanetary shocks might be followed by intense geomagnetic activity than during solar minimum. One can extrapolate, for forecasting goals, that during a whole solar cycle a shock has a probability of around 50–60% to be followed by intense/moderate geomagnetic activity.     

The Mechanism involved in the Reversals of the Sun's Polar Magnetic Fields

Models of the polarity reversals of the Sun's polar magnetic fields based on the surface transport of flux are discussed and are tested using observations of the polar fields during Cycle 23 obtained by the National Solar Observatory at Kitt Peak. We have extended earlier measurements of the net radial flux polewards of ±60° and confirm that, despite fluctuations of 20%, there is a steady decline in the old polarity polar flux which begins shortly after sunspot minimum (although not at the same time in each hemisphere), crosses the zero level near sunspot maximum, and increases, with reversed polarity during the remainder of the cycle. We have also measured the net transport of the radial field by both meridional flow and diffusion across several latitude zones at various phases of the Cycle. We can confirm that there was a net transport of leader flux across the solar equator during Cycle 23 and have used statistical tests to show that it began during the rising phase of this cycle rather than after sunspot maximum. This may explain the early decrease of the mean polar flux after sunspot minimum. We also found an outward flow of net flux across latitudes ±60° which is consistent with the onset of the decline of the old polarity flux. Thus the polar polarity reversals during Cycle 23 are not inconsistent with the surface flux-transport models but the large empirical values required for the magnetic diffusivity require further investigation.     

Relationships Among Magnetic Clouds, CMES, and Geomagnetic Storms

During solar cycle 23, 82 interplanetary magnetic clouds (MCs) were identified by the Magnetic Field Investigation (MFI) team using Wind (1995 – 2003) solar wind plasma and magnetic field data from solar minimum through the maximum of cycle 23. The average occurrence rate is 9.5 MCs per year for the overall period. It is found that some of the anomalies in the frequency of occurrence were during the early part of solar cycle 23: (i) only four MCs were observed in 1999, and (ii) an unusually large number of MCs (17 events) were observed in 1997, just after solar minimum. We also discuss the relationship between MCs, coronal mass ejections (CMEs), and geomagnetic storms. During the period 1996 – 2003, almost 8000 CMEs were observed by SOHO-LASCO. The occurrence frequency of MCs appears to be related neither to the occurrence of CMEs as observed by SOHO LASCO nor to the sunspot number. When we included “magnetic cloud-like structures” (MCLs, defined by Lepping, Wu, and Berdichevsky, 2005), we found that the occurrence of the joint set (MCs + MCLs) is correlated with both sunspot number and the occurrence rate of CMEs. The average duration of the MCL structures is ~40% shorter than that of the MCs. The MCs are typically more geoeffective than the MCLs, because the average southward field component is generally stronger and longer lasting in MCs than in MCLs. In addition, most severe storms caused by MCs/MCLs with Dst _min≤ −100 nT occurred in the active solar period.     

Structural Invariance of Sunspot Umbrae over the Solar Cycle: 1993 – 2004

Measurements of maximum magnetic flux, minimum intensity, and size are presented for 12 967 sunspot umbrae detected on the National Aeronautics and Space Administration/National Solar Observatory (NASA/NSO) spectromagnetograms between 1993 and 2004 to study umbral structure and strength during the solar cycle. The umbrae are selected using an automated thresholding technique. Measured umbral intensities are first corrected for center-to-limb intensity dependence. Log-normal fits to the observed size distribution confirm that the size-spectrum shape does not vary with time. The intensity – magnetic-flux relationship is found to be steady over the solar cycle. The dependence of umbral size on the magnetic flux and minimum intensity are also independent of the cycle phase and give linear and quadratic relations, respectively. While the large sample size does show a low-amplitude oscillation in the mean minimum intensity and maximum magnetic flux correlated with the solar cycle, this can be explained in terms of variations in the mean umbral size. These size variations, however, are small and do not substantiate a meaningful change in the size spectrum of the umbrae generated by the Sun. Thus, in contrast to previous reports, the observations suggest the equilibrium structure, as manifested by the invariant size-magnetic field relationship, as well as the mean size (i.e., strength) of sunspot umbrae do not significantly depend on the solar-cycle phase.     

Statistical Properties Of Sunspots In 1996–2004: I. Detection, North–South Asymmetry And Area Distribution

The first statistical results in sunspot distributions in 1996–2004 obtained from the Solar Feature Catalogues (SFC) are presented. A novel robust technique is developed for automated identification of sunspots on SOHO/MDI white-light (WL) full-disk solar images. The technique applies image standardization procedures for elimination of the limb darkening and non-circular image shape, uses edge-detection methods to find the sunspot candidates and their edges and morphological operations to smooth the features and fill in gaps. The detected sunspots are verified with the SOHO/MDI magnetograms by strong magnetic fields being present in sunspots. A number of physical and geometrical parameters of the detected sunspot features are extracted and stored in the relational SFC database including umbra/penumbra masks in the form of run-length data encoding of sunspot bounding rectangles. The detection results are verified by comparison with the manual daily detection results in Meudon and Locarno Observatories in 2002 and by correlation (about 96%) with the 4 year sunspot areas produced manually at NOAA. Using the SFC data, sunspot area distributions are presented in different phases of the solar cycle and hemispheres which reveals a periodicity of the north–south asymmetry with a period of about 7–8 years. The number of sunspots increases exponentially with the area decrease with the index slightly increasing from −1.15 (1997) to −1.34 (2001).     

Regularities in the growth of background magnetic fields

The cyclicity in the latitudinal distribution of the growth and decay rates of the total magnetic fluxes for weak magnetic fields is investigated. The synoptic maps of the line-of-sight solar magnetic field strength obtained at the Kitt Peak Observatory (USA) from January 1, 1977, to September 30, 2003, are used as the observational material. The latitudinal distributions of the growth rates of total magnetic fluxes with various strengths constructed from them and their evolution during three solar cycles have been compared with the analogous distribution of the total powers of rotation with various periods as well as the relative sunspot numbers and areas. The results obtained allow a unified picture of the development of solar cycles for weak and strong magnetic fields to be formulated. A new cycle begins with the growth of weak magnetic fields with a strength of 0–200 G at latitudes 20°–25° in both hemispheres. This occurs one year before the activity minimum determined from sunspots. Two years later, the growth rate of the total magnetic flux, which begins to propagate equatorward and poleward, reaches a maximum. This process coincides with the onset of the growth of strong sunspot magnetic fields at the corresponding latitudes and the formation of zones with a stable rotation. Subsequently, a fall-off in growth rate and then a flux decay for weak magnetic fields correspond to the growth of the sunspot areas. In light of the dynamo theory, the results obtained suggest that strong and weak magnetic fields are generated near the bottom of the convection zone, while the observed differences in their behavior are determined by the interaction of emerging magnetic flux tubes of various strengths with turbulent plasma motions inside the Sun.     

A Study of the Frequency of Occurrence of Large-Fluence Solar Proton Events and the Strength of the Interplanetary Magnetic Field

It has been shown previously that the number of very-large-fluence solar proton events inferred for the period since 1561 were more frequent at times of low solar activity (e.g., following the recovery from the Maunder minimum), than in the present epoch of high solar activity. An inverse dependence is demonstrated between the probability of observation of the very large-fluence solar proton events and the strength of the interplanetary magnetic field derived from empirical predictions. Using the observed dependence, it is predicted and demonstrated that large-fluence solar proton events have been observed at Earth more frequently near the recurrent minima of the solar activity cycle in the past than during the present epoch. We show that these results are explicable in terms of the linear dependence of the Alfvén velocity upon the strength of the interplanetary magnetic field, leading to higher shock compression ratios in the past. These results indicate that this aspect of “solar weather” will be significantly influenced by the prevailing strength of the interplanetary magnetic field, and that recurrence of solar conditions similar to those of the solar activity minimum of solar cycles 12–14 (1878.9–1913.6) would be accompanied by a factor of ∼4 increase in the occurrence of large-fluence solar proton events.