Background magnetic fields during last three cycles of solar activity

This paper describes our studies of evolution of the solar magnetic field with different sign and field strength in the range from –100 G to 100 G. The structure and evolution of large‐scale magnetic fields on the Sun during the last 3 cycles of solar activity is investigated using magnetograph data from the Kitt Peak Solar Observatory. This analysis reveals two groups of the large‐scale magnetic fields evolving differently during the cycles. The first group is represented by relatively weak background fields, and is best observed in the range of 3–10 Gauss. The second group is represented by stronger fields of 75–100 Gauss. The spatial and temporal properties of these groups are described and compared with the total magnetic flux. It is shown that the anomalous behaviour of the total flux during the last cycle can be found only in the second group. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heliospheric magnetic fields, energetic particles, and the solar cycle

The heliosphere is the region filled with magnetized plasma of mainly solar origin. It extends from the solar corona to well beyond the planets, and is separated from the interstellar medium by the heliopause. The latter is embedded in a complex and still unexplored boundary region. The characteristics of heliospheric plasma, fields, and energetic particles depend on highly variable internal boundary conditions, and also on quasi-stationary external ones. Both galactic cosmic rays and energetic particles of solar and heliospheric origin are subject to intensity variations over individual solar cycles and also from cycle to cycle. Particle propagation is controlled by spatially and temporally varying interplanetary magnetic fields, frozen into the solar wind. An overview is presented of the main heliospheric components and processes, and also of the relevant missions and data sets. Particular attention is given to flux variations over the last few solar cycles, and to extrapolated effects on the terrestrial environment.     

Global solar dynamo models: Simulations and predictions

Flux-transport type solar dynamos have achieved considerable success in correctly simulating many solar cycle features, and are now being used for prediction of solar cycle timing and amplitude. We first define flux-transport dynamos and demonstrate how they work. The essential added ingredient in this class of models is meridional circulation, which governs the dynamo period and also plays a crucial role in determining the Sun’s memory about its past magnetic fields. We show that flux-transport dynamo models can explain many key features of solar cycles. Then we show that a predictive tool can be built from this class of dynamo that can be used to predict mean solar cycle features by assimilating magnetic field data from previous cycles.     

Differential rotation of solar magnetic fields

The connection of the differential rotation of solar magnetic fields with the field sign and strength is studied. The synoptic maps of magnetic fields over the last three solar cycles taken at the Kitt Peak Observatory served as input data for the study. The algorithm of magnetic field filtering over 14 chosen strengt intervals and successive 5-degree latitude zones was applied to these data. The Fourier transform of the time series obtained was then used. Analysis of the power spectra led to the conclusion that there are two types of magnetic fields. These differ in strength (0–50 and 50–700 G) and rotation characteristics. The rotation differentiality for strong magnetic field is almost twice as large as that for weak magnetic fields.     

Dynamics of the solar magnetic field from SOHO/MDI

The investigation of the dynamics of magnetic fields from small scales to the large scales is very important for the understanding of the nature of solar activity. It is also the base for producing adequate models of the solar cycle with the purpose to predict the level of solar activity. Since December 1995 the Michelson Doppler Imager (MDI) on board of the Solar and Heliospheric Observatory (SOHO) provides full disk magnetograms and synoptic maps which cover the period of solar cycle 23 and the current minimum. In this paper, I review the following important topics with a focus on the dynamics of the solar magnetic field. The synoptic structure of the solar cycle; the birth of the solar cycle (overlapping cycles 23 and 24); the relationship of the photospheric magnetic activity and the EUV solar corona, polar magnetic fields and dynamo theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Interactions between solar neutrinos and solar magnetic fields

We attempt to correlate all of the available solar-neutrino data with the strong magnetic fields these neutrinos encounter in the solar interior along their Earth-bound path. We approximate these fields using the photospheric, magnetograph-measured flux from central latitude bands, time delayed to proxy the magnetic fields in the solar interior. Our strongest evidence for anticorrelation is for magnetic fields within the central ±5° solar-latitude band that have been delayed by 0.85 ± 0.55 yr. Assuming a neutrino-magnetic interaction, this might indicate that interior fields travel to the solar surface in this period of time. As more solar-neutrino flux information is gathered, the question of whether this result arises from a physical process or is merely a statistical fluke should be resolved, providing that new data are obtained spanning additional solar cycles and that correlation studies focus on these same regions of the solar magnetic field.     

Study on the onsets of solar energetic electron events

Fine time resolution observations of the angular distributions of the intensities of energetic electrons (220 ≤ E _e ≤ 500 keV) by the IMP-7 and 8 spacecraft during the onsets of solar electron events and the technique of mapping the solar wind to the solar corona have been incorporated in this work in order to obtain the large-angle scattering distance of these particles under different configurations of the large scale structure of the interplanetary medium. It is found that in the presence of stream-stream interaction regions with compressed magnetic fields beyong 1 AU, the large-angle scattering is determined by the distance along the streamlines from the spacecraft to their intersection by a faster solar wind stream. In cases of diverging magnetic fields the estimated large-angle scattering distance exceeds 1 AU.     

Meridional circulation and the period of the solar dynamo cycle

We consider the conditions in the transition from the tachocline to the solar convective zone with changing diffusion coefficient. The topology of the magnetic fields involved in the solar dynamo is revised under the assumption that intermediate fields (of the order of 10 mT) have a dominant role in generating the fields in new cycle. The inclusion of meridional circulation is found to increase the dynamo wave period in comparison to the observed period. This suggests that the αΩ-effects are unimportant in calculating the solar cycle period but hold significance in determining the cycle amplitude.     

A technique for predicting the amplitude of the solar cycle

Predictions of the amplitude of the last three solar cycles have demonstrated the value and accuracy of the group of prediction methods known as the precursor techniques. These are based on a correlation between cycle amplitude and phenomena observed on the Sun, or originating from the Sun, during the declining phase of the cycle or at solar minimum. In many cases, precursor predictions make use of the long record of geomagnetic disturbance indices, assuming that these indices are indicative of solar phenomena such as the occurrence of coronal holes.This paper describes a precursor technique for predicting the amplitude of the solar cycle using geomagnetic indices. The technique is accurate — it would have predicted each of the last 11 cycles with a typical error of less than 20 in sunspot number. It has also advantage that a prediction of the lower limit of the amplitude can be made throughout the declining phase, this limit building to a final value at the onset of the new cycle.     

Radial variation of differential rotation in the solar electron corona

Long-lived brightness structures in the solar electron corona persist over many solar rotation periods and permit an observational determination of coronal magnetic tracer rotation as a function of latitude and height in the solar atmosphere. For observations over 1964–1976 spanning solar cycle 20, we compare the latitude dependence of rotation at two heights in the corona. Comparison of rotation rates from East and West limbs and from independent computational procedures is used to estimate uncertainty. Time-averaged rotation rates based on three methods of analysis demonstrate that, on average, coronal differential rotation decreases with height from 1.125 to 1.5 R _S. The observed radial variation of differential rotation implies a scale height of approximately 0.7 R _S for coronal differential rotation.Model calculations for a simple MHD loop show that magnetic connections between high and low latitudes may produce the observed radial variations of magnetic tracer rotation. If the observed tracer rotation represents the rotation of open magnetic field lines as well as that of closed loops, the small scale height for differential rotation suggests that the rotation of solar magnetic fields at the base of the solar wind may be only weakly latitude dependent. If, instead, closed loops account completely for the radial gradients of rotation, outward extrapolation of electron coronal rotation may not describe magnetic field rotation at the solar wind source. Inward extrapolations of observed rotation rates suggest that magnetic field and plasma are coupled a few hundredths of a solar radius beneath the photosphere.     

Changes of solar magnetic asymmetry

The results of an analysis of the north–south asymmetry in solar activity and solar magnetic fields are reported. The analysis is based on solar mean magnetic field and solar polar magnetic field time series, 1975–2015 (http://wso.stanford.edu), and the Greenwich sunspot data, 1875–2015 (http://solarscience.msfc.nasa.gov/greenwch.shtml). A long-term cycle (small-scale magnetic fields, toroidal component) of ~140 years is identified in the north–south asymmetry in solar activity by analyzing the cumulative sum of the time series for the north–south asymmetry in the area of sunspots. A comparative analysis of the variations in the cumulative sums of the time series composed of the daily values of the sun’s global magnetic field and in the asymmetry of the daily sunspot data over the time interval 1975–2015 shows that the photospheric large-scale magnetic fields may also have a similar long-term cycle. The variations in the asymmetry of large-scale and small-scale solar magnetic fields (sunspot area) are in sync until 2005.5 and in antiphase since then.     

The Gnevyshev-Ohl rule for physical parameters of the solar magnetic field: The 400-year interval

We consider a number of questions pertaining to the famous Gnevyshev-Ohl rule. We discuss various formulations of the rule and show that it is not violated in its exact formulation in the last pair of 11-year cycles 22 and 23. The rule has been found to hold not only for statistical indices of solar activity but also in the context of physical parameters of the solar magnetic field: the sunspot magnetic flux and the open magnetic flux. We have established that the hypothesis by Usoskin et al. (2001) about the “loss“ of one cycle at the end of the 18th century allows the Gnevyshev-Ohl rule, which regulates the behavior of physical parameters of the solar magnetic field, to be made universal, without any exceptions, at least in the last 400 years. Thus, in fact, we can talk about the Gnevyshev-Ohl law of the long-term dynamics of the solar magnetic field, a law that holds at both normal and extreme levels of solar activity.     

Double maxima of 11-year solar cycles

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ?ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ?ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ?ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.     

A summary of major solar proton events

Solar proton events have been routinely detected by satellites since the 20th solar cycle; however, before that time only very major proton events were detected at the Earth. Even though the detection thresholds differed between the 19th and more recent cycles, more than 200 solar proton events with a flux of over 10 particles (cm² s ster)^–1 above 10 MeV have been recorded at the Earth in the last three solar cycles. At least 15% of these events had protons with energies greater than 450 MeV detected at the Earth. Other than an increase in solar proton event occurrence with increasing solar cycle, no recognizable pattern could be identified between the occurrence of solar proton events and the solar cycle. The knowledge we have gained from the data acquired over the past 40 years illustrates the difficulty in extrapolating back in time to infer the number and intensity of major solar proton events at the Earth.The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.     

Flux-dominated solar dynamo model with a thin shear layer

Flux-dominated solar dynamo models have demonstrated to reproduce the main features of the large scale solar magnetic cycle, however the use of a solar like differential rotation profile implies in the the formation of strong toroidal magnetic fields at high latitudes where they are not observed. In this work, we invoke the hypothesis of a thin-width tachocline in order to confine the high-latitude toroidal magnetic fields to a small area below the overshoot layer, thus avoiding its influence on a Babcock-Leighton type dynamo process. Our results favor a dynamo operating inside the convection zone with a tachocline that essentially works as a storage region when it coincides with the overshoot layer. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Small scale solar magnetic fields and their relation to various solar activity indices

Correlation studies between various solar activity indices and a long time series of annual sums of the maximum value of solar magnetic field intensity, observed for each group of sunspots during each passage of it over the visible solar hemisphere, have pointed out a couple of interesting points. First, the faculae have a significant contribution to the numerical representation of the small scale solar magnetic coefficients and low standard errors of estimation to the above mentioned maximum values of the solar magnetic field. These properties give to the area index an important physical meaning which is a first approximation to the small scale solar magnetic fields expressed by the above-mentioned maximum values of it. Finally, the main point which comes out is that long term studies of the solar magnetic fields, especially extrapolated studies to the past, could be supported by photospheric indices of the solar activity. This paper constitutes the expanded version of a report presented to theIAU Symposium No. 102 ‘Solar and Stellar magnetic fields: Origins and coronal effects’, held in Zürich 2–6 August, 1982.     

Interannual variability of the solar constant

It can be concluded from the calculations performed of interannual variations of the distance between the Sun and the Earth in the moments of the Earth’s position in the equinoctial and solstitial points that the mean amplitude (approximately the same for all the equinoctial and solstitial points) is determined to be equal to 5700 km (at the maximum values being approximately equal to 15000 km). The values of the solar constant have been calculated on the basis of the data of varying distances, and the values of its interannual variability (for the period from 1900 up to 2050) have determined. Based on the analysis of the series, new periodic characteristics of a long-term variation of the solar constant, related to the celestial-mechanical process, namely, to the perturbed orbital motion of the Earth, are obtained. A three-year cycle is distinguished in the interannual variability of the solar constant, which alternates with a two-year cycle every eight and eleven years. The amplitude of the interannual variability in the series of equinoctial and solstitial points is on average about 0.1 W/m² (about 0.008% of the solar constant value). This is comparable to the interannual variability of the solar constant in the eleven-year cycle of the solar activity. The series obtained can be represented by alternation of eleven-year and eight-year cycles. The eleven-year cycle is composed of three three-year cycles and one two-year cycle, and the eight-year cycle is composed of two three-year cycles and one two-year cycle.     

Diurnal variations of cosmic rays during a solar magnetic cycle

We have used data from five neutron monitor stations with primary rigidity (Rm) ranging from 16 GeV to 33 GeV to study the diurnal variations of cosmic rays over the period: 1965–1986 covering one 22-year solar magnetic cycle. The heliosphere interplanetary magnetic field (IMF) and plasma hourly measurements taken near Earth orbit, by a variety of spacecraft, are also used to compare with the results of solar diurnal variation. The local time of maximum of solar diurnal diurnal variations displays a 22-year cycle due to the solar polar magnetic field polarities. In general, the annual mean of solar diurnal amplitudes, magnitude of IMF and plasma parameters are found to show separte solar cycle variations. Moreover, during the declining period of the twenty and twenty-ne solar cycles, large solar diurnal amplitudes are observed which associated with high values of solar wind speed, plasma temperature and interplanetary magnetic field magnitude B3.