Nonlinear Coupling of Langmuir Waves with Whistler Waves in the Solar Wind

Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations, a theory is formulated to describe the nonlinear coupling of Langmuir waves and whistler waves. It is shown that a Langmuir wave can interact nonlinearly with a whistler wave to produce either right-hand or left-hand circularly polarized electromagnetic waves. Nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind. Numerical examples of whistler frequency, nonlinear growth rate and modulation frequency for solar wind parameters are calculated.     

Solar activity cycles,north/south asymmetries,and differential rotation associated with solar spin-orbit variations

The possible role of the Sun's planetary-induced spin-orbit dynamics in the generation of various solar oscillations is examined using simple approaches and heuristic models. Theoretically, the 22.5-yr dipole inversion magnetic cycle and the recently described 17-yr neutral line topology cycle can be derived from the non-linear mixing of two oscillations with periods of approximately 20 and 165 years. Oscillations with such periods are observed in two aspects of the Sun's spin-orbit dynamics. The 20-yr oscillation is the fundamental variation in the angular momentum of the solar body with respect to the solar system center-of-mass, while the 165-yr oscillation is the lowest-frequency component of the spin projection variations. It is shown that these two oscillations when mixed non-linearly yield, to a 1st-order approximation, the correct phase and frequency of the observed 17.5- and 22.5-yr magnetic cycles. By allowing an asymmetric shape to the 165-yr oscillation, the frequency modulation inherent in the Hale cycle (and sunspot cycle) is reproduced, yielding a more accurate estimate of solar activity. The asymmetric 165-yr oscillation matches the combination of the two lowest frequency components (165- and 84-yr periods) of the spin projection variations. Hemispheric sunspot asymmetry cycles, north/south differences in convective zone rotational velocities, and meridional flows are also shown to be expected byproducts of classical spin-orbit effects. Finally, the problem of low activity epochs (e.g., Maunder minimum) can be seen as a natural outcome of the interactions among the driving and driven oscillations involved in the conservation of solar system angular momentum.     

Modulation of Acoustic Waves by Solar Convection

Amplitude and phase of an acoustic oscillation in the solar convection zone vary in response to the local variation of the speed of sound and the convection velocity. Such wave modulation is considered by means of a two-dimensional periodic model, with alternating vertical channels of hot rising and cool sinking gas. According to this model, vertically propagating waves show only amplitude modulation. For low wave frequencies the amplitude is larger in the upflow channels, for high frequencies it is larger in the downflow channels. The transition occurs at a frequency for which the vertical wavelength is approximately equal to the horizontal period of the model. Waves with an inclined propagation direction show a similar amplitude modulation but, in addition, a modulation of their phase. The present results are compared with recent observational studies. There is evidence that wave modulation indeed occurs on the Sun, on the granular as well as on the mesogranular scale, in addition to the episodic amplitude enhancement that has been interpreted in terms of local acoustic events.     

Periodicities in solar activity

The techniques of power spectral analysis are used to determine significant periodicities in the annual mean relative sunspot numbers. The main conclusion is that a period of 10.45 yr is very basic and can be associated with an excitation of new solar cycles. When combined with a period of 11.8 yr, associated here with the free-running length of a solar cycle, the mean cycle length of 11.06 yr and a phase variation of 190 yr are explained. Similarly the amplitude variations with periods 88 and 59 yr (previously described as the 80-yr cycle) are due to an amplitude modulation of the solar cycle by a period of 11.9±0.3 yr. The results dispute several associations of planetary position and solar activity.Radiophysics Publication RPP 1647, January, 1973.     

Modulation of Atmospheric 14C Concentration by the Solar Wind and Irradiance Components of the Hale and SCHWABE Solar Cycles

¹⁴C abundance on the Earth can be modulated by both the solar wind and irradiance components of the solar cycle. The magnetic field component of the solar wind modulates ¹⁴C production whereas the irradiance component can result in a change in the exchange rate between the various reservoirs of the carbon biogeochemical cycle. The effects would be nearly synchronous and difficult to separate. The 0.1% amplitude of irradiance variation during the two most recent solar cycles is well known. A 22-yr cycle exists also in the measured global temperature record.We have divided the University of Washington high-precision data on¹⁴C in tree rings into three 91-yr intervals: AD 1540–1630, 1630–1720 and 1715–1805, before, during and after the Maunder Minimum. Unfortunately the AD 1540–1630 interval includes part of the Spörer Minimum as well as the intermediate interval of high solar activity. These data were analyzed by the DFT, MEM and MTM methods of spectral time series analysis. The ca. 22-yr cycle is prominent during the Maunder Minimum, whereas the 11-yr cycle is most prominent after the Maunder Minimum but totally suppressed during the Maunder Minimum. The lesser amplitude of the 11-yr cycle before the Maunder Minimum is most probably due to overlap with the Spörer Minimum.Vasiliev and Kocharov VK83 have previously suggested that the 22-yr cycle persists through the Maunder Minimum whereas the 11-yr cycle is suppressed. Our calculations show that irradiance forcing of the carbon cycle during the 11-yr cycle is negligible, so the observed 11-yr cycle in¹⁴ C must be the result of production rate changes. The presence of the 22-yr cycle and suppression of the 11-yr cycle during the Maunder Minimum is in accord with a model by Jokipii Jok91.     

Nonlinear dispersive waves on the surface of a self-gravitating fluid layer

The evolution of two dimensional wave packets on the surface of a self-gravitating fluid layer is investigated and shown to be governed by a nonlinear Schrödinger equation. The wave train of finite amplitude is modulationally unstable. Obtained also are the dynamical equations for the second harmonic resonance. The analysis reveals that the general motion consists of both amplitude and phase modulated waves of which the pure phase and amplitude modulated waves, solitary waves, and phase jump are just the special cases.     

Reconstruction of Wolf Sunspot Numbers on the Basis of Spectral Characteristics and Estimates of Associated Radio Flux and Solar Wind Parameters for the Last Millennium

A reconstruction of sunspot numbers for the last 1000 years was obtained using a sum of sine waves derived from spectral analysis of the time series of sunspot number R _z for the period 1700–1999. The time series was decomposed in frequency levels using the wavelet transform, and an iterative regression model (ARIST) was used to identify the amplitude and phase of the main periodicities. The 1000-year reconstructed sunspot number reproduces well the great maximums and minimums in solar activity, identified in cosmonuclides variation records, and, specifically, the epochs of the Oort, Wolf, Spörer, Maunder, and Dalton Minimums as well the Medieval and Modern Maximums. The average sunspot number activity in each anomalous period was used in linear equations to obtain estimates of the solar radio flux F _10.7, solar wind velocity, and the southward component of the interplanetary magnetic field.     

Long-term variations in north-south asymmetry of solar activity

We present a new set of data on relative sunspot number (total, northern hemisphere, and southern hemisphere), taken for the 37-yr period 1947 to 1983; this constitutes a particularly coherent and consistent set of data, taken by the same observer (Hisako Koyama) using the same observing instrument. These data are combined with earlier data (White and Trotter, 1977) on the variation of sunspot areas for both solar hemispheres from 1874 to 1971. The combined data, covering 110 years and 10 solar cycles, are examined for periodicity in solar activity north-south asymmetry. We show that, in general, northern hemisphere activity, displayed as either An/(An + As) or Rn/(Rn + Rs), peaks about two years after sunspot minimum. This peak is greater during even cycles, pointing to a 22-yr periodicity in north-south asymmetry in solar activity, suggesting that the asymmetry is related to the 22-yr solar magnetic cycle. We demonstrate that the largest and most protracted period of northern-hemisphere activity excess in the last 110 years has occurred from 1959 to 1970; we show that there is a strong correlation between northern activity excess and a cosmic-ray density gradient perpendicular to the ecliptic plane, pointing southward, which is evident in cosmic-ray diurnal variation data from the Embudo underground cosmic-ray telescope.     

Solar cycle according to mean magnetic field data

To investigate the shape of the solar cycle, we have performed a wavelet analysis of the large–scale magnetic field data for 1960–2000 for several latitudinal belts and have isolated the following quasi-periodic components: ∼22, 7 and 2 yr. The main 22-yr oscillation dominates all latitudinal belts except the latitudes of ±30° from the equator. The butterfly diagram for the nominal 22-yr oscillation shows a standing dipole wave in the low-latitude domain  (∣θ∣≤ 30°)  and another wave in the sub-polar domain  (∣θ∣≥ 35°)  , which migrates slowly polewards. The phase shift between these waves is about π. The nominal 7-yr oscillation yields a butterfly diagram with two domains. In the low-latitude domain  (∣θ∣≤ 35°)  , the dipole wave propagates equatorwards and in the sub-polar region, polewards. The nominal 2-yr oscillation is much more chaotic than the other two modes; however the waves propagate polewards whenever they can be isolated.
We conclude that the shape of the solar cycle inferred from the large-scale magnetic field data differs significantly from that inferred from sunspot data. Obviously, the dynamo models for a solar cycle must be generalized to include large-scale magnetic field data. We believe that sunspot data give adequate information concerning the magnetic field configuration deep inside the convection zone (say, in overshoot later), while the large-scale magnetic field is strongly affected by meridional circulation in its upper layer. This interpretation suggests that the poloidal magnetic field is affected by the polewards meridional circulation, whose velocity is comparable with that of the dynamo wave in the overshoot layer. The 7- and 2-yr oscillations could be explained as a contribution of two sub-critical dynamo modes with the corresponding frequencies.     

Quasi-periodic climate teleconnections between northern and southern Europe during the 17th–20th centuries

The North Atlantic Oscillation (NAO) is the leading mode of atmospheric variability in the North Atlantic region, influencing storm tracks and creating a dipole pattern of precipitation from north to south across Western Europe. This distinct spatial distribution of precipitation provides a framework that can be potentially used to identify and reconstruct patterns of past NAO-forced climate variability. In this study we use tree-ring width series from Western Europe, in conjunction with principal components analysis and advanced spectral methods, to prospect for quasi-periodic climate signals that are forced by the NAO. We identify a robust 25-yr anti-phased synchronization in climate variability between Scandinavia and the Mediterranean during the 17th–20th centuries. The amplitude of the 25-yr beat displays a long-term modulation in northern and southern Europe, with minimum amplitude during the late Maunder Minimum. This amplitude minimum coincides with a maximum in Δ¹⁴C, suggesting a potential solar or oceanic influence on the intensity of the 25-yr band of quasi-periodic variability.     

Hydromagnetic field line resonances and modulation of particle precipitation

Hydromagnetic wave and modulated particle precipitation data are reported from conjugate areas near the particledrift shell L ～ 4. A modulation of electrons precipitating from the magnetosphere is observed in the conjugate regions when the accompanying hydromagnetic wave period is ~ 90 s and the wave polarization is linear. When the wave period changes abruptly to ~ 30 s and the polarizations at the observing stations are no longer linear, the modulation of the precipitating electrons is no longer observed. The change in hydromagnetic wave characteristics does not appear to be related to interplanetary plasma and magnetic field conditions. Rather, it is proposed to arise from a change in the wave generation mechanism from an internal magnetospheric source near the inner edge of the plasmapause (lower frequency) to an externally driven source outside the magnetosphere (higher frequency). This observation of a change in the wave characteristics (frequency and polarization) associated with modulated electron precipitation appears to be related to two previous examples wherein modulated electron precipitation was reported to be closely associated with the existence of a wave resonance region near the observing site.     

160 m Pulsations in the magnetosphere of the Earth possibly caused by oscillations of the Sun

The measurements of the amplitudes envelope of Pc 3–4 geomagnetic micropulsations obtained at the Borok Geophysical Observatory were analysed by the cosinor method to search for magnetospheric pulsations with a period of about 160 m. 216 days of observations in 1974–1978 were used. It was found that Pc 3–4 amplitudes are modulated by the period 160.010 m with a stable phase. The maximum of the Pc 3–4 amplitudes follows approximately 20 m after the maximum of the solar expansion velocity (for the center of the disk) in the optical observations of Severny et al. This modulation of the Pc 3–4 amplitudes could be caused by the presence of an oscillating component in solar UV radiation over the wavelength range 100–900 Å. The amplitude of the UV flux variation may be as large as 2–4%.     

Modulation of the Solar Magnetic Cycle

The modulation model of the solar magnetic cycle for the time interval from 1650 to 1996 A.D. describes an harmonic oscillator with a basic (22.13 ± 0.05)-yr period, which is subjected to amplitude and phase variations that can be represented by a sum of trigonometric series. The simulated sunspot data explain 97.9% of cycle peak height variance and the residual standard deviation is 8.6 mean annual sunspots. A peak height of 139 for cycle 23 occurring in 2001 is predicted, whereas cycle 24 would have a maximum around 132 in 2014. Simulation of the sunspot numbers from 1000 until 2400 A.D. shows that the model recreates recurring minima (Maunder and Spörer Minimum). The prediction also expects a high level of amplitude modulation in the interval 1950–2010 with a rapid decrease afterwards. A greatly reduced cycle activity is reproduced by the simulation from about 2065 to 2100 A.D. No direct explanation of the long-term periodicities of the model can be advanced. The high-frequency contribution of the phase modulation, which accounts for the skewness of the solar cycle, shows coincidences with the orbital periods of Jupiter and Saturn, but no physical basis for the matching periodicities can be conceived.     

Frequency modulation and stochastic variability of the elatina varve record: A proxy for solar cyclicity?

A sequence of 1337 laminae of cyclically varying thickness, interpreted as periglacial varves, obtained from drill cores of the late Precambrian Elatina Formation may record by proxy an ancient solar activity cycle similar to that of the present epoch Sun. This inferred ancient activity cycle, represented by a sequence of 110 varve-cycles, has a variable period which approximates a normal distribution (chi square = 3.5), with mean and median values of 12 varve years, standard deviation 1.6 varve years, and maximum variability of ± 4 varve years. The time-sequence of varve-cycle periods consists of both deterministic and stochastic elements. The intrinsic period of the varve-cycle is modulated principally by a longer period of 160 varve years, during which the varve-cycle period displays superimposed stochastic variation. The power spectral density of the varve thickness sequence is endowed with a strong multiplet of spectral lines centered on the median period, a second weaker multiplet at 22–25 varve years, and several very long periods. The line spacing within the multiplets favors a separation of period mainly of about 160 varve years, while the superimposed random variability of the varve-cycle period is expressed in the amplitude of the sideband envelope. Running autocorrelation of the varve sequence supports the interpretation of frequency modulation (deviation ratio 1.5) of the late Precambrian solar activity cycle principally by a period of 160 varve years.     

The sun's rotation and perturbations of geopotential height and temperature fields in the stratosphere

The morphology of a solar activity effect apparently connected with the Sun's rotation and showing up in 25-day and 13.6-day oscillations of stratospheric geopotential and temperature fields is analysed in this study. The used data cover the height range between roughly 20 and 30 km and a timespan from July 1965 to October 1971. Most prominent responses are found for zonal harmonic wave number 1 at the oscillation period of 25 days (solar rotation period modulated by seasonal changes) and for the zonally averaged meteorological quantities at the oscillation period of 13.6 days. Additional statistically significant effects show up in the zonal harmonics with wave number 1 and 3 at half the solar rotation period and in the zonal means with periodicities near 25–27 days. The results point towards a modulation of the quasistationary stratospheric planetary wave with a positive geopotential anomaly around roughly 180° longitude by solar activity changes. The direct physical mechanisms of this Sun-climate relationship are not yet clear, but it can be concluded that atmospheric dynamics is an important factor for its morphology and that downward propagation of such effects seems possible and should be investigated in future studies.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Radiocarbon content variations and Maunder Minimum of solar activity

We summarize our experimental data on radiocarbon variations in tree rings covering the last several hundred years. Special attention was devoted to the Maunder Minimum of solar activity which is displayed in ¹⁴C. It is shown that the modulation of galactic cosmic rays at Wolf numbersW 0 does really exist and that the 22-yr periodicity at that period is more pronounced than the 11-yr periodicity. The properties of future theoretical models of solar activity are briefly discussed.     

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.     

Variations of solar coronal hole area and terrestrial lower tropospheric air temperature from 1979 to mid-1998: astronomical forcings of change in earth''s climate?

The temperature anomaly of the terrestrial lower troposphere, inferred from the Microwave Sounding Unit (MSU) radiometers, is found to be inversely correlated with the area of the Sun covered by coronal holes. The correlation between the monthly time series of global tropospheric temperature anomaly and total coronal hole area from January 1979 to April 1998 has a Pearson coefficient of −0.46, which is different from zero at a 95% confidence level. Physical reasonings for the explained and unexplained parts of the correlation are discussed. The coronal hole area is a physical proxy for both the global-scale, 22-yr geometrical and shorter-term, dynamical components of the cosmic ray modulation, as well as the corpuscular emission of the Sun. Other solar parameters that may indicate a solar radiative effect on climate are also evaluated. It is concluded that variable fluxes either of solar charged particles or cosmic rays modulated by the solar wind, or both, may influence the terrestrial tropospheric temperature on timescale of months to years.     

Linear MHD Wave Propagation in Time-Dependent Flux Tube

MHD waves and oscillations in sharply structured magnetic plasmas have been studied for static and steady systems in the thin tube approximation over many years. This work will generalize these studies by introducing a slowly varying background density in time, in order to determine the changes to the wave parameters introduced by this temporally varying equilibrium, i.e. to investigate the amplitude, frequency, and wavenumber for the kink and higher order propagating fast magnetohydrodynamic wave in the leading order approximation to the WKB approach in a zero-β plasma representing the upper solar atmosphere. To progress, the thin tube and over-dense loop approximations are used, restricting the results found here to the duration of a number of multiples of the characteristic density change timescale. Using such approximations it is shown that the amplitude of the kink wave is enhanced in a manner proportional to the square of the Alfvén speed, $V_{\mathrm{A}}^{2}$ . The frequency of the wave solution tends to the driving frequency of the system as time progresses; however, the wavenumber approaches zero after a large multiple of the characteristic density change timescale, indicating an ever increasing wavelength. For the higher order fluting modes the changes in amplitude are dependent upon the wave mode; for the m=2 mode the wave is amplified to a constant level; however, for all m≥3 the fast MHD wave is damped within a relatively small multiple of the characteristic density change timescale. Understanding MHD wave behavior in time-dependent plasmas is an important step towards a more complete model of the solar atmosphere and has a key role to play in solar magneto-seismological applications.     

Rieger quasi-periodicity in solar indices

Using wavelet analysis and Fourier analysis, the temporal behavior of ??156-day quasi-periodicity (Rieger quasi-periodicity, RQ) is investigated for series of daily solar indices: Wolf numbers W for 161 years (from 1849), the flux F_10.7 of the Sun??s radio emission at a frequency of 2800 MHz for 63 years (from 1947), the number of X-ray flares N _X for 29 years (from 1981), and the number of optical flares N _?? for 11 years in cycle 21. The N _?? series are studied for four quadrants of the solar disk. It is found for the W series that there is no stable dependence of the amplitude RQ on the cycle phase and the W value. It is associated with the fact that, corresponding to a period of around eight years, in the power spectrum changes in the amplitude of the Rieger quasiperiodicity of the index W are dominated by the peak. Moreover, the peaks corresponding to the 11-year cyclicity are also significant. The comparative study of the temporal behavior of the Rieger quasi-periodicity amplitude of the indices W, F_10.7, and N _X has shown that the quasi-periodicity covers the processes, occurring in active regions on the Sun at different altitudes, almost simultaneously. It is found that for N _??, the lag of variations of the Rieger quasi-periodicity amplitude for series of the Sun??s western hemisphere, relative to those for series of the eastern hemisphere, is on average less than for the flare series. Thus, if the flare occurrence is modulated by the Rieger quasi-periodicity process as a wave propagating over the Sun??s disc, then the wave is not a retrograde one. Different interpretations of the nature of the Rieger quasi-periodicity are discussed including the hypothesis of Rossby waves.