An experiment to observe the vertical gradient in line-of-sight velocity oscillations

Using intermediate degree p-mode frequency datasets for solar cycle 22, we find that the frequency shifts and magnetic indices show a `hysteresis' phenomenon. It is observed that the magnetic indices follow different paths for the ascending and descending phases of the solar cycle, as the descending path always seems to follow a higher track than the ascending one. However, for the radiative indices, the paths cross each other indicating phase reversal.     

The phase variations of the solar cycle

It has previously been shown that the statistics of the phase fluctuation of the sunspot cycle are compatible with the assumption that the solar magnetic field is generated deep in the Sun by a frequency stable oscillator and that the observed substantial phase fluctuation in the sunspot cycle is due to variation in the time required for the magnetic field to move to the solar surface (Dicke, 1978, 1979). It was shown that the observed phase shifts are strongly correlated with the amplitude of the solar cycle. It is shown here that of two empirical models for the transport of magnetic flux to the surface, the best fit to the data is obtained with a model for which the magnetic flux is carried to the surface by convection with the convection velocity proportional to a function of the solar cycle amplitude. The best fit of this model to the data is obtained for a 12-yr transit time. The period obtained for the solar cycle is T = 22.219 ± 0.032 yr. It is shown that the great solar anomaly of 1760–1800 is most likely real and not due to poor data.     

Periodicities of solar irradiance and solar activity indices,II

Using a dynamic power spectral analysis technique, the time-varying nature of solar periodicities is investigated for background X-ray flux, 10.7 cm flux, several indices to UV chromospheric flux, total solar irradiance, projected sunspot areas, and a sunspot blocking function. Many prior studies by a host of authors have differed over a wide range on solar periodicities. This investigation was designed to help resolve the differences by examining how periodicities change over time, and how the power spectra of solar data depend on the layer of the solar atmosphere. Using contour diagrams that show the percent of total power over time for periods ranging from 8 to 400 days, the transitory nature of solar periodicities is demonstrated, including periods at 12–14, 26–28, 51–52, and approximately 154 days. Results indicate that indices related to strong magnetic fields show the greatest variation in the number of periodicities, seldom persist for more than three solar rotations, and are highly variable in their frequency and amplitude. Periodicities found in the chromospheric indices are fewer, persist for up to 8–12 solar rotations, and are more stable in their frequency and amplitude. An additional result, found in all indices to varying degrees and related to the combined effects of solar rotation and active region evolution, is the fashion in which periodicities vary from about 20 to 36 days. I conclude that the solar data examined here are both quasi-periodic and quasistationary, with chromospheric indices showing the longest intervals of stationarity, and data representing strong magnetic fields showing the least stationarity. These results may have important implications to the results of linear statistical analysis techniques that assume stationarity, and in the interpretation of time series studies of solar variability.     

Helioseismology and the solar interior dynamics

The inversion of helioseismic modes leads to the sound velocity inside the Sun with a precision of about 0.1 per cent. Comparisoons of solar models with the “seismic sun” represent powerful tools to test the physics: depth of the convection zone, equation of state, opacities, element diffusion processes and mixing inside the radiative zone. We now have evidence that microscopic diffusion (element segregation) does occur below the convection zone, leading to a mild helium depletion in the solar outer layers. Meanwhile this process must be slowed down by some macroscopic effect, presumably rotation-induced mixing. The same mixing is also responsible for the observed lithium depletion. On the other hand, the observations of beryllium and helium 3 impose specific constraints on the depth of this mildly mixed zone. Helioseismology also gives information on the internal solar rotation: while differential rotation exists in the convection zone, solid rotation prevails in the radiative zone, and the transition layer (the so-called “tachocline”) is very small. These effects are discussed, together with the astrophysical constraints on the solar neutrino fluxes.     

The green corona,the solar wind and geoactivity

The long-term distribution of the Green Corona Low Brightness Regions (GCLBR) on the solar surface is investigated. The frequency curves of the GCLBR follow the solar cycle, but are displaced considerably relative to the curve of the sunspot number cycle. The observed displacement increases with the size of the GCLBR and reaches up to 4–5 years for the largest regions. It is, however, interesting that the displacement in the equatorial zone is opposite to that in the higher-latitude zones.An older idea on the physical affinity between GCLBR and coronal holes led us to study the frequency of GCLBR and the properties of High-Speed Plasma Streams (HSPS) in the solar wind. Maximum velocity and duration of the coronal-hole-related HSPS seem to be well correlated with the number and size of GCLBR located in the N 60-N 20 and S 20-S 60 latitudinal zones. This is particularly evident at the end of the solar cycle.Geophysical Kp and aa indices are used to demonstrate a possible genetic dependence of geoactivity on the size, position on the Sun's surface and frequency of the GCLBR. In this sense, the most pronounced period is 1973–1976.

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Empirical estimate of p-mode frequency shift for solar cycle 23

We have obtained empirical relations between the p-mode frequency shift and the change in solar activity indices. The empirical relations are determined on the basis of frequencies obtained from BBSO and GONG stations during solar cycle 22. These relations are applied to estimate the change in mean frequency for the cycle 21 and 23. A remarkable agreement between the calculated and observed frequency shifts for the ascending phase of cycle 23, indicates that the derived relations are independent of epoch and do not change significantly from cycle to cycle. We propose that these relations could be used to estimate the shift in p-mode frequencies for past, present and future solar activity cycles, if the solar activity index is known. The maximum frequency shift for cycle 23 is estimated to be 265±90 nHz, corresponding to a predicted maximum smoothed sunspot number 118.1±35.     

Coronal structures as tracers of sub-surface processes

The solar corona – one of the most spectacular celestial shows and yet one of the most challenging puzzles – exhibits a spectrum of structures related to both the quiet Sun and active regions. In spite of dramatic differences in appearance and physical processes, all these structures share a common origin: they are all related to the solar magnetic field. The origin of the field is beneath the turbulent convection zone, where the magnetic field is not a master but a slave, and one can wonder how much the coronal magnetic field “remembers” its dynamo origin. Surprisingly, it does. We will describe several observational phenolmena that indicate a close relationship between coronal and sub-photospheric processes.     

Periodic variation of the north-south asymmetry of solar activity phenomena

We report here a study of various solar activity phenomena occurring in both north and south hemispheres of the Sun during solar cycles 8–23. In the study we have used sunspot data for the period 1832–1976, flare index data for the period 1936-1993, Hα flare data 1993–1998 and solar active prominences data for the period 1957–1998. Earlier Verma reported long-term cyclic period in N-S asymmetry and also that the N-S asymmetry of solar activity phenomena during solar cycles 21, 22, 23 and 24 will be south dominated and the N-S asymmetry will shift to north hemisphere in solar cycle 25. The present study shows that the N-S asymmetry during solar cycles 22 and 23 are southern dominated as suggested by Verma.     

The secular modulation of solar rotation from 1943 to 1992 and its time-delayed correlation with the 55-year grand cycle of the 11-year solar cycle

We devised a new method, which we call the running-segment method, to achieve high-resolution time series of indices of solar rotation for determining the latitude dependence of the differential rotation by a least-squares fitting of the daily translation of positions of sunspot groups during a fixed time segment of 11 years. The segment is moved by an amount of one year to determine the differential profile of the next point of time. Time of the determined rotation data is defined by an arithmetic mean of the beginning and ending years of the segment. The rotation underwent an acceleration from 1948 to 1974 and a deceleration from 1974 to 1987. We found that the time profile of the indexM, the angular momentum surface layer density defined by integration of the angular momentum volume density over the whole surface, follows almost exactly the time profile of the 11-year running mean of the yearly mean of the sunspot relative number with a delay time of about 20 years. The acceleration (deceleration) phase corresponds to the ascending (descending) phase of amplitude of the 11-year solar cycle of cycle 16 (19) to cycle 19 (20) with a delay time of about 20 years. The cycles 15–20 correspond to the 55-year grand cycle V of the 11-year cycle. The delay time of about 20 years agrees well with the delay time predicted by a nonlinear dynamo theory of the solar cycle for driving the 55-year modulation of the 11-year solar cycle. The agreement suggests that the Lorentz force of the magnetic field of the solar cycle during grand cycle V drives the solar rotation modulation from 1948 to 1987 and that the force needed about 20 years to modify the rotation during 1943–1992.     

22-Year periodicity in the solar differential rotation

Using the data on sunspot groups compiled during 1879–1975, we determined variations in the differential rotation coefficientsA andB during the solar cycle. The variation in the equatorial rotation rateA is found to be significant only in the odd numbered cycles, with an amplitude ∼ 0.01 μ rads^-1. There exists a good anticorrelation between the variations of the differential rotation rateB derived from the odd and even numbered cycles, suggesting existence of a ‘22-year’ periodicity inB. The amplitude of the variation ofB is ∼ 0.05 μ rad s^-1.     

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.     

Wavelet Analysis of solar,solar wind and geomagnetic parameters

The sunspot number, solar wind plasma, interplanetary magnetic field, and geomagnetic activity index A _p have been analyzed using a wavelet technique to look for the presence of periods and the temporal evolution of these periods. The global wavelet spectra of these parameters, which provide information about the temporal average strength of quasi periods, exhibit the presence of a variety of prominent quasi periods around 16 years, 10.6 years, 9.6 years, 5.5 years, 1.3 years, 180 days, 154 days, 27 days, and 14 days. The wavelet spectra of sunspot number during 1873–2000, geomagnetic activity index A _p during 1932–2000, and solar wind velocity and interplanetary magnetic field during 1964–2000 indicate that their spectral power evolves with time. In general, the power of the oscillations with a period of less than one year evolves rapidly with the phase of the solar cycle with their peak values changing from one cycle to the next. The temporal evolution of wavelet power in R _z, v _sw, n, B _y, B _z, |B|, and A _p for each of the prominent quasi periods is studied in detail.     

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.     

Periodicities of solar irradiance and solar activity indices,I

Using a standard FFT time series analysis, our results show an 8–11 months periodicity in the solar total and UV irradiances, 10.7 cm radio flux, Ca-K plage index, and sunspot blocking function. The physical origin of this period is not known, but the evidence in the results exclude the possibility that the observed period is a harmonic due to the FFT transform or detrending. Periods at 150–157 and 51 days are found in those solar data which are related to strong magnetic fields. The 51-day period is the dominant period in the projected areas of developing complex sunspot groups, but it is missing from the old decaying sunspot areas. This evidence suggests that the 51-day period is related to the emergence of new magnetic fields. A strong 13.5-day period is found in the total irradiance and projected areas of developing complex groups. This confirms those results (e.g., Donnelly et al., 1983, 1984; Bai, 1987, 1989) which show that active centers are located 180 deg apart from each other.Our study also shows that the modulation of various solar data due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion. This arises from that the active regions and their magnetic fields are better organized and more long-lived during the maximum and declining portion of solar cycle than during its rising portion.     

Solar wind variation with the cycle

The cyclic evolution of the heliospheric plasma parameters is related to the time-dependent boundary conditions in the solar corona. &amp;#x201C;Minimal&amp;#x201D; coronal configurations correspond to the regular appearance of the tenuous, but hot and fast plasma streams from the large polar coronal holes. The denser, but cooler and slower solar wind is adjacent to coronal streamers. Irregular dynamic manifestations are present in the corona and the solar wind everywhere and always. They follow the solar activity cycle rather well. Because of this, the direct and indirect solar wind measurements demonstrate clear variations in space and time according to the minimal, intermediate and maximal conditions of the cycles. The average solar wind density, velocity and temperature measured at the Earth&amp;#x2019;s orbit show specific decadal variations and trends, which are of the order of the first tens per cent during the last three solar cycles. Statistical, spectral and correlation characteristics of the solar wind are reviewed with the emphasis on the cycles.     

Power-law distribution for solar energetic proton events

Analyses of the time-integrated fluxes of solar energetic particle events during the period 1965–1990 show that the differential distribution of events with flux F is given by a power law, with indices between 1.2 and 1.4 depending on energy. The power law represents a good fit over three to four orders of magnitude in fluence. Similar power-law distributions have been found for peak proton and electron fluxes, X-ray flares and radio and type III bursts. At fluences greater than 10⁹ cm^–2, the slope of the distribution steepens and beyond 10¹⁰ cm^–2 the power-law index is estimated to be 3.5. At energies greater than 10 MeV, the slope of the distribution was found to be essentially independent of solar cycle, when the active years of solar cycles 20, 21, and 22 were analysed. The results presented are the first for a complete period of 27 years, covering nearly 3 complete solar cycles. Other new aspects of the results include the invariance of the exponent with solar cycle and also with integral energy.     

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.     

Spectral peculiarities of strong solar bursts

We have investigated spectral features of strong radio burst emission for the 21st cycle of solar activity. The maximum daily radio fluxes in 8 frequency ranges are analyzed. For every year, the classification of these daily spectra is obtained by the cluster analysis method.We have shown that strong bursts are characterized by the stable shape of the mean radio emission spectra. For these bursts the total level of radio emission does not depend on the phase of the solar 11-yr cycle and varies with the quasi-period of 4 yr.The basic features of burst spectra can be explained by the gyrosynchrotron radiation of nonthermal electrons and plasma radiation at the second harmonic of plasma frequency. We supposed that in the generation region of centimetric emission, if the strength of the magnetic field B 100 G, the number of microbursts can amount to (6–7) × 10³. In the generation region of decimetric emission, the energy of Langmuir waves changes as W _l n _e ^0.4.     

Reflections on solar variability

The Sun is a variable star in many respects: there are secular varitions related to the general solar evolution, and - as discovered in recent years - there are many short period variations of which the 5 min and 160 min pulsations are the most important ones. Magnetic fields in the outer convective mantle play a dominant role in the 22-years cycle. The origin of solar magnetic variability is a key problem in astrophysics. The relation between solar variability and changes in the Earth's climate is a crucial element in climatology.Introductory talk to the 14th ESLAB Symposium: Physics of Solar Variations, 16–19 September, 1980, Scheveningen, The Netherlands.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.