Planetary tides and sunspot cycles

There is an empirical function of the heights of tides on the Sun produced by Venus, Earth, and Jupiter whose period is nearly equal to that of the 11-yr sunspot cycle (Wood, 1972). This period match has been used in suggestions that planetary tides cause sunspots and, indirectly, terrestrial climate changes and earthquakes. We derive the period of the tidal function in terms of the planetary orbital periods and show that it is artificially lengthened by aliasing. Furthermore, there exists a class of functions whose measure in frequency space is so great that, in the absence of a physical justification for preferring one member, no statistically significant period match can possibly be made with current sunspot data.     

Polar faculae and sunspot cycles

The monthly number of polar faculae of the Sun were determined from white-light images at spectral band (eff) = (4100 ± 200) Å obtained at the Kislovodsk Solar Station during 1960–1994. Corrected monthly numbers were obtained with the help of the visibility function. The level of polar activity larger than 1 above the monthly running mean was calculated, and the relation between the polar faculae and sunspot cycle was studied. We confirmed earlier results (Makarov and Makarova, 1987) that the monthly number of polar faculae, NPF _m (t) correlates with the monthly sunspot area A _m (Sp)(t + T) with a time shift T 6 yr. The new polar faculae cycle began in the middle of 1991. Peculiarities of the first part of sunspot cycle 23 are discussed.Guest scientist with the University of Arizona and Zetetic Institute. Tucson, Arizona 85719, U.S.A.     

Rhythm of physical sunspot cycles

The time series of the relative sunspot number is interpreted as a sequence of physical cycles of sunspot activity overlapping in the minimum. The cycle periodicity, i.e., the time interval between neighboring cycles, can be considered as a quantitative characteristic of the sequence. Estimates of this interval have been obtained for 11 and 22-year cycles. In the growth phase and in the century cycle maximum, the 22-year cycles follow one another with an interval of 21 ± 0.4 years, and in the decline phase, 23 ± 0.3 years. This division of intervals into two groups depending on the century cycle phase should be taken into consideration when developing a theory of solar activity cycles.     

On the center-to-limb variation of sunspot brightness

A preliminary analysis of recent measurements of the brightness ratio spot-photosphere of various authors leads to the result, that the limb-darkening of the umbra is considerably less than that of the photosphere. The small value of the center-to-limb variation implies a very small temperature gradient, which is, for optical depths >0.2, about one order of magnitude smaller than previously thought (Figure 3). This result would seem to rule out radiative equilibrium in the deeper layers (\S>0.2) of sunspot umbrae.Mitteilung aus dem Fraunhofer Institut Nr. 83.     

Periodic variation and phase analysis of grouped solar flare with sunspot activity

Studies on the periodic variation and the phase relationship between different solar activity indicators are useful for understanding the long-term evolution of solar activity cycles.Here we report the statistical analysis of grouped solar flare(GSF) and sunspot number(SN) during the time interval from January 1965 to March 2009.We find that,(1) the significant periodicities of both GSF and SN are related to the differential rotation periodicity,the quasi-biennial oscillation(QBO),and the eleven-year Schwabe cycle(ESC),but the specific values are not absolutely identical;(2) the ESC signal of GSF lags behind that of SN with an average of 7.8 months during the considered time interval,which implies that the systematic phase delays between GSF and SN originate from the inter-solar-cycle signal.Our results may provide evidence about the storage of magnetic energy in the corona.     

Solar cycle variation of sunspot intensity

Broad band pinhole photometer intensity observations of 15 large sunspots covering the spectral region 0.387–2.35 m are presented. The data are based on measurements on approximately 500 days during the period June, 1967 to December, 1979.We have found real and significant intensity differences between large sunspots. These differences may be explained by a systematic variation in the umbral temperature throughout the solar cycle. A connection between umbra intensity and heliographic latitude is discussed.No center-limb variation in the umbra/photosphere intensity ratio is detected. We have searched for possible connections between umbra intensity and a number of other sunspot parameters, like the spot size, without detecting any significant correlation. We conclude that the umbra/photosphere intensity ratio seems to be a unique function of epoch for large sunspots.     

On the maximum rate of change in sunspot number growth and the size of the sunspot cycle

Statistically significant correlations exist between the size (maximum amplitude) of the sunspot cycle and, especially, the maximum value of the rate of rise during the ascending portion of the sunspot cycle, where the rate of rise is computed either as the difference in the month-to-month smoothed sunspot number values or as the average rate of growth in smoothed sunspot number from sunspot minimum. Based on the observed values of these quantities (equal to 10.6 and 4.63, respectively) as of early 1989, one infers that cycle 22's maximum amplitude will be about 175 ± 30 or 185 ± 10, respectively, where the error bars represent approximately twice the average error found during cycles 10–21 from the two fits.     

Meridional motions of sunspot groups during eleven activity cycles

Greenwich data (1874–1976) are used for a time-dependent analysis of meridional motions of sunspot groups. We obtain the latitude-dependence of meridional motions of sunspot groups with respect to a mean latitude determined for half-year intervals. The daily meridional motions of groups are also given separately for growing and decaying sunspot groups. The development is determined from changes of sunspot areas. Our results are compared with the reductions performed by Howard (1991b) using the Mt. Wilson sunspot data from 1917 until 1985: Although we have smaller errors, we do not find any significant drift. We also do not find different trends in the meridional motions of growing as compared to decreasing sunspots.     

Limb-darkening and solar cycle variation of sunspot intensities

New observations of the umbral limb-darkening are presented. We find a real and significant decrease in the umbra/photosphere intensity ratio towards the limb. This result contrasts the findings of previous authors and we believe this to be the first time such a decrease is reported. Our conclusion is based on broad band pinhole photometer intensity observations of 22 large sunspots covering the spectral region 0.387–2.35 m. The data are selected from measurements on approximately 600 days during the last 15.5 yr. The application of the limb-darkening data to the study of the temperature stratification in the umbra is briefly discussed. The observations confirm the suggestion that the umbra/photosphere intensity ratio seems to be a linear function of the phase in the solar cycle.     

The variation of the mean size of the photospheric granules close to and away from a sunspot

We study the mean size of granules as a function of distance from the boundaries of the sunspot penumbra. We use for the determination of the mean size two different methods, a visual and a photometric. In all cases the mean diameter of the granules away from the spot was greater than the mean diameter of the granules in the neighbourhood of the penumbra. Our study is based on an excellent sequence of photos, taken at the Pic-du-Midi Observatory on May 11, 1979.     

Search for relationship between duration of the extended solar cycles and amplitude of sunspot cycle

Duration of the extended solar cycles is taken into the consideration. The beginning of cycles is counted from the moment of polarity reversal of large-scale magnetic field in high latitudes, occurring in the sunspot cycle n till the minimum of the cycle n + 2. The connection between cycle duration and its amplitude is established. Duration of the “latent” period of evolution of extended cycle between reversals and a minimum of the current sunspot cycle is entered. It is shown, that the latent period of cycles evolution is connected with the next sunspot cycle amplitude and can be used for the prognosis of a level and time of a sunspot maximum. The 24th activity cycle prognosis is made. The found dependences correspond to transport dynamo model of generation of solar cyclicity, it is possible with various speed of meridional circulation. Long-term behavior of extended cycle's lengths and connection with change of a climate of the Earth is considered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral analysis of sunspot flares

We have qualitatively analyzed, in the H and K lines spectral region, 31 flares covering part of umbrae or penumbrae of sunspots. A strong narrowing of the emission lines has been observed over the umbrae, and the lines are, in general, much weaker than in common flares suggesting that the optical thickness is quite low in these parts. We have calculated the Stark broadening of the H line from the general theory, and it has been applied to obtain the electron density in 9 flare spectra. In all cases it has been found that n _e > 10¹³ cm^–3. Goldberg's method has been applied to find the kinetic temperature from the H and K lines of Ca ii, and from the ratio between the central intensities of the lines we have calculated the optical thickness in the K line. Much evidence supports the assumption that the flare emission is highly diluted in the cases considered, and we propose a two-component model for the calcium emission lines.

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Shapes and centre-to-limb variation of the H and K lines in sunspot umbrae

The shapes of the Ca ii H and K lines in sunspot umbral spectra vary from single asymmetric peaks near the centre of the disk to almost symmetric double peaks at the limb. In addition, there are other differences in the behaviour of both H and K lines in sunspots compared to the quiet Sun. The whole complex of the phenomena observed can not be explained by large scale chromosphere motions. Instead, a satisfactory model reproducing in detail peculiarities of the umbral emission reversals contains a cloud of emitting and absorbing gas located above the chromosphere, which flows into the sunspot. The radiation field parameters in such a cloud are consistent with the concept of weak quiescent prominences above the umbra.     

The latitude of filament bands at the sunspot minimum and the activity level in the two following 11-year solar cycles

The zonal structure of the distribution of filaments is considered. The mean latitudes of two filament bands are calculated in each solar hemisphere at the minima of the sunspot cycle in the period 1924–1986: middle latitude _{2, m} and low latitude _{1, m} . It is shown that the mean latitude of the filament band _{2, m} at the minimum -m of the cycle correlates, with = 0.94, with the maximum - M sunspot area S(M) and maximum Wolf number W(M) in the succeeding solar cycle M. It is shown that the mean latitude of the low-latitude filament band _{1, m} is linearly dependent on the mean latitude filament band _{2, m + 1} at the succeeding minimum. We found a correlation of the latitude of the low-latitude filament band _{1, m} with the maximum sunspot area in the M + 1 cycle. This enables us to predict the power of two succeeding 11-year solar cycles on the basis of the latitude of filament bands at the minimum of activity, 1985–1986: W(22) - 205 ± 10, W(23) - 210 ± 10. The importance of the relationships found for theory and applied aspects is emphasized. An attempt is made to interpret the relationships physically.     

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude of a cycle and the length of the previous cycle. This allows for an estimate of the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7–12 years of the cycle. The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

A digital analysis of sunspot areas

Full-disk white light images of the Sun have been digitized, calibrated, and examined to determine objective sunspot areas for the early part of the operation of the Solar Maximum Mission satellite. We find that published sunspot areas determined from synoptic programs compare favorably with our digital areas. The mean residual between published areas and our digital areas is approximately 80 millionths of a hemisphere. The largest residual found is 642 millionths on April 1980 for Hale No. 16752.     

The nature of the sunspot phenomenon

Heat transport in the Sun is describable by a Fokker-Planck, or diffusion, transfer equation. A study of the general character of the solutions of the transfer equation shows that the inhibition of convective transport beneath the photosphere produces a photospheric dark ring surrounded by a bright ring, or at best, a dark area surrounded by a bright ring. The mean temperature beneath the sunspot is unavoidably above normal, so that the enhanced gas pressure would disperse, rather than concentrate, the magnetic field. Hence we conclude that the inhibition of convection cannot be the cause of a sunspot.We suggest, instead, that a sunspot is a region of enhanced, rather than inhibited, energy transport and emissivity. The magnetic field of the sunspot causes a dynamical overstability in the outer thousand km of the convective zone, generating copious fluxes of hydromagnetic waves, which propagate rapidly out of the region along the magnetic field. We suggest that this heat engine is so efficient as to convert at least three fourths of the heat flux into waves. Solutions of the heat transport equation in the presence of a heat sink automatically resemble the observed sunspot, including a dark interior, a sharp transition at the edge of the umbra, and an extended grey area around the outside, the penumbra. The mean temperature is reduced, causing the observed concentration of the magnetic field.The enhanced radiation is in the form of hydromagnetic waves, which do not appear in ordinary photographs, but which light up the sky over the sunspot in a manner conspicuous in any UV or X-ray picture. In this respect, then, a sunspot is effectively a hole in the Sun, extending down to temperatures of 2 × 10⁴ K or more.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.