Global modes constituting the solar magnetic cycle

We show that the axisymmetric odd degree SHF modes of 21.4-yr periodicity and degrees l 29 in the solar magnetic field (as inferred from sunspot data during 1874–1976), are at least approximately stationary. Among the sine and cosine components of these SHF modes we find four groups, each defining the geometry of a coherent global oscillation characterized by a distinct power hump and its own level of variation. The first two of these geometrical eigenmodes (viz., B ₁ and B ₂), define the large-scale structure of the butterfly diagrams. Remaining SHF modes define the orderliness of the field distribution even within the wings of the butterflies down to scales l 29. These include the geometrical eigenmodes B ₃ and B ₄, which are not present in simulated data sets in which the latitudes of the sunspot groups are randomly redistributed within the wings of the butterflies.Superposition of B ₁, B ₂, B ₃, and B ₄ is necessary and sufficient to reproduce important observed properties of the latitude-time distribution of the real field, not only in the sunspot zone, but also in the middle (35°–75°) and the high (75°) latitudes, with appropriate relative orders of magnitude and phases. Thus, B ₁, B ₂, B ₃, and B ₄ seem to represent really existing global oscillations in the Sun's internal magnetic field. The geometrical form of B ₁ may also be the form of the forcing oscillation.     

The two components in the distribution of sunspot groups with respect to their maximum areas

From an analysis of the distribution of sunspot groups with respect to their maximum areas we find that this distribution consists of two distinct components. One component contributes to spot groups of all possible values of A_* with a distribution density varying as ∼ exp (b₁ á _* ^1/2 ) with b₁ nearly constant from cycleto cycle and having a mean value ∼10^-4 km^-1. The other component is predominantly responsible for spot groups withA* ≲, 30 *10^-6 hemisphere but may provide a few spot groups even above 50 * l0^-6 hemisphere. This component may follow a distribution density ∼ exp (-b₂ A_*). We also determine the widths of the latitude zones over which spot groups in various intervals of A_* appear and study their variation with time. These widths and their variations indicate that the two statistical samples of spot groups may be produced by two families of flux-tube clusters as suggested earlier in a phenomenological model. Very thin flux-tube clusters in the statistical samples seem to be related to the ephemeral active regions and X-ray bright points.     

Global modes constituting the solar magnetic cycle

The spherical-harmonic-Fourier analysis of the Sun's magnetic field inferred from the Greenwich sunspot data is refined and extended to include the full length (1874–1976) of the data on the magnetic tape provided by H. Balthasar. Perspective plots and grey level diagrams of the SHF power spectra for the odd and the even degree axisymmetric modes are presented. Comparing these with spectra obtained from two simulated data sets with random redistribution within the wings in the butterfly diagrams, we conclude that there is no clear evidence for the existence of any relation between the harmonic degree and the temporal frequency of the power concentrations of the inferred field. Apart from the power ridge in the narrow frequency band at 1/21.4 y ^–1, and low ridges at odd multiples of this frequency, there are no other spectral features. This strongly suggests that the solar magnetic cycle consists of some global oscillations of the Sun forced at a frequency 1/21.4 y ^–1 and, perhaps, weak resonances at its odd harmonics. The band width of the forcing frequency seems to be much less than 1/107 y ^–1. In case the global oscillations are torsional MHD, the significance of their parity and power peak is pointed out.     

Periodicities in the solar differential rotation,surface magnetic field and planetary configurations

Using Greenwich data on sunspot groups during 1874–1976, we have studied the temporal variations in the differential rotation parametersA andB by determining their values during moving time intervals of lengths 1–5 yr successively displaced by 1 yr. FFT analysis of the temporal variations ofB (orB/A) shows periodicities 18.3 ± 3 yr, 8.5 ± 1 yr, 3.9 ± 0.5 yr, 3.1 ± 0.2 yr, and 2.6 ± 0.2 yr at levels 2. This analysis also shows five more periodicities at levels 1–2. The maximum entropy method is used to set narrower limits on the values of these periods. The reality of the existence of all these periodicities ofB (orB/A ) except the one at 2.8 yr is confirmed by analyzing the simulated time series ofB andB/A with values ofA andB randomly distributed within the limits of their respective uncertainties. Four of the prominent periods ofB agree, within their uncertainties, with the known periods in the the large-scale photospheric magnetic field. The deviations from the average differential rotation are larger near the sunspot minima. On longer time scales, the variations in the amount of sunspot activity per unit time are well correlated to the variations in the amplitudes of the torsional oscillation represented by the 22-yr periodicity inB. All the periods inB found here are in good agreement with the synodic periods of two or more consecutive planets. The possibility of planetary configurations providing perturbations needed for the Sun's MHD torsional oscillations is speculated upon and briefly discussed.     

Examining the feasibility of air shower core-location from polarization properties of associated Cherenkov light

Based on this exploratory investigation involving CORSIKA simulation code generated Cherenkov photons and a linearly polarized, hypothetical photon beam, we make a case here for exploiting polarization properties of atmospheric Cherenkov events for providing an independent method for locating air-shower cores by a TACTIC-like array of atmospheric Cherenkov telescopes. Preliminary results based on simulations indicate that for a 3 TeV γ-ray having ∼30% degree of polarization for its associated Cherenkov light at a core distance of ∼100 m, core location can be found with an error of ∼27 m. Deceased This revised version was published online in July 2006 with corrections to the Cover Date.