ALBERT

Notes: Abstract Steady photospheric flows can be represented by a spectrum of spherical harmonic modes. A technique is described in which full disc doppler velocity measurements are analysed using the spherical harmonic functions to determine the characteristics of this spectrum and the nature of these flows. Synthetic data is constructed for testing this technique. This data contains limb shift, rotation, differential rotation, meridional circulation, supergranules, giant cells and various levels of noise. The data is analysed in several steps. First, the limb shift is calculated by finding the average velocity in concentric rings about disc center. A polynomial representation of the limb shift is then removed from the data. Secondly, the rotation profile is calculated by finding an average slope in the velocity across the disc at each latitude position. This rotation profile is fit with Legendre polynomials and removed from the data. The third step is to find the meridional circulation by calculating the spherical harmonic transform for the axisymmetric poloidal modes and correcting for the effects of the limb shift analysis. The final step is to calculate the full spectrum of spherical harmonic components for the convective flows. Supergranules are separated from giant cells by spectral filtering for high (l 〉32) and low (l 〈32) wavenumbers, respectively. Some information about the spectrum is lost because only one hemisphere is seen, only the line-of-sight velocity is measured and the measurements contain noise. The lack of information about the motions on the backside of the Sun produces a broad smearing of the spectrum into nearby modes. The lack of information about the transverse velocity component produces a mixing between modes whose longitudinal wavenumbers differ by two and between the poloidal and toroidal components with the same wavenumber. In spite of this mode mixing much can be learned from this analysis. Solar rotation and differential rotation can be accurately measured and monitored for secular changes. Meridional circulations with small amplitudes can be measured and monitored and giant cells can be separated from supergranules.

Notes: Abstract A variety of temporal filters are tested on artificial data with 60 and 75 s sampling intervals to determine their accuracy in separating the nearly-steady photospheric flows from the p-mode oscillations in Doppler velocity data. Longer temporal averages are better at reducing the residual signal due to p-modes but they introduce additional errors from the rotation of the supergranule pattern across the solar disk. Unweighted filters (boxcar averages) leave residual r.m.s. errors of about 6 m s−1 from the p-modes after 60 min of averaging. Weighted filters, with nearly Gaussian shapes, leave similar residual errors after only 20 min of averaging and introduce smaller errors from the rotation of the supergranule pattern. The best filters found are weighted filters that use data separated by 150 or 120 s so that the p-modes are sampled at opposite phases. These filters achieve an optimum error level after about 20 min, with the r.m.s. errors due to the p-mode oscillations and the rotation of the supergranules both at a level of only 1.5 m s−1.

Notes: Abstract A method is described for constructing artificial data that realistically simulate photospheric velocity fields. The velocity fields include rotation, differential rotation, meridional circulation, giant cell convection, supergranulation, convective limb shift, p-mode oscillations, and observer motion. Data constructed by this method can be used for testing algorithms designed to extract and analyze these velocity fields in real Doppler velocity data.

Notes: Abstract The use of the spherical harmonic functions to analyse the nearly steady flows in the solar photosphere is extended to situations in which B 0, the latitude at disk center, is nonzero and spurious velocities are present. The procedures for extracting the rotation profile and meridional circulation are altered to account for the seasonal tilt of the Sun's rotation axis toward and away from the observer. A more robust and accurate method for separating the limb shift and meridional circulation signals is described. The analysis procedures include the ability to mask out areas containing spurious velocities (velocity-like signals that do not represent true flow velocities in the photosphere). The procedures are shown to work well in extracting the various flow components from realistic artificial data with a broad, continuous spectrum for the supergranulation. The presence of this supergranulation signal introduces errors of a few m s -1 in the measurements of the rotation profile, meridional circulation, and limb shift from a single Doppler image. While averaging the results of 24 hourly measurements has little effect in reducing these errors, an average of 27 daily measurements reduces the errors to well under 1 m s -1.

Notes: Abstract 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.

Notes: Abstract Nonlinear calculations for the three-dimensional and time dependent convective flow in a plane parallel layer of fluid are carried out with parameter values appropriate for supergranules on the Sun. A rotation vector is used which is tilted from the vertical to represent various latitudes. For the incompressible fluid used in this model the solar rotation produces turning motions sufficient to completely twist a fluid column in about one day. It is suggested that this effect will be greatly enhanced in a compressible fluid. The tilted rotation vector produces anisotropies and systematic Reynolds stresses which drive mean flows. The resulting flows produce a rotation rate which increases inward and a meridional circulation with poleward flow along the outer surface.