Following the recent evidence for the presence of an excess of power around 1 mHz in the frequency spectrum of the Doppler shift measurements for Procyon (Martic et al., 1999), we searched for individual frequencies of p-modes from three independent observing runs (5, 10 and 15 nights). All observations (December 1997, November 1998, January 1999) were made with the ELODIE spectrograph on the 1.93 m telescope at Observatoire de Haute Provence. The individual peaks in cleaned power spectra of each time series in the interval of excess power are compared with the predicted p-mode frequencies from stellar models (Chaboyer et al., 1999) for Procyon A.

Using flare index data sets for solar cycles 21 and 22 we find that flare index and some solar activity indicators show a hysteresis phenomenon. It is observed that total sunspot area, mean magnetic field and coronal index follow different paths for the ascending and descending phases of the solar cycles while saturation effect exists at the extreme phases. However, we notice that the separations between the paths are not the same during the past two cycles of 21 and 22.

The solar convection zone exhibits a differential rotation with radius and latitude that poses major theoretical challenges. Helioseismology has revealed that a smoothly varying pattern of decreasing angular velocity Ω with latitude long evident at the surface largely prints through much of the convection zone, encountering a region of strong shear called the tachocline at its base, below which the radiative interior is nearly in uniform solid body rotation. Helioseismic observations with MDI on SOHO and with GONG have also led to the detection of significant variations in Ω with 1.3 yr period in the vicinity of the tachocline. There is another shearing layer just below the solar surface, and that region exhibits propagating bands of zonal flow. Such rich dynamical behavior requires theoretical explanations, some of which are beginning to emerge from detailed 3-D simulations of turbulent convection in rotating spherical shells. We discuss some of the properties exhibited by such numerical models. Although these simulations are highly simplified representations of much of the complex physics occurring within the convection zone, they are providing a very promising path for understanding the solar differential rotation and its temporal variations.

A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between the α-effect and the inverse cascade of magnetic helicity is highlighted. The possibility of ‘catastrophic’ quenching of the α-effect is explained in terms of the constraint placed by the conservation of magnetic helicity.

The turbulent electromotive force as well as the kinetic and current helicities have been computed for a turbulence subject to magnetic buoyancy and global rotation. The dynamo-alpha is found as positive in the northern hemisphere and negative in the southern hemisphere and the kinetic helicity has just the same signs.

In agreement with the observations the current helicity is negative in the northern hemisphere and positive in the southern hemisphere. Our current helicities and alpha-effects are thus always out of phase. The signs of alpha-effect and both helicities exactly correspond to a numerical simulation by Brandenburg & Schmitt (1998).

The transport of magnetic flux from the convection zone into the stably-stratified tachocline is a key component of the proposed interface scenario for the solar dynamo. In this paper we give a summary of the results from three-dimensional numerical experiments (detailed in Tobias et al. 2000) of pumping of magnetic flux by turbulent, penetrative convection. We also list how the efficiency of pumping depends on the parameters of the convection.

Several techniques are used to study local areas in helioseismology, including time-distance helioseismology, acoustic imaging/holography, and ring diagram analysis. These techniques can be used to study flows, magnetic fields, and temperature inhomogeneities. The “local” area studied can be as small as a supergranule, or as large as the entire convection zone in the case of meridional circulation as studied by Giles and colleagues. Active regions have been studied with some interesting results, with complicated flow patterns below sunspots and detectable sound speed inhomogeneities in the 10 Mm below the spots. Another interesting result is the detection of sunspots on the back side of the Sun by Lindsey and Braun using the holography technique. A confirmation of their result using the time-distance technique is presented.

The development of solar acoustic holography over the past decade has opened a major new diagnostic avenue in local helioseismology (Lindsey & Braun 1990; 1997; 2000b). Its application to SOI-MDI data from SOHO has revealed “acoustic moats” surrounding sunspots, “acoustic glories” surrounding complex activeregions, and “acoustic condensations” suggesting the existence of significant seismic anomalies up to 20 Mm beneath active-region photospheres. It has given us the first seismic images of a solar flare, and has uncovered a remarkable anomaly in the statistical distribution of seismic emission from acoustic glories. A review of these and other accomplishments is given by Braun & Lindsey (2000a).

We describe simulations of the propagation of waves in magnetised structures in the solar atmosphere.

It is well known that a thin layer of angular velocity shear exists just below the solar surface. We propose that this layer is primarily generated by the radial-meridional component of the Reynolds stress. This Reynolds stress component is created by a characteristic upward-equatorward (or equivalently, downward-poleward) correlation of the turbulence velocity over a region in which the shear layer is embedded. Using 2D and 3D numerical experiments, we illustrate that this correlation is caused by vortices that get sucked down from the surface and turn aligned with the rotation vector (a la Taylor columns).

We investigate the structure of the Sun by helioseismic inversion of a set of p-mode frequencies which include new precise observations of modes with high degree obtained from the MDI instrument on the SOHO satellite. Such data have the potential to improve the resolution of the solar structure in the near-surface region, to test the equation of state and constrain the envelope helium abundance.

Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and is expected to provide more accurate inversion results. In the Born approximation, in contrast with ray theory, travel times are sensitive to perturbations to sound speed which are located off the ray path. In an example calculation of travel time perturbations due to sound speed perturbations that are functions only of depth, we see that that the Born and ray approximations agree when applied to perturbations with large spatial scale and that the ray approximation fails when applied to perturbations with small spatial scale.

Ring-diagram analysis of MDI data has revealed systematic patterns in global flow patterns in the early phase of the cycle. We report on variations and trends seen in the flows in subsequent years.

We present results from three-dimensional numerical simulations of the interaction of stratified over-turning solar-like convection with a large-scale magnetic field: By the very nature of stellar convection, even a strong magnetic field may be held down at the bottom of the convection zone, rendering the flux storage problem obsolete. This effect may also explain the observations of some magnetically active but fully convective late type dwarf stars.

We estimate near-surface flows using the techniques of f-mode time-distance helioseismology together with MDI/SOHO data. (1) Synoptic maps of horizontal flows are obtained for 1996, 1998 and 1999. Rotation, torsional oscillations and meridional circulation are measured. We detect weak large-scale flows converging toward active regions. Travel times are found to be shorter at locations of high magnetic activity. In addition, we measure the motion of the supergranulation pattern. (2) Realistic travel-time sensitivity kernels are used in an iterative deconvolution to infer horizontal flows at a high spatial resolution. The radial outflow outside a sunspot penumbra, called the moat, is measured.

We do modeling of the wave propagation in the solar photosphere. NLTE synthesis of the time series of the Fe I 5324 Å line profiles is performed using 3D model atmosphere. Velocity and intensity oscillations resulted from computations are compared with high spatial resolution observations. We conclulde that differences in oscillatory amplitudes above granules and intergranular lanes can be produced by variations of the physical conditions in these structures without invoking any excitation mechanisms.

The density stratification effects on the thermal convection in a rotating spherical shell, which is the representative of the solar convection zone, are investigated by three dimensional numerical simulations. It is found that, the convection structure in the strongly stratified system is switched from parallel cells aligned to the rotation axis to zonal rolles dominated by the longitudinally averaged mode, as the Rayleigh number increases much larger than the stability threshold. Corresponding to this structural transition, the averaged kinetic helicity reverses the sign in each hemisphere (from negative to positive in the northern hemisphere). The results indicate that the density stratification is much important for the nonlinear convection process in the rotating spherical shell.

Based on an improved MLT that takes the anisotropy and dissipation of the turbulence into account, we found that the dissipation of the turbulence in the solar convection zone should be fairly strong, while the turbulence anisotropy plays a less significant role.

As a first step toward a more realistic model of the solar tachocline, we report simulations of rotating, stably-stratified turbulence in a thin spherical shell.

The association between the different scales of convection on the solar photosphere and the field strengths/flux content of discrete magnetic flux concentrations is analyzed using simultaneously recorded SOHO/MDI high resolution filtergrams and magnetograms. The convective flow field is derived using the Local Correlation Tracking (LCT) technique. The locations and strengths of the flux elements with respect to the flow cells are analyzed to obtain information about different scales of convection.