ALBERT

Description: What is already known about the structure of the Sun, the motion of its convective zone, and the solar cycle is reviewed. Topics discussed include solar variability, solar 'seismology', velocity patterns, magnetic fields, and the dynamo theory. Observations are needed to determine global properties (solar luminosity and radius), oscillations (p and g models), velocities (variation of rotation with time and depth), and magnetic fields.

Description: Numerical experiments on two-dimensional thermosolutal convection reveal a transition from periodic oscillations to chaos through a sequence of period-doubling bifurcations. Within the chaotic region there are narrow periodic windows. This is the first example of period-doubling in solutions of partial differential equations. A truncated model indicates that this behavior is associated with heteroclinic explosions.

Description: X-ray observations have provided information about magnetic fields on the sun, and the implications of these observations are discussed. The pattern of small-scale flux emergence is quite different from that of active regions. It is inferred that the small-scale fields originate fairly high in the convective zone, while the fields in active regions have a deeper origin. The small-scale turbulent fields are only loosely related to the fields that define the normal solar cycle. The way in which dynamo models must be modified in the light of these results is indicated.

Description: Observations show that magnetic activity in late-type stars is correlated with rotation rates and that there is a discontinuous change in behavior at a critical rotation period. This can be explained as a consequence of a transition from convection in rolls parallel to the rotation axis to normal convection cells as the angular velocity is decreased.

Description: We develop kinematic models of diffusion generated by supergranulation at the solar surface. These models use current observations for the size, horizontal velocity, and lifetime of supergranules. Because there is no observational description of the appearance and disappearance of supergranules, we investigate models using several plausible evolution processes, including the effect of different lifetime distribution functions for the cells. The results are quite insensitive to the methods chosen to replace old supergranules, the distribution of cell lifetimes, and even the cell lifetime itself, for mean lifetimes between 15 to 30 hr. Calculated diffusion coefficients range between 500 and 700 sq km/s, in agreement with the best fit diffusion coefficients used by Sheeley and his collaborators to model the large-scale distribution of magnetic fields over the solar surface. However, our models do not explain the field distribution in plage, and they predict that virtually all the strong field in quiet Sun exists in relatively isolated clumps. We suggest possible mechanisms for the creation of plage and the bright network seen in quiet Sun.

Description: High-resolution coronal observations with the Normal Incidence X-ray Telescope (NIXT) reveal previously unobserved structure in the magnetic fields above a sunspot. The X-ray images are precisely aligned with a continuum photospheric image taken at the same time. The X-ray brightness traces magnetic field lines and shows: (1) that none of the bright loops originate in the spot umbra and (2) that some field lines emerging from the inner penumbra connect to regions far away from the spot. Such large-scale structures must remain distinct from the shallowly inclined fields in the outer penumbra. In particular, they cannot be involved in any interchange between the bright and dark filaments. This imposes constraints on models of penumbral convection.

Description: The partial differential equations governing two-dimensional thermosolutal convection in a Boussinesq fluid with free boundary conditions have been solved numerically in a regime where oscillatory solutions can be found. A systematic study of the transition from nonlinear periodic oscillations to temporal chaos has revealed sequences of period-doubling bifurcations. Overstability occurs if the ratio of the solutal to the thermal diffusivity tau is less than 1 and the solutal Rayleigh number Rs is sufficiently large. Solutions have been obtained for two representative values of tau. For tau = 0.316, R(s) = 10,000, symmetrical oscillations undergo a bifurcation to asymmetry, followed by a cascade of period-doubling bifurcations leading to aperiodicity, as the thermal Rayleigh number R(T) is increased. At higher values of R(T), the bifurcation sequence is repeated in reverse, restoring simple periodic solutions. As R(T) is further increased more period-doubling cascades, followed by chaos, can be identified. Within the chaotic regions there are narrow periodic windows, and multiple branches of oscillatory solutions coexist. Eventually the oscillatory branch ends and only steady solutions can be found. The development of chaos has been investigated for tau = 0.1 by varying R(T) for several different values of R(s). When R(s) is sufficiently small there are periodic solutions whose period becomes infinite at the end of the oscillatory branch. As R(s) is increased, chaos appears in the neighborhood of these heteroclinic orbits. At higher values of R(s), chaos is found for a broader range in R(T). A truncated fifth-order model suggest that the appearance of chaos is associated with heteroclinic bifurcations.