Peter A. Gilman

LIMITS TO PENETRATION OF MERIDIONAL CIRCULATION BELOW THE SOLAR CONVECTION ZONE

We show that meridional circulation, such as that observed at the top of and in the solar convection zone (CZ) by direct doppler and helioseismic techniques, cannot penetrate significantly below the bottom (~0.7 R☉) of the overshoot layer at the bottom of the CZ. Therefore, solar dynamo models that rely on penetration as deep as to 0.6 R☉ are ruled out. The analysis we carried out to reach this conclusion elucidates two boundary layers, one of which we have not seen applied to astrophysical problems before. This analysis should be relevant to understanding interfaces between convective and radiative zones in stellar interiors generally.

Nonlinear Evolution of Global Magnetoshear Instabilities in a Three-dimensional Thin-Shell Model of the Solar Tachocline

We investigate global instabilities of toroidal fields and differential rotation in the solar tachocline using a three-dimensional thin-shell model. We initiate our nonlinear numerical simulations by superposing random, high-wavenumber perturbations on an equilibrium state and we then allow the system to evolve freely as the instabilities develop, grow exponentially, and saturate. For broad toroidal field profiles the dominant mode is the clamshell instability previously identified in two-dimensional and shallow-water investigations in which loops of field in the northern and southern hemispheres tilt and reconnect, eventually becoming perpendicular to the equatorial plane. If the initial toroidal field is instead confined to thin bands of alternating polarity in the northern and southern hemispheres, the evolution is more complex. At early times, a previously unidentified instability occurs near the edges of each band that is characterized by a high longitudinal wavenumber m. These edge instabilities are later superseded by an m = 1 tipping instability whereby field lines tilt in latitude as in the broad-field case. The tipping instability saturates by forming a jet of fluid within each band, which provides gyroscopic stabilization. Both the clamshell and the tipping instabilities are quasi-two-dimensional and proceed most efficiently near the impenetrable boundaries where the vertical velocity vanishes. Strong stable stratification enhances this tendency by decoupling horizontal layers. These simulations demonstrate the robustness of global m = 1 instabilities in differentially rotating spherical shells threaded by toroidal magnetic fields and as such have important implications for tachocline dynamics, including dynamo processes and tachocline confinement.

CONSTRAINTS ON THE APPLICABILITY OF AN INTERFACE DYNAMO TO THE SUN

Taking into account the helioseismically inferred interior structure, we show that a pure interface-type dynamo does not work for the Sun if the skin effect for poloidal fields does not allow them to penetrate the tachocline. Using a simple mean-field kinematic α-Ω dynamo model, we demonstrate that, in the absence of tachocline radial shear participating in the dynamo process, a latitudinal differential rotation can provide the necessary Ω-effect to drive an oscillation in an interface dynamo, but it alone cannot produce the latitudinal migration. We show that to make an interface dynamo work with the constraints of interior structure and skin depth, a meridional circulation is essential. We conclude that a flux-transport dynamo driven by both the Babcock-Leighton and interface/bottom α-effects is a robust large-scale dynamo for the Sun.

Dynamo theory for the interface between the convection zone and the radiative interior of a star part

Abstract We discuss numerical solutions of nonlinear equations that model magnetic field generation in a thin layer beneath the convection zone of a late type star. The model equations were derived previously in Paper I (DeLuca and Gilman, 1986b). Three main results are found: first, the oscillating, dynamo wave solutions discussed in DeLuca and Gilman (1986a) are shown to be a result of the severe truncation used in those calculations; second, the induced velocity feld is shown to have an important role in determining the spatial structure of the magnetic field solutions; time dependent solutions have been found. These are not wave-like solutions, rather the amplitude of different horizontal wave modes vary in time. Further, we show that the exact solutions found in Paper I are generally unstable, with the exception of those that are independent of ŷ (latitude in our Cartesian geometry), which are stable if the transient induced velocity field remains small. We conclude that the induced velocity fields a...

Global solar dynamo models: simulations and predictions of cyclic photospheric fields and long-term non-reversing interior fields

We review progress made in simulating and predicting principal properties of solar cycles using flux-transport dynamo models and predictive tools. We show that such models provide a consistent plausible theory for the following solar cycle properties: cycle period, phase relation between poloidal and toroidal magnetic fields, field symmetry about the equator, cycle 23 polar field amplitudes and reversal timings, timing of the end of cycle 23, and the relative peaks of cycles 16?23, as well as forecasts for the upcoming peak of cycle 24. The same model is also used to show that so-called interface dynamo solutions do not calibrate well to solar observations, and that the current solar dynamo may be a significant source of high amplitude very long lived non-reversing toroidal field in the solar interior.