A sandwich interface dynamo: Linear dynamo waves in the Sun

The existence of the solar tachocline inferred from helioseismology leads to the concept of an interface dynamo. The tachocline, where the strong toroidal magnetic field is generated and stored, is sandwiched between and magnetically coupled to the radiative interior and the overlying convection zone. We investigate a linear sandwich interface dynamo in Cartesian geometry. The dynamo model consists of four horizontal layers: an electrically conducting layer at -infinity < z < -Delta, a tachocline at -Delta < z < 0, a convection zone at 0 < z < d, and a vacuum exterior at d < z < infinity, where z denotes the vertical coordinate and Delta and d are the thicknesses of the tachocline and convection layer, respectively. The four layers, with different magnetic diffusivities, are magnetically coupled by the three sets of interface-matching conditions for the generated magnetic field. Exact solutions of the coupled dynamo system (the dispersion relation and the generated magnetic field describing growing, horizontally propagating dynamo waves) are obtained. It is shown that the magnetic diffusivities in both the tachocline and radiative interior play an essential role in determining the primary properties of the sandwich interface dynamo. The generated strong toroidal magnetic field is usually concentrated in two different locations: at the top of the tachocline, just below the interface between the tachocline and convection zone, and at the bottom of the tachocline, just above the top of the radiative interior. We find that a reduced magnetic diffusivity in the tachocline or radiative interior has a strong stabilizing effect: a smaller magnetic diffusivity requires a larger magnetic Reynolds number to sustain dynamo action. The relevance of the sandwich interface dynamo to the Sun is also discussed.