Polar Interface Dynamo Mode

This page is a short introduction to the polar interface dynamo mode. This interface dynamo mode is concentrated at high latitudes because the toroidal field regeneration occurs through the agency of the negative radial shear at high latitudes, below the core-envelope interface. This is a true interface mode. An animation and butterfly diagrams can be viewed by clicking on their respective iconic images below.

Animation

On the animation, the dynamo mode is displayed in a full meridional plane (left), with the rotation axis located along the right edge of the panel. The solution is also displayed in a cartesian closeup about the core-envelope interface (right), with the polar axis corresponding to the left edge of the panel, the equatorial plane to the right edge, and the core-envelope interface running horizontally through the middle of the panel. Note that vertically, this closeup covers only 20% of the solar radius. The color scale codes the magnitude of the toroidal component of the magnetic field: yellow-orange-red is positive, green-cyan-blue negative, each covering 5 orders of magnitude in field strength. The poloidal magnetic component is shown as fieldlines (white/gray=clockwise/counterclockwise orientation).

Click here to view animation [Size: 843 KB]

Butterfly diagram

Butterfly diagrams are constant-radius cuts showing the latitudinal distribution (vertical) of the magnetic field evolving in time (horizontal). The bottom panel is a butterfly diagram for the toroidal field within the shear layer (color coding as on animation). The top panel is a butterfly diagram for the radial component of the poloidal field at the solar surface.

Click here to view butterfly diagram

The toroidal field butterfly diagram should be compared to the observational butterfly diagram for sunspots (see slide 18 of the HAO Slide Set), which are believed to be surface manifestations of the deep-seated toroidal magnetic field of the Sun.

Technical details:

This linear solution is computed for dynamo numbers C_Omega=100000, C_alpha=27.5, diffusivity ratio=0.1, shear layer thickness=0.1, and a alpha-effect concentrated near the poles (as cos(theta)) This mode has a growth time of 2.9 yr and a period P=10.5 yr (for an envelope magnetic diffusivity of 10^12 cm^2/s). Although this solution is supercritical, for the purpose of constructing the animation and butterfly diagram the growth rate has been set artificially to zero in the linear eigenvalue solution.

Last revised June 28, 1996 - P. Charbonneau