Solar and stellar dynamo models

In this dissertation the problem of generating stellar magnetic fields by hydromagnetic dynamo action is considered through numerical solutions of the kinematic α – ω dynamo equations. The aim is to compare the results to observations both to explain the observed fields and to evaluate current models for stellar dynamos.; The first topic considered is the dynamo generation of magnetic fields in the convective envelopes of white dwarf stars. This investigation is motivated by results from asteroseismology, which suggest a magnetic field $\sim$1 kG varying on time scales $\sim$ for the white dwarf GD 358. A simple dynamo model is first calibrated by choosing solar values for the dynamo parameters and matching the 22 yr cycle period and $\sim$104–105 G toroidal field strength for the Sun. Parameters from white-dwarf convective envelope models are then used with the calibrated dynamo model to estimate a field strength $\sim$300 G and a period $\sim$1 yr for GD 358. Even stronger fields are found for cooler white dwarfs, although these fields consist of high-order multipoles.; Next, the development and testing of a 2-D finite difference code to solve the dynamo equations in the realistic geometry of spherical shells is described. The 2-D code is used to study solar dynamo models including a realistic rotation profile as determined from helioseismology. Specifically, interface models are considered, in which the production of the toroidal and poloidal fields occur in different layers coupled by diffusion. A radial variation in the turbulent diffusivity, modeling the transition region between the convection zone and the stable interior, is considered and the location and width of this transition layer is varied. The latitudinal variation of the solar rotation rate is found to dominate the solution and produce results that do not match the solar case. Solar-like solutions are found only when the alpha effect is restricted to low latitudes. With this assumption super-equipartition toroidal field strengths are found for models with a thick diffusivity transition layer. These results support the interface model of the solar dynamo and argue that a realistic solar rotation profile should be included in future models.