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Sunspot fine structure has been modeled in the past by a combination of idealized magneto-convection simulations and simplified models that prescribe the magnetic field and flow structure to a large degree. Advancement in numerical methods and computing power has enabled recently 3D radiative MHD simulations of entire sunspots with sufficient resolution to address details of umbral dots and penumbral filaments. After a brief review of recent developments we focus on the magneto-convective processes responsible for the complicated magnetic structure of the penumbra and the mechanisms leading to the driving of strong horizontal outflows in the penumbra (Evershed effect). The bulk of energy and mass is transported on scales smaller than the radial extent of the penumbra. Strong horizontal outflows in the sunspot penumbra result from a redistribution of kinetic energy preferring flows along the filaments. This redistribution is facilitated primarily through the Lorentz force, while horizontal pressure gradients play only a minor role. The Evershed flow is strongly magnetized: While we see a strong reduction of the vertical field, the horizontal field component is enhanced within filaments.
Objects in the universe from the scale of a planet to the size of a galaxy show evidence of large-scale magnetic fields. Despite the fact that the physical conditions in such objects are quite different, the creation and destruction of magnetic fields is closely linked to turbulent motions of a highly conducting fluid within these bodies. Dynamo theory focuses on the characterization of conditions under which a flow of highly conducting fluid can sustain a magnetic field against resistive decay. This chapter is an introduction to dynamo theory with a primary focus on general concepts rather than detailed applications; the latter are discussed in Vol. III of this series. We start this introduction with a brief overview of the properties of objects with large-scale magnetic fields in the universe.
The Earth and other planets
The magnetic field of the Earth has a strength of about 0.5 gauss and a mainly dipolar character. Currently the dipole axis is tilted by about 11° with respect to the axis of rotation. From studies of rock magnetism (when rocks cool below the Curie point they preserve the magnetic field that was present in them at that time) it is known that the Earth has had a magnetic field over the past 3.5 × 109 years and that the strength and orientation of the field has varied significantly on time scales of 103 to 104 years.
The seismology and physics of localized structures beneath the surface of the Sun takes on a special significance with the completion in 2006 of a solar cycle of observations by the ground-based Global Oscillation Network Group (GONG) and by the instruments on board the Solar and Heliospheric Observatory (SOHO). Of course, the spatially unresolved Birmingham Solar Oscillation Network (BiSON) has been observing for even longer. At the same time, the testing of models of stellar structure moves into high gear with the extension of deep probes from the Sun to other solar-like stars and other multi-mode pulsators, with ever-improving observations made from the ground, the success of the MOST satellite, and the recently launched CoRoT satellite. Here we report the current state of the two closely related and rapidly developing fields of helio- and asteroseimology.
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