4 Simulations

Two types of numerical studies of magneto-convection are being undertaken: “idealized” and “realistic”. Both approaches give valuable, but different, insights into the properties of magneto-convection. Idealized simulations were pioneered by Weiss (1966Jump To The Next Citation Point) and extensively used by Tao et al. (1998b), Cattaneo (1999Jump To The Next Citation Point), Abbett et al. (2000), Hurlburt and Rucklidge (2000), Emonet and Cattaneo (2001Jump To The Next Citation Point), Weiss et al. (2002Jump To The Next Citation Point), Cattaneo et al. (2003), and Bushby et al. (2008Jump To The Next Citation Point). See reviews by Weiss (1991) and Schüssler (2001). They are especially useful for gaining physical insights into convective properties. In these calculations an ideal gas equation of state is assumed and energy transport is assumed to be only by convection and thermal conduction. For modeling magneto-convection in the solar interior anelastic or reduced sound speed calculations with an ideal gas equation of state and diffusive radiation transport are appropriate (Miesch, 2005Jump To The Next Citation Point; Miesch et al., 2008; Fan, 2009Jump To The Next Citation Point; Miesch et al., 2011; Hotta et al., 2012Jump To The Next Citation Point). An alternative approach applicable to the deep convective layers is to reduce the sound speed (Hotta et al., 2012). This, as in the anelastice approximation, allows larger time steps. “Realistic” simulations were pioneered by Nordlund (1982) and have been extensively developed by Stein and Nordlund (1998, 2006Jump To The Next Citation Point), Steiner et al. (1998Jump To The Next Citation Point); Vögler et al. (2005Jump To The Next Citation Point), Schaffenberger et al. (2005Jump To The Next Citation Point), Hansteen et al. (2007), Abbett (2007Jump To The Next Citation Point), Jacoutot et al. (2008), Carlsson et al. (2010), and Gudiksen et al. (2011Jump To The Next Citation Point). A tabular equation of state is used, which includes the partial ionization of hydrogen, helium and other abundant elements, because below 40,000 K in the Sun ionization energy dominates over thermal energy in convective energy transport. The radiation transfer equation is solved to determine the radiative heating and cooling, because the optical depth is of order unity near the visible solar surface, so that neither the diffusion nor optically thin approximations are valid. Such detailed physics is necessary to make quantitative comparisons with observations. Here we restrict ourselves to the more “realistic” surface simulations. Magneto-convection and dynamo action in the deeper layers of the convection zone are reviewed by Miesch (2005Jump To The Next Citation Point) and Miesch and Toomre (2009Jump To The Next Citation Point).

 4.1 Turbulent convection and dynamo action
 4.2 Subsurface rise and emergence of magnetic flux
 4.3 Small scale flux concentrations
 4.4 Pores and sunspots

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