Simulations of solar granulation. I. General properties

Numerical simulations provide information on solar convection not available by direct observation. We present results of simulations of near surface solar convection with realistic physics: an equation of state including ionization and three-dimensional, LTE radiative transfer using a four-bin opacity distribution function. Solar convection is driven by radiative cooling in the surface thermal boundary layer, producing the familiar granulation pattern. In the interior of granules, warm plasma ascends with approximate to 10% ionized hydrogen. As it approaches and passes through the optical surface, the plasma cools, recombines, and loses entropy. It then turns over and converges into the dark intergranular lanes and further into the vertices between granulation cells. These vertices feed turbulent downdrafts below the solar surface, which are the sites of buoyancy work that drives the convection. Only a tiny fraction of the fluid ascending at depth reaches the surface to cool, lose entropy, and form the cores of these downdrafts. Granules evolve by pushing out against and being pushed in by their neighboring granules, and by being split by overlying fluid that cools and is pulled down by gravity. Convective energy transport properties that are closely related to integral constraints such as conservation of energy and mass are exceedingly robust. Other properties, which are less tightly constrained and/or involve higher order moments or derivatives, are found to depend more sensitively on the numerical resolution. At the highest numerical resolution, excellent agreement between simulated convection properties and observations is found. In interpreting observations it is crucial to remember that surfaces of constant optical depth are corrugated. The surface of unit optical depth in the continuum is higher above granules and lower in the intergranular lanes, while the surface of optical depth unity in a spectral line is corrugated in ways that are influenced by both thermal and Doppler effects.