Size-dependent properties of simulated 2-D solar granulation

Two time-dependent sets of two-dimensional hydrodynamic models of solar gra nulation have been analyzed to obtain dependence of simulated thermal conve ction on the horizontal size of the convection cells. The two sets of model s treat thermal convection either as fully non-stationary, multiscale conve ction (granular convection is a surface phenomenon) or as quasi-steady-stat e convection cells (they treat granular convection as a collection of deep- formed cells). The following results were obtained: 1) quasi-steady convection cells can be divided into 3 groups according to their properties and evolution, namely small-scale (up to L similar to 900 km)? intermediate-scale (1000 - 1500 km) and large-scale (larger 1500 km) c onvection cells. For the first group thermal damping due to radiative excha nge of energy, mostly ill the horizontal direction, is very important. Larg e-scale cells build up a pressure excess, which can lead to their total fra gmentation. Similar precesses also acts on the fully non-stationary convect ion. 2) The largest horizontal size of convection cells for which steady-state s olutions can be obtained is about 1500 km. This corresponds to granules, i. e. the bright parts of the convection cells, with a diameter of about 1000 km. 3) In addition to the zone of high convective instability associated with t he partial ionization of hydrogen, we identify another layer harboring impo rtant dynamic processes in steady-state models. Just below the hydrogen-ion ization layer pressure fluctuations and the acoustic flux are reduced. Stea dy-state models with reflecting lateral boundaries even exhibit an inversio n of pressure fluctuations there. 4) From observational point of view the surface convection differs from ste ady-state deep treatment of thermal convection in the dependence of vertica l granular velocities on their sizes for small-scale inhomogeneous. However , they cannot be distinguished by the dependence of temperature or emergent intensity of brightness structures. 5) Both kinds of models demonstrate the inversion of density in subphotosph eric layers. It is more pronounced in small-scale cells and inside hot upfl ows. 6) The brightness of simulated granules linearly increases with their size for small granules and is approximately constant or even decreases slightly for larger granules. For intergranular lanes the simulations predict a dec rease of their brightness with increasing size. It falls very rapidly for n arrow lanes and remains unchanged for broader lanes. 7) A quantitative comparison of the brightness properties of simulated gran ulation with real observations shows that the strong size-dependence of the properties of the smallest simulated granules is not accessible to current observations due to their limited spatial resolution. The observed size de pendences result rather from spatial smoothing and the granule-finding algo rithm. We do not exclude, however, an influence of the limitations of the 2 -D treatment of thermal convection on the present results.