The Stagger-grid: A grid of 3D stellar atmosphere models - VI. Surface   appearance of stellar granulation
  In the surface layers of late-type stars, stellar convection is manifested with its typical granulation pattern due to the presence of convective motions. The resulting photospheric up- and downflows leave imprints in the observed spectral line profiles. We perform a careful statistical analysis of stellar granulation and its properties for different stellar parameters. We employ realistic 3D radiative hydrodynamic (RHD) simulations of surface convection from the Stagger-grid, a comprehensive grid of atmosphere models that covers a large parameter space in terms of Teff, logg, and [Fe/H]. Individual granules are detected from the (bolometric) intensity maps at disk center with an efficient granulation pattern recognition algorithm. From these we derive their respective properties: diameter, fractal dimension (area-perimeter relation), geometry, topology, variation of intensity, temperature, density and velocity with granule size. Also, the correlation of the physical properties at the optical surface are studied. We find in all of our 3D RHD simulations stellar granulation patterns imprinted, which are qualitatively similar to the solar case, despite the large differences in stellar parameters. The granules exhibit a large range in size, which can be divided into two groups - smaller and larger granules - by the mean granule size. These are distinct in their properties: smaller granules are regular shaped and dimmer, while the larger ones are increasingly irregular and more complex in their shapes and distribution in intensity contrast. This is reflected in their fractal dimensions, which is close to unity for the smaller granules, and close to two for larger granules, which is due to the fragmentation of granules. Stellar surface convection seems to operate scale-invariant over a large range in stellar parameters, which translates into a self-similar stellar granulation pattern. 
Zazralt Magic, Martin Asplund
astro-ph.SR