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Astron. Astrophys. Suppl. Ser. 146, 267-291

Size-dependent properties of simulated 2-D solar granulation

A.S. Gadun1$^\dagger$ - A. Hanslmeier4 - K.N. Pikalov1 - S.R.O. Ploner2,3 - K.G. Puschmann4 - S.K. Solanki2,3

Send offprint request: A. Hanslmeier,
$^\dagger$  deceased.

1 - Main Astronomical Observatory, Goloseevo, 03680 Kiev-127, Ukraine
2 - Max Planck Institute for Aeronomy, D-37191 Katlenburg-Lindau, Germany
3 - Institut für Astronomie, ETH-Zentrum, CH-8092 Zürich, Switzerland
4 - Institute for Geophysics, Astrophysics and Meteorology, Universitätsplatz 5, A-8010 Graz, Austria

Received April 14; accepted July 26, 2000


Two time-dependent sets of two-dimensional hydrodynamic models of solar granulation have been analyzed to obtain dependence of simulated thermal convection on the horizontal size of the convection cells. The two sets of models treat thermal convection either as fully non-stationary, multiscale convection (granular convection is a surface phenomenon) or as quasi-steady-state 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 $L \sim$ 900 km), intermediate-scale (1000-1500 km) and large-scale (larger 1500 km) convection cells. For the first group thermal damping due to radiative exchange of energy, mostly in the horizontal direction, is very important. Large-scale cells build up a pressure excess, which can lead to their total fragmentation. Similar processes also acts on the fully non-stationary convection.
2) The largest horizontal size of convection cells for which steady-state solutions 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 the partial ionization of hydrogen, we identify another layer harboring important dynamic processes in steady-state models. Just below the hydrogen-ionization layer pressure fluctuations and the acoustic flux are reduced. Steady-state models with reflecting lateral boundaries even exhibit an inversion of pressure fluctuations there.
4) From observational point of view the surface convection differs from steady-state deep treatment of thermal convection in the dependence of vertical 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 subphotospheric layers. It is more pronounced in small-scale cells and inside hot upflows.
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 decrease of their brightness with increasing size. It falls very rapidly for narrow lanes and remains unchanged for broader lanes.
7) A quantitative comparison of the brightness properties of simulated granulation 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 dependences result rather from spatial smoothing and the granule-finding algorithm. We do not exclude, however, an influence of the limitations of the 2-D treatment of thermal convection on the present results.

Key words: hydrodynamics -- convection -- Sun: granulation -- photosphere

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