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
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