## 2. Surface convection simulationsThe 3D model atmospheres of the solar granulation which form the basis for the spectral line calculations presented here have been obtained with a 3D, time-dependent, compressible, radiative-hydrodynamics code developed to study solar and stellar surface convection (e.g. Nordlund & Stein 1990; Stein & Nordlund 1989, 1998; Asplund et al. 1999). The hydrodynamical equations of mass, momentum and energy conservation: coupled to the equation of radiative transfer along a ray (in total eight inclined rays): are solved on a non-staggered Eulerian mesh with 200 x 200 x 82
gridpoints; simulations with resolutions 100 x 100 x 82, 50 x 50 x 82
and 50 x 50 x 41 have also been computed but have not been utilized
here since they are hampered by less good agreement between predicted
and observed line profiles (Asplund et al. 2000a). In these equations,
denotes the density,
the velocity,
the gravitational acceleration,
The physical dimension of the simulation box corresponds to
6.0 x 6.0 x 3.8 Mm of which about 1.0 Mm is located above continuum
optical depth unity. Again, initial solar simulations extending only
to heigths of 0.6 Mm suffered from problems in the predicted line
asymmetries for strong lines which was traced to the influence of the
outer boundary and that non-negligible optical depths were present in
the line cores already at the outermost layers. Though not completely
removed with the current more extended simulations, the problems have
largely disappeared as discussed further in Sect. 6 and 7. The depth
scale has been optimized to provide the best resolution where it is
most needed, i.e. in those layers with the steepest gradients in terms
of d In order to obtain a realistic atmospheric structure it is crucial
to correctly describe the internal energy of the gas and the energy
exchange between radiation and gas. For this purpose a
state-of-the-art equation-of-state (Mihalas et al. 1988), which
includes the effects of ionization, excitation and dissociation, has
been used. Since the solar photosphere is located in the layers where
the convective energy flux from the interior is transferred to
radiation, a proper treatment of the 3D radiative transfer is
necessary, which has been included under the assumption of LTE and
using detailed continuous (Gustafsson et al. 1975 and subsequent
updates) and line (Kurucz 1993) opacities. The 3D equation of
radiative transfer was solved at each timestep of the convection
simulation for eight inclined rays (2 It is noteworthy that the convection simulations contain no
adjustable free parameters besides those used to characterize the
stars: the effective temperature (or
equivalently, as adopted here, the entropy of the inflowing material
at the bottom boundary), the surface acceleration of gravity
log © European Southern Observatory (ESO) 2000 Online publication: July 7, 2000 |