The envelopes we use [Christensen-Dalsgaard and
Däppen1992] extend from the temperature minimum
in the chromosphere to around 5% fractional radius. They are independent
of time and are therefore functions of 
, 
, mass and
composition only.
They are calculated using the MHD EOS [Mihalas et al.1988]
and OPAL opacities [Rogers and Iglesias1992] smoothly joined with Kurucz-opacities
[Kurucz1992] for low
temperatures. In the atmosphere a semi-empirical T- 
relation is used
and convection is treated with the standard mixing-length theory (MLT).
To be able to compare these 1D models with the 3D simulations we also
include a turbulent pressure in the hydrostatic equilibrium for the 1D models:
where is density, 
is the vertical velocity
and 
is an adjustable parameter.
The turbulent pressure is suppressed by a function of optical depth,
to avoid a very steep gradient at the transition to radiative
transport.