3.8 Average structure
The mean atmospheric structure in the 20 Mm deep simulations is shown in Figures 15 and 16. The
temperature increases by less than two orders of magnitude from the surface to 20 Mm depth (from
4300 K to 143,000 K). The density, on the other hand, increases by 5.5 orders of magnitude from the
temperature minimum to 20 Mm depth and the pressure varies by 7 orders of magnitude. The
50% ionization depths of H, He i, and He ii occur at 1, 6, 16 Mm, respectively.
A 20 Mm deep simulation contains 2/3 of the pressure scale heights within the convection
In general the average structure of 3D models agrees very closely with mixing-length models of the solar
envelope, with the main function of the mixing-length parameter being to calibrate the magnitude of the
entropy jump at the surface (Rosenthal et al., 1999; Brandenburg et al., 2005).
Figure 12: Correlation of radiation temperature at with gas temperature at the depth
where . We never see the radiation from the high temperature gas because it lies at
large local optical depth due to the great temperature sensitivity of the H– opacity ()
(from Stein and Nordlund, 1998).
Figure 13: Temperature as a function of geometric depth at several horizontal locations plus the
average temperature profile (dashed). Locally the temperature profile is much steeper than the
average profile (from Stein and Nordlund, 1998).
Figure 14: Temperature as a function of optical depth at several horizontal locations plus the average
temperature profile (dashed). On an optical depth scale, the temperature profile is similar at all
places in the simulation domain, whether in warm upflows or cool downflows. This is because the
opacity depends very strongly on temperature, and hence a certain optical depth is reached at nearly
the same temperature, whether the temperature rises rapidly (as in upflows) or more slowly (as in
downflows) (from Stein and Nordlund, 1998).
Figure 15: Mean atmosphere structure: T (K), (10–7 g/cm3), P (105 dyne/cm2), S (arbitrary
Figure 16: Mean atmosphere structure: , H ii, He ii, He iii.
Figure 17: Rendering of vorticity around a single granule showing antiparallel vortex tubes (green,
opaque surfaces) at the edges of the intergranular lanes (near the right hand side edge) and a ring
vortex at the head of a downdraft with two trailing vortex tubes leading up to the surface (center
left). The transparent red and blue shows the velocity divergence red (positive) identifies
the diverging flow inside the granule while blue (negative) identifies the converging flow in the
A 20 Mm deep simulation also contains the entire hydrogen ionization region, helium first ionization
and most of the helium second ionization regions (Figure 16). The adiabatic index becomes very small in
the hydrogen ionization zone (reaching a minimum of 1.13). The second helium ionization has only a small
effect, producing a plateau at .