3.8 Average structure

The mean atmospheric structure in the 20 Mm deep simulations is shown in Figures 15View Image and 16View Image. 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 zone.

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., 1999Jump To The Next Citation PointBrandenburg et al., 2005Jump To The Next Citation Point).

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Figure 12: Correlation of radiation temperature at 1.6 μm with gas temperature at the depth where ⟨τ ⟩ = 1 1.6μm. 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 (10 κ ∝ T) (from Stein and Nordlund, 1998Jump To The Next Citation Point).
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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, 1998Jump To The Next Citation Point).
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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, 1998Jump To The Next Citation Point).
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Figure 15: Mean atmosphere structure: T (K), ρ (10–7 g/cm3), P (105 dyne/cm2), S (arbitrary units).
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Figure 16: Mean atmosphere structure: Γ 1, H ii, He ii, He iii.
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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 ∇ ⋅ u red (positive) identifies the diverging flow inside the granule while blue (negative) identifies the converging flow in the intergranular lanes.

A 20 Mm deep simulation also contains the entire hydrogen ionization region, helium first ionization and most of the helium second ionization regions (Figure 16View Image). 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 Γ = 1.55.


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