5.1 Spatially resolved lines

The spatially resolved spectral line shapes across the solar surface come in an amazing variety of strengths, shifts and asymmetries, as demonstrated in Figure 26View Image. This is a direct reflection of properties of granulation and the correlations between temperature and velocity (e.g., Dravins et al., 1981Jump To The Next Citation PointDravins and Nordlund, 1990aJump To The Next Citation PointAsplund et al., 2000bJump To The Next Citation Point). In the warm upflows the continuum intensity is high while the ascending motion shifts the line profiles towards the blue. Furthermore, the steep temperature gradients in the upflows produce strong lines. In contrast, in the downdrafts the continuum intensity is correspondingly lower while the lines are redshifted and weak because of the more shallow temperature structure. The spatially averaged line formation is therefore heavily biased towards the granules, also because of their larger area coverage in the solar atmosphere. This is good news for modeling purposes, since for example the effects of magnetic fields and the use of numerical viscosity on the resulting line formation are then minimized, since both effects tend to be concentrated in the darker intergranular areas. Towards the limb, the relative continuum intensity contrast increases significantly while the correlation between temperature (line strength) and velocities (line shift) becomes much less pronounced.
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Figure 26: Upper panel: A selection of spatially resolved line profiles for a typical Fe i line across the solar granulation pattern. The thick curve denotes the spatially averaged profile. Lower panel: The same as above but instead showing the individual line bisectors. Note that the asymmetry of the spatially resolved lines are not at all representative of the spatially averaged profile (thick line) (from Asplund et al., 2000bJump To The Next Citation Point).

At disk-center, individual line profiles corresponding to different atmospheric columns are largely symmetrical, although the line bisectors in upflows typically have a slight ∖-shape while downflows show slightly more pronounced ∕-bisectors due to the increasing vertical velocities with depth (Figure 26View Image). Closer to the limb the spatially resolved line profiles become quite distorted. In the line-forming region, the horizontal velocities are typically somewhat larger than the vertical velocities and indeed approach and occasionally exceed the sound speed. The total velocity span of profiles at inclined viewing angles is therefore substantially larger than at disk-center and the lines can develop multiple components as the line-of-sight passes inhomogeneities with distinctly different velocity shifts as well as temperatures. As a consequence the spatially resolved bisectors become very distorted and depend critically on the exact region of the surface that is being observed.

Before a proper comparison can be made between predictions and observations for spatially resolved lines the theoretical line profiles must be convolved appropriately to account for the finite instrumental resolution and atmospheric seeing (e.g., Nordlund, 1984), which unfortunately somewhat limits the information gained from the observations. Nevertheless, such exercises clearly demonstrate the remarkably good agreement between observations and predictions in general (e.g., Dravins et al., 1981Jump To The Next Citation PointDravins and Nordlund, 1990aJump To The Next Citation PointKiselman, 1994Asplund et al., 2000bJump To The Next Citation PointKiselman and Asplund, 2001Cauzzi et al., 2006Pereira et al., 2008). Each line has unique fingerprints in correlation maps between for example continuum intensity and line strength, depth, shift, width, and asymmetry across the granulation pattern depending on their height of formation and sensitivity to the atmospheric conditions, as illustrated in Figure 27View Image. Obviously, the agreement between the predicted and observed behavior in this respect is very satisfactory. Indeed, for most lines studied to date this is achieved even within the assumption of LTE in the 3D line formation. Notable exceptions are for weak low-excitation lines of minority species, which strongly suggests that the problem lies with the LTE line formation rather than a shortcoming of the 3D model atmosphere. In fact, when allowing for departures from LTE in the 3D formation of the Li i 670.8 nm line the good agreement is restored (Kiselman, 1998). The unavoidable conclusion is that the statistical properties of photospheric velocity, temperature, and pressure in the 3D simulations closely resemble the real Sun.

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Figure 27: The upper left panel shows the predicted continuum intensity across the granulation pattern of one snapshot of a 3D hydrodynamical solar simulation. The other panels illustrate the variation of the predicted (red) and observed (blue) equivalent widths of individual μ = 1 line profiles over the solar surface as a function of the local continuum intensity; each panel is labeled with the species, wavelength, and lower excitation potential of the different transitions. The two crosses denote the values for a typical down- and upflow, with the locations identified in the granulation image. For most lines the 3D LTE and observed behavior agree very well with the exception of low excitation lines of minority ionization stages, such as the 670.8 nm line of Li i, which strongly suggests the presence of non-LTE effects in the line formation (from Asplund, 2005Jump To The Next Citation Point).

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