Direct observations (e.g., Title et al., 1989; Wilken et al., 1997; Krieg et al., 2000; Müller et al., 2001; Berrilli et al., 2001; Löfdahl et al., 2001; Hirzberger, 2002; Nesis et al., 2002; Hirzberger, 2002; Roudier et al., 2003b; Del Moro, 2004; Puschmann et al., 2005; Nesis et al., 2006; Stodilka and Malynych, 2006, and references therein), have given a wealth of information about the morphology and evolution of the granulation pattern, and about how it is influenced and advected by larger scale flows. However, direct observations of sub-arcsecond size structures are unavoidably affected by image degradation, caused by limited instrumental resolution, scattering in the instrument and, in the case of Earth-based observations, atmospheric blurring and image distortion. Without the access to a sharp reference image or light source, it is not possible to obtain independent measurements of the amount of image degradation, and hence it is also not possible to perform quantitatively well defined image restorations.
In unresolved observations, on the other hand, key properties such as velocity amplitudes and velocity-intensity correlations are encoded in the shapes of the spectral lines. The many photospheric iron lines that can be observed in the solar spectrum are of particular importance, both because they are numerous, which allows a fair number of practically unblended lines to be found, but also because iron is a relatively heavy atom, so the thermal broadening is small (or at least not completely dominating) compared to the Doppler broadening caused by the velocity field.
The widths of spectral lines are thus heavily influenced by the amplitude of the convective velocity field, which overshoots into the stable layers of the solar photosphere where the iron lines are formed. Similarly, correlations of velocity and temperature cause net blueshifts and characteristic asymmetries of spectral lines (cf. Dravins et al., 1981; Dravins, 1982; Asplund, 2005; Gray, 2005). Together, the widths, shifts, and shapes of spectral lines thus constitute a “fingerprint” of the convective motions, which allows detailed and quantitative comparisons between 3D models and observations to be based on spatially unresolved but spectrally very accurate line profile observations. As shown in Asplund et al. (2000a,b), the agreement between observations and high resolution 3D models is excellent. See Section 5 for additional discussion.
Note that the combination of the excellent agreement of spectral line widths (which constrain the velocity amplitudes) and spectral line shifts and asymmetries (which constrain the product of velocity amplitudes and intensity fluctuations) means that the intensity fluctuations obtained from the simulations are very reliable. If they were too large or too small the spectral line shifts and asymmetries would be correspondingly to large or too small as well (cf. Deubner and Mattig, 1975; Nordlund, 1984). Different numerical models give rms intensity fluctuations that agree to within 1 – 2 percent of the continuum intensity. Observed rms intensity fluctuations are generally much smaller, presumably due to the combined effects of seeing, limited telescope resolution, and scattered light. A detailed comparison of the rms intensity fluctuations observed with Hinode with the results of forward modeling from numerical simulations (Danilovic et al., 2008) concludes that the results are essentially consistent.
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