9 Summary and Concluding Remarks

Solar convection is the driver that ultimately controls the Sun’s magnetic field, its explosive events, the interplanetary medium and Earth’s weather and space weather. In this review we have discussed the principles of hydrodynamics as they apply to convection near the solar surface.

In Section 3 we discussed the manifestations and properties of the main energy carrying scales, and the granulation pattern that they give rise to. We emphasized the crucial importance of the density stratification in determining the size and evolution of the granulation pattern, and the importance of the radiative cooling at the solar surface as the provider of the entropy deficient plasma that then drives convective motions over a range of scales.

In Section 4 we discussed how larger scale convective patterns arise and are driven, and how they interact with smaller scale patterns. We introduced the concept of a velocity spectrum, and addressed the question of to what extent or not the traditional concepts of meso- and supergranulation represent distinct scales of motion. We showed that both observations and theoretical models give a smooth velocity spectrum, with velocity amplitudes decreasing approximately linearly with horizontal wave number on scales larger than granulation.

In Section 5 we discussed how spectral line synthesis and comparisons with observed spectral line profiles may be used to assess the accuracy of numerical simulations and how the resulting spectral line profiles may be used to accurately determine solar chemical abundances. We conclude that 3D models with numerical resolutions of the order of 2003 reproduce the widths, shifts, and shapes of photospheric spectral lines with high accuracy, and that the chemical abundances derived from such models have a higher degree of internal consistency with less scatter and fewer systematic trends than the ones obtains from traditional abundance analysis, based on empirical or theoretical one-dimensional model atmospheres.

In Section 6 we discussed applications to global and local helioseismology; wave excitation and damping, the influence of convection on the mean structure, and helioseismic diagnostics related to convective flow patterns. We showed that solar oscillations with realistic overall amplitudes are spontaneously excited in numerical simulations of the solar surface layers, and that solar surface convection directly influences the frequency of the oscillations by changing the size of the resonant cavity.

In Section 7 we discussed the interaction of solar surface convection and solar magnetic fields. In active regions, the presence of magnetic fields causes the brightening of plage regions towards the limb, and increased possibilities for convection to heat the chromosphere and corona.

Finally, in Section 8, we briefly discussed open questions and directions for future work, and emphasized the importance of the Sun as a test bed for astrophysical hydrodynamics, magneto-hydrodynamics, and beyond.

In conclusion, we submit that the Sun is a superb laboratory for investigating dynamical astrophysical processes and especially plasma physics. Combinations of observations and numerical simulations can provide detailed insights into these physical processes, and can also provide data sets that may be used to validate observational analysis methods and to design future observing programs.

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