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Astron. Astrophys. 359, 729-742 (2000)

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9. Concluding remarks

The good agreement with observed line shapes, shifts and asymmetries, lend very strong support to the realism of the 3D convection simulations. No doubt the 3D predictions are superior to those obtained from 1D analyses. In particular the use of mixing length parameters, equivalent widths, macro- and microturbulence no longer appear to be needed. Therefore derived results, such as elemental abundances, should be more reliable. In spite of the minor remaining shortcomings, the overall significant accomplishment is therefore still obvious: starting from only the well-known radiative-hydrodynamical conservation equations and with no adjustable free parameters besides the treatment of the numerical viscosity in the construction of the 3D model atmospheres, detailed line profiles and asymmetries can be predicted which agree almost perfectly with observations and furthermore are far superior to classical 1D predictions with several tunable parameters. It should be stressed, however, that the numerical viscosity is merely introduced for numerical stability purposes and is determined from standard hydrodynamical test cases with no adjustments allowed to improve the agreement with observations. In this respect the viscosity is not a freely adjustable parameter like e.g. the various mixing length parameters in 1D models.

It is important to emphasize that this accomplishment is only possible if the convection simulations are highly realistic, both in terms of input physics (equation-of-state, opacities etc) and numerical details (numerical and physical resolution, extension, boundary conditions, radiative transfer treatment etc). From our various experiments and test calculations we can conclude that of special importance is the dimension (2D is not adequate for spectral synthesis, Asplund et al. 2000a), resolution (even [FORMULA] is not quite sufficient for detailed line shapes, Asplund et al. 2000a) and height extension (to limit the influence from the outer boundary) of the numerical box. Furthermore, in order to achieve the correct temperature structure it is important to include the effects of line-blanketing in the 3D radiative transfer during the simulations (Stein & Nordlund 1998). We believe that we have now addressed all of these specific issues with the new generation of convection simulations, which is supported by the very close resemblance with observed line profiles, shifts and asymmetries, as presented here.

All of the above-mentioned features are currently affordable with present-day supercomputers. The obvious disadvantage with this 3D procedure is of course the time-consuming task to perform the necessary 3D convection simulations and spectral line calculations, even with the simplifying assumptions of opacity binning and LTE. Furthermore, still only a relatively small part of the Hertzsprung-Russell diagram of solar-type stars has been explored. The situation will, however, improve significantly during the coming years due to faster computers and more efficient numerical algorithms. Of particular interest will be to extend the modeling to additional metal-poor stars (cf. Asplund et al. 1999), A-F type stars and red giants, where the granulation is expected to be much more vigorous than for the Sun, which should therefore influence the line formation more.

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© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000