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

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8. The nature of macro- and microturbulence

The concepts of micro- and macroturbulence are introduced in 1D analyses in order to account for the missing line broadening on length scales less than and larger than a unit optical depth, respectively. Naturally such a simplistic division is artificial since the motions occur on a range of scales. Furthermore, they are supposed to represent turbulent motions and thus are normally assumed to be isotropic. In reality the appearance of the photospheric granular velocities is clearly more laminar than turbulent with distinct upflows and downflows, a direct consequence of the strong density stratification (Nordlund et al. 1997). Given the evidences presented here and in Papers II and III, there appears to be no need to invoke any macro- or microturbulence in spectral syntheses based on realistic 3D model atmospheres.

The excellent agreement between predicted and observed line profiles shown in Fig. 8 implies that the theoretical lines have the correct widths without the use of any macroturbulence. The classical concept of macroturbulence can therefore be fully explained by the self-consistently calculated convective velocity fields and the stellar oscillations. It is less obvious that the simulations properly account for the small-scale motions normally referred to as microturbulence given the finite numerical resolution which may or may not resolve all significant velocities. We believe, however, that the currently best solar simulations described here are of sufficiently high resolution to describe also the most important effects of these small-scale motions. Firstly, solar simulations with different numerical grid resolutions indicate that the velocity distributions have essentially converged already at a resolution of 200 x 200 x 82, which is also apparent from the predicted line shapes (Asplund et al. 2000a). The contribution from unresolved scales should therefore be very minor. We emphasize that a high resolution is needed in the construction of the 3D model atmospheres to allow the high-velocity tails of the velocity distributions, but that smaller resolutions can be used for the spectral synthesis, as also verified by extensive testing of the line formation in model atmospheres interpolated to various resolutions from the original 200 x 200 x 82 data cubes prior to the analysis presented here. Secondly, the derived Fe II and Si abundances show no trend with line strength when using profile fitting (Papers II and III), which suggests that the velocities important for the line broadening have already been accounted for without resorting to the use of extra microturbulent-like velocities. There is, however, a minor trend for Fe I lines (Paper II) but since Fe II and Si lines should be affected similarly yet show no dependence with line strength, we attribute the problem with the Fe I lines rather to signatures of departures from LTE. Fe I lines should be more susceptible to NLTE effects while Fe II lines are essentially immune to such effects for solar-type stars (Shchukina & Trujillo Bueno 2000). From the results presented here and in Papers II and III there is no indication that any extra microturbulent broadening must be included in a fashion similar to that of Atroshchenko & Gadun (1994). We attribute this difference mainly to our use of much higher resolution (their solar simulations had only [FORMULA] or [FORMULA] grid-points), height extension (their spectral line calculations only extend up to about 400 km above [FORMULA]) and temporal coverage (their calculations were restricted to only one or two snapshots), which allow our simulations to better describe the full effects of the convective motions. Therefore, either from a pragmatic point of view or by advocating the principle of Occam's razor, both macro- and microturbulence appear redundant in 3D analyses.

Thus the predominant explanation is the same for micro- and macroturbulence, namely the photospheric granular velocity field and temperature inhomogeneities. Additionally, photospheric oscillatory motions play a role in the overall macroturbulent broadening of the lines without affecting the line strengths. The main component for the microturbulence therefore does not at all arise from the microscopic turbulent motions but rather from (gradients in) convective motions that are resolved with the current simulations. The small scale energy cascades and turbulence associated with a high Reynolds-number plasma are present in the solar convection zone but their intensities are very small in the upflows to which the line strengths are strongly biased (Sect. 4.1) and therefore they do not influence the line formation significantly.

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© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000