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Astron. Astrophys. 353, 389-395 (2000)

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4. Discussion and conclusion

Fig. 4 proves that regions with Fourier amplitudes larger than twice the average show a strongly significant preference to coincide spatially with meso-scale convergent regions and to avoid meso-scale divergent regions. For amplitudes with periods in the range 2-15 min we find correspondences as large as 1.3 and as low as 0.7. Although the effects have up to 5-6[FORMULA] significance they imply only small variations in oscillation amplitudes: pixels in sub-map 1 of the divergence maps, i.e., the strongest negative divergence (or strongly convergent) regions, display Fourier amplitudes of 3-3.5% above average, while those in sub-map 10, i.e. the strongest positive divergence regions, are 3-3.5% below average.

We attach some importance to the strong correspondence minimum of 0.7 (enhancement to 1.4) in the top (bottom) panel of Fig. 4 near frequency and [FORMULA] zero. This clearly hints at a relation of average granule brightness to meso-scale structure : brighter than average granules obviously prefer regions of strong positive divergence (bottom panel), while in strongly convergent regions (top panel) they are either darker on average or darker intergranular lanes prevail. This result confirms the earlier findings of Brandt et al. (1991), of increased granule brightness in regions of positive divergence, based on a different data set and a different analysis procedure.

In our opinion it is a puzzling feature of the correspondence maps for strong negative and positive divergence that oscillations of periods around 5 min show much less co-location probability than the other frequencies between 2.5 and 20 min. We cannot think of an explanation for this, the same holds for the features showing up in the top two and in the bottom maps of Fig. 4 around [FORMULA] h and periods of 8-10 min.

Our results for meso-scales are rather similar to those we found on a smaller scale for the normal granulation in Fig. 7 of Paper II. In that figure regions of more than twice the average Fourier amplitudes show much larger correspondences with intergranular lanes (which would be equivalent to meso-convergent regions here) than with granules (meso-divergent regions). While, as mentioned above, the strongest meso-convergent regions at periods below 3-4 min show an enhancement of amplitudes of 3-3.5% above average, in the darkest intergranular lanes the enhancement is about 4-4.5%. However, while there is no evidence that granulation modifies waves of periods longer than about 5 min, the meso-scale flows clearly are important for waves of periods as long as 10 to 15 min.

Whether the meso-scale flows mainly couple to oscillations by the direct influence of their spatial velocity and temperature modulation, or rather more indirectly by modifying the granular pattern is not obvious. On the one hand it is evident from Fig. 4, and the work of e.g., Brandt et al. (1991), that meso-scale flows and granulation are not independent phenomena: as compared to the average there are more granules (low oscillation amplitudes) in meso-scale divergent regions and more intergranular lanes (high oscillation amplitudes) in meso-scale convergent regions. Therefore, it seems highly probable that the variation of the granular pattern on meso-scales has at least some effect. The next article of this series will explore in more detail the relations between meso-scale flows and granulation, i.e., the preponderance of intergranular lanes in convergent and of granules in divergent regions - of which we see the signature in Fig. 4.

On the other hand Fig. 4 proves that there exists a clear relation of oscillations of periods longer than 5 min with meso-scale flows, but a similar relation with the granulation seems absent - at least our results in Papers I and II, and in Hoekzema & Rutten (1998) offer no hint for it. This is hard to understand if meso-scale flows were to have only an impact through modulation of the granular pattern. Also, it is easy to imagine meso-scale flows carrying along p-modes thus concentrating them in convergent regions and diluting them in divergent ones. The recent work on time-distance heloseismology (see for example Duvall et al. 1997) and on acoustic imaging of sub-surface layers (e.g., Chang et al. 1997) stresses the importance of flow fields for the propagation of acoustic waves; our results may well illustrate this.

Finally, we point out that the horizontal velocities of supergranular flows are about as large as those of the meso-scales and the granulation. Since granulation and meso-scale flows display comparable impact on oscillations, it would be interesting to analyse how supergranulation fits into the picture.

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© European Southern Observatory (ESO) 2000

Online publication: December 8, 1999