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

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3. Results

Fig. 4 displays time delay charts of the spatial correspondence C between pixels with Fourier amplitudes exceeding twice the average value and pixels of regions of strong negative divergence (i.e., sub-maps 1 and 2 of Fig. 2), of divergence near zero (i.e., sub-maps 5 and 6 of Fig. 2), or of high positive divergence (i.e., sub-maps 9 and 10 of Fig. 2). Each panel shows the spatial correspondence between the pixels of a given divergence sub-map and the pixels exhibiting over twice the average Fourier amplitude, as function of oscillation frequency (abscissa, corresponding periodicities along the top) and of time delay [FORMULA]; here [FORMULA] when maps of Fourier amplitudes are compared with divergence maps taken later . The correspondence values are displayed as greyscale contours in which values [FORMULA] make up the background. Values of [FORMULA] are brighter than the background, those [FORMULA] are darker. The contours are at 0.1 spacing; the contourline at [FORMULA] is omitted for clarity. The middle panels offer no significant relations, they display the results for the two sub-maps of near-zero divergence and show only a few isolated pixels, thus illustrating that the calculated [FORMULA] is realistic.

The top panel of Fig. 4 refers to the 10% of the pixels with the highest negative divergence (sub-maps 1 of Fig. 2), i.e., strong convergence. Near [FORMULA] it shows high values for C (up to slightly more than 1.3) for almost all periods smaller than about 15 min. The effects set in at the moment that the divergence is observed (as far as we can tell from our limited time resolution of only 0.5 h) and then last 1-2 h for the 7-15 min oscillations and 1 h or less for shorter periods. The relations are less pronounced for periods shorter than 2.5 min and, markedly, also for the 5 min oscillations. The dark blob around [FORMULA] at the lowest frequencies tells us that there is more than a 20% decrease of chance ([FORMULA]) as compared to random to find pixels that are brighter than average in strongly convergent regions; very probably this implies that they contain more (or larger) intergranular lanes. The dark blob for periods between 7 and 10 min at [FORMULA] h suggests that regions tend to have reduced oscillations of this periodicity roughly 1 h before convergence occurs in them. We suppose that all other specks in the panel are noise.

The bottom panel of Fig. 4 is for the 10% of the pixels with the highest divergence, i.e., sub-maps 10 of Fig. 2. These pixels show very much the opposite patterning compared to the highly negative divergence pixels: obviously large Fourier amplitudes tend to avoid regions with high divergence.

The panels in between are (from top to bottom) for sub-maps 2 (high convergence, but less then the highest 10%), for sub-maps 5 and 6 (divergence near zero) and for sub-map 9. They display a smooth transition between the extremes at top and bottom; the two middle panels are almost structureless and probably only display effects of noise. This is an indication that the effects are more or less symmetric, i.e., the excess of oscillation amplitudes in convergent regions is equally large as the deficit in the divergent regions. In this context we note that the correspondence factor C measures deviations from spatial averages, so that a blob of high correspondence in one panel must necessarily be compensated by a region of low correspondence at the same location in one or more of the other panels (including the ones that are not shown). The blankness of the middle panels implies that all effects seen in convergent regions are as strong as those in divergent regions but of opposite sign.

By a simple test we could corroborate that the results refer to the co-location of small-scale features. When we shift the divergence maps in steps spatially with respect to the amplitude maps, then the deviations from 1 of the correspondence factors computed from the shifted fields drop by a factor of order 3 for a shift of 1.2 arcsec, and they exhibit only noise for twice that shift. In other words, for a shift of larger than 2 arcsec the top and bottom panel of Fig. 4 would look like the two middle panels.

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© European Southern Observatory (ESO) 2000

Online publication: December 8, 1999