*Astron. Astrophys. 353, 389-395 (2000)*
## 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
; here
when maps of Fourier amplitudes are
compared with *divergence maps taken later* . The correspondence
values are displayed as greyscale contours in which values
make up the background. Values of
are brighter than the background,
those are darker. The contours are
at 0.1 spacing; the contourline at
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 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 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 at the lowest
frequencies tells us that there is more than a 20% *decrease of
chance* () 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 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.
© European Southern Observatory (ESO) 2000
Online publication: December 8, 1999
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