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Astron. Astrophys. 329, 725-734 (1998)

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2. Data, reduction, analysis

Our input data consist of a double sequence of co-temporal and co-spatial images of the photosphere (G band, called G below) and the overlying chromosphere (Ca II K [FORMULA], called K below). The two sequences consist of 228 processed images at 20 s cadence covering a quiet-sun field of [FORMULA]  Mm2 ([FORMULA]  arc sec2). Examples are shown in Fig. 2 of Paper I.

The two sequences were split in ten partially overlapping 22-min segments. Each was apodized to an effective duration of about 15 min to produce pixel-by-pixel Fourier amplitude maps at different periodicities. This short duration was selected to provide Fourier diagnostics, in particular separation of 5-min and 3-min wave modes, per location with classification as to granular morphology. Examples of the resulting Fourier maps are shown in Fig. 6 of Paper I; they provide the input material for the wave pattern analyses in Figs. 4-6 below. The total 75-min sequence of overlapping segments permits to study temporal evolution and time-delayed co-alignments of the different Fourier maps. Their partial independence also provides root-mean-square error estimates.

As in Paper I, we divide the brightness patterns and the Fourier amplitudes in different classes to which a given pixel of the observed field may belong. The G pixels are again split, per locally-normalized 15-min average, into granules and lanes (above and below average brightness, respectively). "Bright granules" again denote the subset with brightness over 110% of the average value, "dark granules" the subset below 90%.

The K pixels are again split into network and internetwork as specified in Fig. 3 of Paper I. All figures below employ internetwork pixels exclusively. In addition, we now introduce "bright K" and "dark K" pixels, where the bright ones are the internetwork pixels in a K filtergram with brightness over 130% of the mean internetwork value, the dark ones those below 70%. They describe the extrema of the spidery internetwork pattern seen on the K filtergram movie; their filling factors are about 9% and 18% of the internetwork, respectively. The bright K pixels represent a good proxy for the K [FORMULA] grains observed on Ca II K line-core spectrograms, as demonstrated by the spatio-temporal bandwidth comparisons in Fig. 2 of Rutten 1994. A somewhat different definition is used for Fig. 6 below.

The Fourier amplitudes are again split between above and below average. In addition, we now use extreme "large A " regions with Fourier amplitude A over twice the map average and "low A " regions with amplitude less than half the average. Their filling factors are 4-6% and 18-20%, respectively.

Finally, all figures below use the spatial correspondence parameter [FORMULA] defined at the end of Sect. 3 in Paper I. The coincidence filling factor [FORMULA] specifies the fraction of pixels of type A in the internetwork region of one map that also belong to type B in another map. The filling factor [FORMULA] measures the spatial occurrence of the second category in the internetwork. With this normalization the spatial correspondence C quantifies the likelihood that the two types of behavior are cospatial in terms of the random-draw likelihood, so that [FORMULA] suggests that A and B are independent phenomena, values [FORMULA] imply that pixels of type A are preferentially co-located with pixels of type B, values [FORMULA] imply spatial avoidance. Let us clarify its usage by adding an example to those in Paper I. Of all pixels that are designated "bright K" in the internetwork parts of a K image, 10% shows up as a "bright granule" at the corresponding location in the concurrent 15-min G average. Since the bright granules cover only 8% of the internetwork area, the spatial correspondence at [FORMULA] between bright K pixels and bright granules is [FORMULA]. It expresses that bright K occurrence favors co-location with bright granules in G by 30% over the random-draw probability. This statistical probability may be estimated reliably from large data sets even for pixel classes with small filling factor and in the presence of multiple patterning agents. It does not depend on the amplitude of each signal, only its spatial distribution.

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© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997