In Table A.1 we present data on superclusters.
For a given surface the four Minkowski functionals (from the first to the fourth) are proportional to the enclosed volume V, the area of the surface S, the integrated mean curvature C, and the integrated Gaussian curvature χ. Consider an excursion set Fφ0 of a field φ(x) (the set of all points where the density is higher than a given limit, φ(x) ≥ φ0). Then, the first Minkowski functional is the volume of this region (the excursion set): (B.1)The second Minkowski functional is proportional to the surface area of the boundary δFφ of the excursion set: (B.2)The third Minkowski functional is proportional to the integrated mean curvature C of the boundary: (B.3)where R1(x) and R2(x) are the principal radii of curvature of the boundary. The fourth Minkowski functional is proportional to the integrated Gaussian curvature (the Euler characteristic) of the boundary: (B.4)At high (low) densities this functional gives us the number of isolated clumps (void cavities) in the sample (Martínez & Saar 2002; Saar et al. 2007): (B.5)The first three functionals were used to calculate the shapefinders K1 (planarity) and K2 (filamentarity) (Sahni et al. 1998; Shandarin et al. 2004; Saar 2009) and their ratio, the shape parameter K1/K2. The smaller the shape parameter, the more elongated a supercluster is. We used morphological information about superclusters, and their visual appearance to classify them as filaments and spiders. As an example, we present in Fig. B.1 the sky distribution of galaxies in one filament-type and one spider-type supercluster (SCL 001 and SCL 019, respectively).
Sky distribution of galaxies for the supercluster SCl 001 of filament morphology (upper panel), and for the supercluster SCl 019 of spider morphology (lower panel). Red dots correspond to galaxies with low SFR, log SFR < −0.5, and blue dots to galaxies with high SFR, log SFR ≥ −0.5.
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Quantiles of galaxy properties in superclusters of filament and spider morphology, and in the field.
Quantiles of the properties of high and low stellar mass galaxies in superclusters of filament and spider morphology, and in the field.
Quantiles of the properties of red, low SFR (1, see Notes), red, high SFR (2), and blue, high SFR (3) galaxies in superclusters of filament and spider morphology.
Quantiles of the properties of galaxies in groups of different richness in superclusters of filament and spider morphology.
© ESO, 2014