Multimodality in galaxy clusters from SDSS DR8: substructure and
  velocity distribution
  We search for the presence of substructure, a non-Gaussian, asymmetrical
velocity distribution of galaxies, and large peculiar velocities of the main
galaxies in galaxy clusters with at least 50 member galaxies, drawn from the
SDSS DR8. We employ a number of 3D, 2D, and 1D tests to analyse the
distribution of galaxies in clusters: 3D normal mixture modelling, the
Dressler-Shectman test, the Anderson-Darling and Shapiro-Wilk tests and others.
We find the peculiar velocities of the main galaxies, and use principal
component analysis to characterise our results. More than 80% of the clusters
in our sample have substructure according to 3D normal mixture modelling, the
Dressler-Shectman (DS) test shows substructure in about 70% of the clusters.
The median value of the peculiar velocities of the main galaxies in clusters is
206 km/s (41% of the rms velocity). The velocities of galaxies in more than 20%
of the clusters show significant non-Gaussianity. While multidimensional normal
mixture modelling is more sensitive than the DS test in resolving substructure
in the sky distribution of cluster galaxies, the DS test determines better
substructure expressed as tails in the velocity distribution of galaxies.
Richer, larger, and more luminous clusters have larger amount of substructure
and larger (compared to the rms velocity) peculiar velocities of the main
galaxies. Principal component analysis of both the substructure indicators and
the physical parameters of clusters shows that galaxy clusters are complicated
objects, the properties of which cannot be explained with a small number of
parameters or delimited by one single test. The presence of substructure, the
non-Gaussian velocity distributions, as well as the large peculiar velocities
of the main galaxies, shows that most of the clusters in our sample are
dynamically young.
