Optical Substructure and BCG Offsets of Sunyaev-Zel'dovich and X-ray
  Selected Galaxy Clusters
  We used optical imaging and spectroscopic data to derive substructure
estimates for local Universe ($z < 0.11$) galaxy clusters from two different
samples. The first was selected through the Sunyaev-Zel'dovich (SZ) effect by
the Planck satellite and the second is an X-ray selected sample. In agreement
to X-ray substructure estimates we found that the SZ systems have a larger
fraction of substructure than the X-ray clusters. We have also found evidence
that the higher mass regime of the SZ clusters, compared to the X-ray sample,
explains the larger fraction of disturbed objects in the Planck data. Although
we detect a redshift evolution in the substructure fraction, it is not
sufficient to explain the different results between the higher-z SZ sample and
the X-ray one. We have also verified a good agreement ($\sim$60$\%$) between
the optical and X-ray substructure estimates. However, the best level of
agreement is given by the substructure classification given by measures based
on the brightest cluster galaxy (BCG), either the BCG$-$X-ray centroid offset,
or the magnitude gap between the first and second BCGs. We advocate the use of
those two parameters as the most reliable and cheap way to assess cluster
dynamical state. We recommend an offset cut of $\sim$0.01$\times$R$_{500}$ to
separate relaxed and disturbed clusters. Regarding the magnitude gap the
separation can be done at $\Delta m_{12} = 1.0$. The central galaxy paradigm
(CGP) may not be valid for $\sim$20$\%$ of relaxed massive clusters. This
fraction increases to $\sim$60$\%$ for disturbed systems.
