Morphological estimators on Sunyaev--Zel'dovich maps of MUSIC clusters
  of galaxies
  The determination of the morphology of galaxy clusters has important
repercussion on their cosmological and astrophysical studies. In this paper we
address the morphological characterisation of synthetic maps of the
Sunyaev--Zel'dovich (SZ) effect produced for a sample of 258 massive clusters
($M_{vir}>5\times10^{14}h^{-1}$M$_\odot$ at $z=0$), extracted from the MUSIC
hydrodynamical simulations. Specifically, we apply five known morphological
parameters, already used in X-ray, two newly introduced ones, and we combine
them together in a single parameter. We analyse two sets of simulations
obtained with different prescriptions of the gas physics (non radiative and
with cooling, star formation and stellar feedback) at four redshifts between
0.43 and 0.82. For each parameter we test its stability and efficiency to
discriminate the true cluster dynamical state, measured by theoretical
indicators. The combined parameter discriminates more efficiently relaxed and
disturbed clusters. This parameter had a mild correlation with the hydrostatic
mass ($\sim 0.3$) and a strong correlation ($\sim 0.8$) with the offset between
the SZ centroid and the cluster centre of mass. The latter quantity results as
the most accessible and efficient indicator of the dynamical state for SZ
studies.
