Studying the properties of galaxy cluster morphology estimators
  X-ray observations of galaxy clusters reveal a large range of morphologies
with various degrees of disturbance, showing that the assumptions of
hydrostatic equilibrium and spherical shape which are used to determine the
cluster mass from X-ray data are not always satisfied. It is therefore
important for the understanding of cluster properties as well as for
cosmological applications to detect and quantify substructure in X-ray images
of galaxy clusters. Two promising methods to do so are power ratios and center
shifts. Since these estimators can be heavily affected by Poisson noise and
X-ray background, we performed an extensive analysis of their statistical
properties using a large sample of simulated X-ray observations of clusters
from hydrodynamical simulations. We quantify the measurement bias and error in
detail and give ranges where morphological analysis is feasible. A new,
computationally fast method to correct for the Poisson bias and the X-ray
background contribution in power ratio and center shift measurements is
presented and tested for typical XMM-Newton observational data sets. We studied
the morphology of 121 simulated cluster images and establish structure
boundaries to divide samples into relaxed, mildly disturbed and disturbed
clusters. In addition, we present a new morphology estimator - the peak of the
0.3-1 r500 P3/P0 profile to better identify merging clusters. The analysis
methods were applied to a sample of 80 galaxy clusters observed with
XMM-Newton. We give structure parameters (P3/P0 in r500, w and P3/P0_max) for
all 80 observed clusters. Using our definition of the P3/P0 (w) substructure
boundary, we find 41% (47%) of our observed clusters to be disturbed.
