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 established 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 r 500 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 r 500 , 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.

Context. Galaxy clusters are the last and largest objects to form in the standard hierarchical structure formation scenario through merging of smaller systems. The substructure frequency in the past and present epoch provides excellent means for studying the underlying cosmological model. Aims. Using X-ray observations, we study the substructure frequency as a function of redshift by quantifying and comparing the fraction of dynamically young clusters at different redshifts up to z = 1.08. We are especially interested in possible biases due to the inconsistent data quality of the low-z and high-z samples. Methods. Two well-studied morphology estimators, power ratio P3/P0 and center shift w, were used to quantify the dynamical state of 129 galaxy clusters, taking into account the different observational depth and noise levels of the observations. Results. Owing to the sensitivity of P3/P0 to Poisson noise, it is essential to use datasets with similar photon statistics when studying the P3/P0-z relation. We degraded the high-quality data of the low-redshift sample to the low data quality of the high-z observations and found a shallow positive slope that is, however, not significant, indicating a slightly larger fraction of dynamically young objects at higher redshift. The w-z relation shows no significant dependence on the data quality and gives a similar result. Conclusions. We find a similar trend for P3/P0 and w, namely a very mild increase of the disturbed cluster fraction with increasing redshifts. Within the significance limits, our findings are also consistent with no evolution.