Calibration of systematics in constraining modified gravity models with galaxy cluster mass profiles

4noJoint lensing and dynamical mass profile determinations of galaxy clusters are an excellent tool to constrain modification of gravity at cosmological scales. However, search for tiny departures from General Relativity (GR) calls for an accurate control of the systematics affecting the method. In this analysis we concentrate on the systematics in the reconstruction of mass profiles from the dynamics of cluster member galaxies, while assuming that lensing provides unbiased mass profile reconstructions. In particular, in the case study of linear f(R) gravity, we aim at verifying whether in realistic simulations of cluster formation a spurious detection of departure from GR can be detected due to violation of the main assumptions (e.g. dynamical equilibrium and spherical symmetry) on which the method is based. We aim at identifying and calibrating the impact of those systematics by analyzing a set of Dark Matter halos taken from ΛCDM N-body cosmological simulations performed with the GADGET-3 code. We evaluate how the constraints on the additional degree of freedom mfR suffer the lack of dynamical relaxation and departures from spherical symmetry. If no selection criteria are applied, ∼ 60% of clusters in a ΛCDM Universe (where GR is assumed) produce a spurious detection of modified gravity. {We find that the probability of finding cluster in agreement with GR predictions PGR mainly depends on the properties of the halo's projected phase-space and on shape orientation of the cluster along the line-of-sight projection.} We further define two observational criteria which correlate with PGR and which can be used to select, among a generic population of galaxy clusters in the local Universe, those objects that are more suitable for the application of the proposed method. In particular, we find that according to these criteria the percentage of spurious detection can be lowered down to ∼ 20% in the best case. We discuss how PGR changes when a simplified treatment of the chameleon screening mechanism is considered. Our results are relevant in view of the availability of precise measurements of lensing mass profiles from imaging data and dynamics mass profiles from spectroscopic data that will be available with the next generation surveys.reservedmixedPizzuti L.; Sartoris B.; Borgani S.; Biviano A.Pizzuti, L.; Sartoris, B.; Borgani, S.; Biviano, A