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In the context of chameleon gravity, we present a semi-analytical solution of the chameleon field profile in an accurately modelled galaxy cluster’s mass components, namely the stellar mass of the Brightest Cluster Galaxy (BCG), the baryonic mass in galaxies other than the BCG, the mass of the Intra-Cluster Medium (ICM) and the diffuse cold dark matter (CDM). The obtained semi-analytic profile is validated against the numerical solution of the chameleon field equation and implemented in the MG-MAMPOSSt code for kinematic analyses of galaxy clusters in modified gravity scenarios. By means of mock halos, simulated both in GR and in modified gravity, we show that the combination of the velocities and positions of cluster member galaxies, along with the data of the stellar velocity dispersion profile of the BCG, can impose constraints on the parameter space of the chameleon model; for a cluster generated in GR, these constraints are at the same level as a joint lensing+kinematics analysis of a cluster modelled with a single mass profile, without the BCG data.
Pizzuti et al. (Sat,) studied this question.