We perform a weak-lensing study of the nearby cool-core galaxy clusters, Hydra A ($z=0.0538$) and A478 ($z=0.0881$), of which brightest cluster galaxies (BCGs) host powerful activities of active galactic nuclei (AGNs). For each cluster, the observed tangential shear profile is well described either by a single Navarro--Frenk--White model or a two-component model including the BCG as an unresolved point mass. For A478, we determine the BCG and its host-halo masses from a joint fit to weak-lensing and stellar photometry measurements. We find that the choice of initial mass functions (IMFs) can introduce a factor of two uncertainty in the BCG mass, whereas the BCG host halo mass is well constrained by data. We perform a joint analysis of weak-lensing and stellar kinematics data available for the Hydra A cluster, which allows us to constrain the central mass profile without assuming specific IMFs. We find that the central mass profile ($r<300$kpc) determined from the joint analysis is in excellent agreement with those from independent measurements, including dynamical masses estimated from the cold gas disk component, X-ray hydrostatic total mass estimates, and the central stellar mass estimated based on the Salpeter IMF. The observed dark-matter fraction around the BCG for Hydra A is found to be smaller than those predicted by adiabatic contraction models, suggesting the importance of other physical processes, such as the the AGN feedback and/or dissipationless mergers.
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