Context: Understanding the evolution of the dark matter halos of galaxies after they become part of a cluster is essential for understanding the evolution of these satellite galaxies. Aims: We investigate the potential of galaxy-galaxy lensing to map the halo density profiles of galaxies in clusters. Methods: We propose a method that separates the weak-lensing signal of the dark-matter halos of galaxies in clusters from the weak-lensing signal of the cluster's main halo. Using toy cluster models as well as ray-tracing through N-body simulations of structure formation along with semi-analytic galaxy formation models, we test the method and assess its performance. Results: We show that with the proposed method, one can recover the density profiles of the cluster galaxy halos in the range 30 - 300 kpc. Using the method, we find that weak-lensing signal of cluster member galaxies in the Millennium Simulation is well described by an Navarro-Frenk-White (NFW) profile. In contrast, non-singular isothermal mass distribution (like PIEMD) model provide a poor fit. Furthermore, we do not find evidence for a sharp truncation of the galaxy halos in the range probed by our method. Instead, there is an observed overall decrease of the halo mass profile of cluster member galaxies with increasing time spent in the cluster. This trend, as well as the presence or absence of a truncation radius, should be detectable in future weak-lensing surveys like the Dark Energy Survey (DES) or the Large Synoptic Survey Telescope (LSST) survey. Such surveys should also allow one to infer the mass-luminosity relation of cluster galaxies with our method over two decades in mass. Conclusions: It is possible to recover in a non-parametric way the mass profile of satellite galaxies and their dark matter halos in future surveys, using our proposed weak lensing method.
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