Constraining the mass distribution of galaxies using galaxy–galaxy lensing in clusters and in the field

We present a maximum‐likelihood analysis of galaxy–galaxy lensing effects in galaxy clusters and in the field. The aim is to determine the accuracy and robustness of constraints that can be obtained on galaxy halo properties in both environments: the high‐density cluster and the low‐density field. This paper is theoretically motivated, therefore we work exclusively with simulated data (nevertheless defined to match observations) to study the accuracy with which input parameters for mass distributions for galaxies can be extracted. We model galaxies in the cluster and the field using a wide range of mass profiles: the truncated pseudo‐isothermal elliptical mass distribution, the Navarro–Frenk–White profile, and a power‐law model with a core radius. We find that independent of the choice of profile the mean mass of galaxies (of the order of 10 12 M ⊙ ) can be estimated to within 15 per cent from ground‐based data and with an error of less than 10 per cent with space observations. Additionally, robust constraints can be obtained on the mean slope of the mass profile. The two standard parameters that characterize galaxy halo models, the central velocity dispersion and the truncation radius, can also be retrieved reliably from the maximum‐likelihood analysis. We find that there is an optimal scale R max which marks the boundary between lenses that effectively contribute to the measured shear. Lenses beyond R max in fact dilute the shear signal. Furthermore, going beyond the usual formulation, we propose a reparametrization of the mass models that allows us to put yet stronger constraints on the aperture mass of a galaxy halo (with less than 10 per cent error). The gain in signal‐to‐noise using space observations, expected for instance with the proposed SuperNova/Acceleration Probe ( SNAP ) satellite compared to ground‐based data in terms of accuracy of retrieving input parameters, is highly significant.