Dynamical models of cluster members to probe the total mass properties of cluster subhalos. I. A comparison with parametric strong lensing models

In this series of papers, we present dynamical models of cluster members in strong lensing (SL) galaxy clusters to independently probe the persistent discrepancy reported between SL models and cosmological simulations, in terms of total mass properties for the cluster subhalos. In this work, we focused our study on early-type galaxies within Abell 2744 ($z=0.309$) and MACS J0416.1-2403 ($z=0.397$). We took advantage of deep MUSE spectroscopic data, complemented with HFF photometry. We used a pipeline based on spectral fitting to perform kinematic measurements of the LOS velocity dispersion profiles of 109 cluster members. We modeled the galaxies assuming a dPIE total mass density distribution and a Jaffe stellar mass density distribution. From the models, we inferred the values of the central stellar velocity dispersion, $\sigma_0$, and the truncation radius, $r_t$, for the galaxies in our sample. We found that $\sigma_0$ is accurately recovered for all of the cluster members, while $r_t$ is reliably measured for a fraction of galaxies in our sample, with sufficiently extended radial kinematic coverage. Our dynamical models predicted LOS velocity dispersion profiles that fit the measured ones better than those inferred from SL models. We then exploited the $\sigma_0$ measurements obtained from the dynamical models to calibrate the Faber-Jackson scaling relations for the cluster members in both galaxy clusters. When comparing our relations to those obtained in previous kinematics and SL works, we found systematically higher normalization and compatible slope and scatter values. We conclude that our dynamical measurements of $\sigma_0$ and $r_t$, along with calibrated scaling relations, are more robust than previous kinematic estimates which are biased by not taking into account the effects of the PSF, and should therefore be adopted as improved initial prescriptions in future SL models.