Aims. From accurate photometric and spectroscopic information, we build the Fundamental Plane (FP) relation for the early-type galaxies of the cluster Abell S1063. We use this relation to develop an improved strong lensing model of the cluster, and we decompose the cluster’s cumulative projected total mass profile into its stellar, hot gas, and dark matter mass components. We compare our results with the predictions of cosmological simulations. Methods. We calibrate the FP using Hubble Frontier Fields photometry and data from the Multi Unit Spectroscopic Explorer on the Very Large Telescope. The FP allows us to determine the velocity dispersions of all 222 cluster members included in the model from their measured structural parameters. As for their truncation radii, we test a proportionality relation with the observed half-light radii. Fixing the mass contribution of the hot gas component from X-ray data, the mass density distributions of the diffuse dark matter haloes are optimised by comparing the observed and model-predicted positions of 55 multiple images of 20 background sources distributed over the redshift range 0.73 − 6.11. We determine the uncertainties on the model parameters with Monte Carlo Markov chains. Results. We find that the most accurate predictions of the positions of the multiple images are obtained when the truncation radii of the member galaxies are approximately 2.3 times their effective radii. Compared to earlier work on the same cluster, our model allows for the inclusion of some scatter on the relation between the total mass and the velocity dispersion of the cluster members. We notice a lower statistical uncertainty on the value of some model parameters. For instance, the main dark matter halo of the cluster has a core radius of 86 ± 2 kpc: the uncertainty on this value decreases by more than 30% with respect to previous work. Taking advantage of a new estimate of the stellar mass of all cluster members from the HST multi-band data, we measure the cumulative two-dimensional mass profiles out to a radius of 350 kpc for all baryonic and dark matter components of the cluster. At the outermost radius of 350 kpc, we obtain a baryon fraction of 0.147 ± 0.002. We study the stellar-to-total mass fraction of the high-mass cluster members in our model, finding good agreement with the observations of wide galaxy surveys and some disagreement with the predictions of halo occupation distribution studies based on N-body simulations. Finally, we compare the features of the sub-haloes as described by our model with those predicted by high-resolution hydrodynamical simulations. We obtain compatible results in terms of the stellar over total mass fraction. On the other hand, we report some discrepancies both in terms of the maximum circular velocity, which is an indication of the halo compactness, and the sub-halo total mass function in the central cluster regions.

Context. Recent observations found that observed cluster member galaxies are more compact than their counterparts in ΛCDM hydrodynamic simulations, as indicated by the difference in their strong gravitational lensing properties, and they reported that measured and simulated galaxy–galaxy strong lensing events on small scales are discrepant by one order of magnitude. Among the possible explanations for this discrepancy, some studies suggest that simulations with better resolution and implementing different schemes for galaxy formation could produce simulations that are in better agreement with the observations. Aims. In this work, we aim to assess the impact of numerical resolution and of the implementation of energy input from AGN feedback models on the inner structure of cluster sub-haloes in hydrodynamic simulations. Methods. We compared several zoom-in re-simulations of a sub-sample of cluster-sized haloes obtained by varying mass resolution and softening the length and AGN energy feedback scheme. We studied the impact of these different setups on the sub-halo (SH) abundances, their radial distribution, their density and mass profiles, and the relation between the maximum circular velocity, which is a proxy for SH compactness Results. Regardless of the adopted numerical resolution and feedback model, SHs with masses of MSH ≲ 1011 h−1 M⊙, the most relevant mass range for galaxy–galaxy strong lensing, have maximum circular velocities ∼30% smaller than those measured from strong lensing observations. We also find that simulations with less effective AGN energy feedback produce massive SHs (MSH ≳ 1011 h−1 M⊙) with higher maximum circular velocity and that their Vmax − MSH relation approaches the observed one. However, the stellar-mass number count of these objects exceeds the one found in observations, and we find that the compactness of these simulated SHs is the result of an extremely over-efficient star formation in their cores, also leading to larger than observed SH stellar mass. Conclusions. Regardless of the resolution and galaxy formation model adopted, simulations are unable to simultaneously reproduce the observed stellar masses and compactness (or maximum circular velocities) of cluster galaxies. Thus, the discrepancy between theory and observations that emerged previous works. It remains an open question as to whether such a discrepancy reflects limitations of the current implementation of galaxy formation models or the ΛCDM paradigm.

Context. An excess of galaxy-galaxy strong lensing (GGSL) in galaxy clusters compared to expectations from the Λ cold-dark-matter (CDM) cosmological model has recently been reported. Theoretical estimates of the GGSL probability are based on the analysis of numerical hydrodynamical simulations in ΛCDM cosmology. Aims. We quantify the impact of the numerical resolution and active galactic nucleus (AGN) feedback scheme adopted in cosmological simulations on the predicted GGSL probability, and determine if varying these simulation properties can alleviate the gap with observations. Methods. We analyze cluster-size halos (M 200 > 5 × 10 14 M ) simulated with different mass and force resolutions and implementing several independent AGN feedback schemes. Our analysis focuses on galaxies with Einstein radii in the range 0 .5 ≤ θ E ≤ 3 . Results. We find that improving the mass resolution by factors of 10 and 25, while using the same galaxy formation model that includes AGN feedback, does not affect the GGSL probability. We find similar results regarding the choice of gravitational softening. On the contrary, adopting an AGN feedback scheme that is less efficient at suppressing gas cooling and star formation leads to an increase in the GGSL probability by a factor of between 3 and 6. However, we notice that such simulations form overly massive galaxies whose contribution to the lensing cross section would be significant but that their Einstein radii are too large to be consistent with the observations. The primary contributors to the observed GGSL cross sections are galaxies with smaller masses that are compact enough to become critical for lensing. The population with these required characteristics appears to be absent from simulations. Conclusions. Based on these results, we reaffirm the tension between observations of GGSL and theoretical expectations in the framework of the ΛCDM cosmological model. The GGSL probability is sensitive to the galaxy formation model implemented in the simulations. Still, all the tested models have difficulty simultaneously reproducing the stellar mass function and the internal structure of galaxies.

Context. The wavelength dependence of the projection of the fundamental plane along the velocity dispersion axis, namely the Kormendy relation, is well characterised at low redshift but poorly studied at intermediate redshifts. The Kormendy relation provides information on the evolution of the population of early-type galaxies (ETGs). Therefore, by studying it, we may shed light on the assembly processes of these objects and their size evolution. As studies at different redshifts are generally conducted in different rest-frame wavebands, it is important to investigate whether the Kormendy relation is dependent on wavelength. Knowledge of such a dependence is fundamental to correctly interpreting the conclusions we might draw from these studies. Aims. We analyse the Kormendy relations of the three Hubble Frontier Fields clusters, Abell S1063 at z = 0.348, MACS J0416.1-2403 at z = 0.396, and MACS J1149.5+2223 at z = 0.542, as a function of wavelength. This is the first time the Kormendy relation of ETGs has been explored consistently over such a large range of wavelengths at intermediate redshifts.Methods. We exploit very deep Hubble Space Telescope photometry, ranging from the observed B-band to the H-band, and VLT/MUSE integral field spectroscopy. We improve the structural parameter estimation we performed in a previous work by means of a newly developed python package called morphofit.Results. With its use on cluster ETGs, we find that the Kormendy relation slopes increase smoothly with wavelength from the optical to the near-infrared (NIR) bands in all three clusters, with the intercepts becoming fainter at lower redshifts due to the passive ageing of the ETG stellar populations. The slope trend is consistent with previous findings at lower redshifts. Conclusions. The slope increase with wavelength implies that smaller ETGs are more centrally concentrated than larger ETGs in the NIR with respect to the optical regime. As different bands probe different stellar populations in galaxies, the slope increase also implies that smaller ETGs have stronger internal gradients with respect to larger ETGs.