Enhanced cluster lensing models with measured galaxy kinematics

¹ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
e-mail: pietro.bergamini@phd.unipd.it
² Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
³ INAF – Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
⁴ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁵ DARK, Niels-Bohr Institute, Lyngbyvej 2, 2100 Copenhagen, Denmark
⁶ INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
⁷ INFN, Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁸ INAF – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy
⁹ Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AV Groningen, The Netherlands

Received: 28 May 2019
Accepted: 18 September 2019

Abstract

We present an improved determination of the total mass distribution of three massive clusters from the Cluster Lensing and Supernova Survey with Hubble and Hubble Frontier Fields, MACS J1206.2−0847 (z = 0.44), MACS J0416.1−2403 (z = 0.40), Abell S1063 (z = 0.35). We specifically reconstructed the sub-halo mass component with robust stellar kinematics information of cluster galaxies, in combination with precise strong lensing models based on large samples of spectroscopically identified multiple images. We used integral-field spectroscopy in the cluster cores, from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, to measure the stellar velocity dispersion, σ, of 40−60 member galaxies per cluster, covering four to five magnitudes to m_F160W ≃ 21.5. We verified the robustness and quantified the accuracy of the velocity dispersion measurements with extensive spectral simulations. With these data, we determined the normalization and slope of the galaxy L–σ Faber–Jackson relation in each cluster and used these parameters as a prior for the scaling relations of the sub-halo population in the mass distribution modeling. When compared to our previous lens models, the inclusion of member galaxies’ kinematics provides a similar precision in reproducing the positions of the multiple images. However, the inherent degeneracy between the central effective velocity dispersion, σ₀, and truncation radius, r_cut, of sub-halos is strongly reduced, thus significantly alleviating possible systematics in the measurements of sub-halo masses. The three independent determinations of the σ₀ − r_cut scaling relation in each cluster are found to be fully consistent, enabling a statistical determination of sub-halo sizes as a function of σ₀, or halo masses. Finally, we derived the galaxy central velocity dispersion functions of the three clusters projected within 16% of their virial radius, finding that they are well in agreement with each other. We argue that such a methodology, when applied to high-quality kinematics and strong lensing data, allows the sub-halo mass functions to be determined and compared with those obtained from cosmological simulations.