Cosmography from accurate mass modeling of the lens group SDSS J0100+1818: Five sources at three different redshifts

Systems where multiple sources at different redshifts are strongly lensed by the same deflector allow one to directly investigate the evolution of the angular diameter distances as a function of redshift, and thus to learn about the geometry of the Universe. We present measurements of the values of the total matter density, Ω_m, and of the dark energy equation of state parameter, w, through a detailed strong lensing analysis of SDSS J0100+1818, a group-scale system at z = 0.581 with five lensed sources, from z = 1.698 to 4.95. We take advantage of new spectroscopic data from the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope to securely measure the redshift of 65 sources, including the 5 multiply imaged background sources (lensed into a total of 18 multiple images) and 19 galaxies on the deflector plane, all employed to build robust strong lensing models with the software GLEE. The total mass distribution of the deflector is described in a relatively simple way, and includes an extended halo, the brightest group galaxy (BGG) with a measured stellar velocity dispersion of (380.5 ± 4.4) km s^‑1, and fainter members. We measure Ω_m = 0.14_‑0.09^+0.16 in a flat Λ cold dark matter (CDM) model, and Ω_m = 0.19_‑0.10^+0.17 and w = ‑1.27_‑0.48^+0.43 in a flat wCDM model. Given the presence of different sources angularly close in projection, we quantify through a multiplane approach their impact on the inferred values of the cosmological parameters. We obtain consistent median values, with uncertainties for only Ω_m increasing by approximately a factor of 1.5. Thanks to the remarkably wide radial interval where the multiple images are observed, ranging from 15 to 77 kpc from the BGG, we accurately measure the total mass profile and infer the stellar over total mass profile of the deflector. They result in a total mass of (1.55 ± 0.01)×10¹³ M_⊙ within 50 kpc and a stellar over total mass profile decreasing from 45.6_‑8.3^+8.7% at the BGG effective radius to (6.6 ± 1.1)% at R ≈ 77 kpc. Our results confirm that SDSS J0100+1818 is one of the most massive (lens) galaxies known at intermediate redshift and one of the most distant candidate fossil systems. We also show that group-scale systems that act as lenses for ≥3 background sources at different redshifts enable one to estimate the values of the cosmological parameters Ω_m and w with an accuracy that is competitive with that obtained from lens galaxy clusters.