We investigate galaxies in the Galaxies at All Redshifts Deciphered and Explained with the NIRSpec microshutter array (MSA; GARDEN) survey that exhibit auroral emission lines, enabling spatially resolved measurements of electron temperature and direct oxygen abundances. Two galaxies in this survey have spectra suitable for this analysis: CANDELS 8005 at z = 3.794 and CANDELS 7986 at z = 4.702. For both galaxies, we measure auroral and key nebular emission-line fluxes across their full extent, allowing direct-method oxygen abundance determinations in individual spatial pixels (spaxels). These observations demonstrate the viability of deep JWST/NIRSpec MSA spectroscopy for spatially resolved chemical analyses at high redshift, aided by weak nebular continua and low interstellar extinction. We derive global direct abundances of log(O/H)+12 = 8.008 (+0.025)(-0.027) for CANDELS 8005 and 7.89 (+0.027)(-0.028) for CANDELS 7986. Emission-line diagnostics indicate neither galaxy hosts an active galactic nucleus. A first-order kinematic analysis suggests a potential merger in CANDELS 8005. The direct abundances are consistent with strong-line estimates based on our data and recent high-redshift calibrations. We build emission line, radial velocity, strong-line abundance indices, electron temperature, and direct abundance maps for both galaxies, thanks to the excellent spatial resolution. From the direct abundance maps, we measure linear radial metallicity gradients of -0.111(-0.025)(+0.026 )dex kpc(-1) for CANDELS 8005 (statistically significant) and -0.0928 +/- 0.0880 dex kpc(-1) for CANDELS 7986, where the large uncertainties limit the significance of the result. These results provide a rare direct measurement of a radial metallicity gradient at z > 0 from direct-method abundances, offering key observational support for inside-out galaxy growth with feedback-regulated chemical enrichment.

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

MOSAIC is the Multi-Object Spectrograph for the ESO-ELT (European Southern Observatory-Extremely Large Telescope). The Laboratoire d'Astrophysique de Marseille (LAM) is in charge of the "Assembly, Integration, Test and Verification (AIT/ V)" activities for both the Front-End channel level and the instrument level in Europe (LAM) and at the Telescope. AITV for AO instruments, in laboratory as well as at the telescope, always represent numerous technical challenges. We already started the preparation and planning for the Front-End and instrument AIT activities, from identification of needs, challenges, risks, to defining the optimal AIT strategy. In this paper, we present the state of this study and describe the MOSAIC AITV organization, give an overview of the Front-End and the Instrument MAIT flows. We also describe the visible and near-infrared channels MAIT flows as well as the different AITV responsibilities during the AITV phases both in Europe and in Chile.

MOSAIC* is the multi-object spectrograph (MOS) for the ESO 39m European Extremely Large Telescope (ELT) approved to enter phase B at the of beginning 2023. MOSAIC combines visible and near-infrared channels, from resolved stars up to the most distant galaxies, with multi-object and multi-integral field spectroscopy capabilities. The NIR-spectrograph (130K-90K) is one sub-system of the NIR-channel, led by the Universidad Complutense de Madrid (UCM, Spain). The NIR Spectrograph (NIRSPEC) comprises 2 identical spectrographs, each one equipped with Teledyne H4RG science detectors (4kx4k, 15 mu m pixels). Each spectrograph operates at 130K (with detectors at 90K) and covers the 2 observing bands J (1 - 1.38 mu m) and H (1.43 - 1.85 mu m in low-resolution mode and 1.52 - 1.65 mu m in high-resolution mode). This paper presents the optical design of the NIRSPEC.