The metal-poorest tail of the Galactic halo: hypothesis on its origin from precise spectral analysis

The origin of the Galactic halo is one of the fundamental topics linking the study of galaxy formation and evolution to cosmology. We aim at deriving precise and accurate stellar parameters, Mg abundances, and ages for a sample of metal-poor stars with [Fe/H] $<$ -2 dex from high signal-to-noise and high resolution spectra. We derive effective temperatures from H$\alpha$ profiles using three-dimensional non local thermodynamic equilibrium (3D NLTE) models, and surface gravities and ages from isochrone fitting based on Gaia data. Iron abundances were derived in one-dimensional (1D) NLTE, while Mg abundances were derived in 1D LTE, 1D NLTE, 3D LTE, and 3D NLTE to show the increasing level of accuracy. The stars show a tight trend in the [Mg/Fe] vs [Fe/H] plane with a knee at [Fe/H]$\sim$ -2.8 dex, which indicates a low level of stochasticity. Their location in the Lindblad diagram confirms their belonging to the Galactic halo, but does not show a distinct clustering that might be expected for a merger with a single low-mass galaxy. Comparison with chemical evolution models is also not definitive on whether the sample stars were born in-situ or in accreted low-mass galaxy mergers. We find two plausible explanations for the chemical sequence traced by the stars in the [Mg/Fe] vs [Fe/H] plane. One is that the sample stars originated in the already formed Milky Way, which at that time (12.5 Gyr ago) was already the main galaxy of its Local Group surroundings. Another one is that the sample stars originated in several small galaxies with similar properties, which later merged with the Galaxy. Only accurate spectroscopic analysis such as that done here can reveal trustworthy chemical diagrams required to observe the traces of the Galaxy evolution. Other elements are required to discern between the two hypotheses.