Context. The discrepancy between the predictions of Big Bang nucleosynthesis and the lithium abundance observed in the oldest stars of our Galaxy, known as the cosmological lithium problem, has long been regarded as a challenge to the fields of both cosmology and astrophysics. Aims. In light of recent theoretical advances concerning the transport of chemicals and angular momentum in Population I low-mass stars, we re-examine the stellar depletion hypothesis to explain the lithium plateau, which spans a wide range of metallicities over a specific range of stellar effective temperature. Methods. We computed stellar evolution models with the code STAREVOL, including the same input physics that enable self-consistent reproduction of the Li depletion in the Sun and stars in open clusters, while accounting for internal rotation consistent with asteroseismic constraints. In addition to atomic diffusion and parametric turbulence, which were considered in previous studies of Li depletion along the plateau, our models include rotation-induced hydrodynamical processes and additional parametric viscosity for the transport of angular momentum as well as penetrative convection with a rotational dependence, and magnetic braking. Results. As in the case of Pop I stars, the mixing obtained with the current prescriptions for vertical and horizontal shear turbulence induced by rotation is insufficient to reproduce the Li constraints, and parametric turbulence is required. Even if the nature of the turbulence has yet to be identified, we show that the compactness of Pop II low-mass dwarf stars shall naturally lead to similar Li depletion over a large domain in the [Fe/H]–Teff plane, resulting in a plateau with little dispersion. We calibrated the efficiency of the turbulence to fit the abundance of Li in Pop II stars selected from the GALAH DR3 spectroscopic survey and from an homogeneous reanalysis of abundances from the literature. This calibration also enables the reproduction of lithium and magnesium trends in post-turnoff stars of the globular cluster NGC 6752. The same stellar structure considerations consistently explain the observed change of Li depletion and the dispersion regime for [Fe/H] above −1.5 dex, that is, at the transition in metallicity between Pop II to Pop I stars. Conclusions. Our results provide new constraints to the physical processes that transport chemicals and angular momentum in stellar interiors. They offer a comprehensive way to reproduce the observed Li patterns in low-mass dwarf stars across the entire Galactic metallicity range covered by spectroscopic surveys, including the most Fe-poor regime, as supported by the Li value in the non-CEMP star that lies on the plateau at [Fe/H] below −5.8 dex. Our careful analysis of the other very metal-poor stars with lower Li abundances supports the environmental origin of the so-called meltdown regime. Finally, the expected plateau-to-scatter transition pattern further supports the stellar solution to the cosmological problem.
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