  The estimate of stellar metallicities (Z*) of high-z galaxies are of
paramount importance in order to understand the complexity of dust effects and
the reciprocal interrelations among stellar mass, dust attenuation, stellar
age, and metallicity. Benefiting from uniquely deep FUV spectra of >500
star-forming galaxies at redshifts 2<z<5 extracted from the VANDELS survey and
stacked in bins of stellar mass (M*) and UV continuum slope (beta), we estimate
their stellar metallicities Z* from stellar photospheric absorption features at
1501 and 1719 Angstrom, which are calibrated with Starburst99 models and are
largely unaffected by stellar age, dust, IMF, nebular continuum or interstellar
absorption. Comparing them to photometric based spectral slopes in the range
1250-1750 Angstrom, we find that the stellar metallicity increases by ~0.5 dex
from beta ~ -2 to beta ~ -1 (1 < A(1600) < 3.2), and a dependence with beta
holds at fixed UV absolute luminosity M(UV) and stellar mass up to 10^(9.65)
Msun. As a result, the metallicity is a fundamental ingredient for properly
rescaling dust corrections based on M(UV) and M*. Using the same absorption
features, we analyze the mass-metallicity relation (MZR) and find it is
consistent with the previous VANDELS estimation based on a global fit of the
FUV spectra. Similarly, we do not find a significant evolution between z=2 and
z=3.5. Finally, the slopes of our MZR and Z*-beta relation are in agreement
with the predictions of well-studied semi-analytic models of galaxy formation
(SAM), while some tensions with observations remain as to the absolute
metallicity normalization. The relation between UV slope and stellar
metallicity is fundamental for the exploitation of large volume surveys with
next-generation telescopes and for the physical characterization of galaxies in
the first billion years of our Universe.
