The VANDELS survey: The relation between the UV continuum slope and stellar metallicity in star-forming galaxies at z   ∼  3

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 far-UV 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 (β), we estimate their stellar metallicities Z∗ from stellar photospheric absorption features at 1501 and 1719 Å, 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 1250-1750 Å range, we find that the stellar metallicity increases by ∼0.5 dex from β  ∼  -2 to β  ∼  -1 (1 ≲  A1600 ≲  3.2), and a dependence with β holds at fixed UV absolute luminosity MUV and stellar mass up to ∼109.65  M⊙ . As a result, metallicity is a fundamental ingredient for properly rescaling dust corrections based on MUV and M∗. Using the same absorption features, we analyzed the mass-metallicity relation (MZR), and find it to be 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∗ - β relation are in agreement with the predictions of well-studied semi-analytic models (SAM) of galaxy formation, while some tensions remain concerning the absolute metallicity normalization. The relation between the UV slope and stellar metallicity is fundamental to 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.