The NIRVANDELS Survey: the stellar and gas-phase mass-metallicity relations of star-forming galaxies at z = 3.5

We present determinations of the gas-phase and stellar metallicities of a sample of 65 star-forming galaxies at z 3.5 using rest-frame far-ultraviolet (FUV) spectroscopy from the VANDELS survey in combination with follow-up rest-frame optical spectroscopy from VLT/KMOS and Keck/MOSFIRE. We infer gas-phase oxygen abundances (Zg; tracing O/H) via strong optical nebular lines and stellar iron abundances (Z_; tracing Fe/H) from full spectral fitting to the FUV continuum. Our sample spans the stellar mass range 8.5 < log(M_/M_) < 10.5 and shows clear evidence for both a stellar and gas-phase mass-metallicity relation (MZR). We find that our O and Fe abundance estimates both exhibit a similar mass-dependence, such that Fe/H∝ M_0.30±0.11 and O/H∝ M_0.32±0.09. At fixed M_ we find that, relative to their solar values, O abundances are systematically larger than Fe abundances (i.e., α-enhancement).We estimate an average enhancement of (O/Fe) = 2.65 ± 0.16 × (O/Fe)_ which appears to be independent of M_. We employ analytic chemical evolution models to place a novel constraint on the strength of galactic-level outflows via the mass-outflow factor (η). We show that outflow efficiencies that scale as η ∝ M_-0.32 can simultaneously explain the functional form of of the stellar and gas-phase MZR, as well as the degree of α-enhancement at fixed Fe/H. Our results add further evidence to support a picture in which α-enhanced abundance ratios are ubiquitous in high-redshift star-forming galaxies, as expected for young systems whose interstellar medium is primarily enriched by core-collapse supernovae.