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 |$z \simeq 3.5$| 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 (⁠|$Z_{\mathrm{g}}$|⁠ ; tracing O/H) via strong optical nebular lines and stellar iron abundances (⁠|$Z_{\star }$|⁠ ; tracing Fe/H) from full spectral fitting to the FUV continuum. Our sample spans the stellar mass range |$8.5 \lt \mathrm{log}(M_{\star }/\mathrm{M}_{\odot }) \lt 10.5$| 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 |$\mathrm{Fe/H}\propto M_{\star }^{0.30\pm 0.11}$| and |$\mathrm{O/H}\propto M_{\star }^{0.32\pm 0.09}$|⁠. At fixed |$M_{\star }$| 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 |$\mathrm{(O/Fe)} = 2.65 \pm 0.16 \times \mathrm{(O/Fe)_\odot }$| which appears to be independent of |$M_{\star }$|⁠. We employ analytic chemical evolution models to place a constraint on the strength of galactic-level outflows via the mass-outflow factor (⁠|$\eta$|⁠). We show that outflow efficiencies that scale as |$\eta \propto M_{\star }^{-0.32}$| 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. [ABSTRACT FROM AUTHOR]