The MUSE Ultra Deep Field (MUDF). V. Characterizing the Mass-Metallicity Relation for Low-mass Galaxies at z ∼ 1-2

Using more than 100 galaxies in the MUSE Ultra Deep Field with spectroscopy from the Hubble Space Telescope's (HST) Wide Field Camera 3 and the Very Large Telescope's Multi Unit Spectroscopic Explorer, we extend the gas-phase mass-metallicity relation (MZR) at z approximate to 1-2 down to stellar masses of M-star approximate to 10(7.5)M(circle dot). The sample reaches 6 times lower in stellar mass and star formation rate (SFR) than previous HST studies at these redshifts, and we find that galaxy metallicities decrease to log(O/H) + 12 approximate to 7.8 +/- 0.1 (15% solar) at log(M-star/M-circle dot) approximate to 7.5, without evidence of a turnover in the shape of the MZR at low masses. We validate our strong-line metallicities using the direct method for sources with [O iii] lambda 4363 and [O iii] lambda 1666 detections, and find excellent agreement between the techniques. The [O iii] lambda 1666-based metallicities double existing measurements with a signal-to-noise ratio >= 5 for unlensed sources at z > 1, validating the strong-line calibrations up to z similar to 2.5. We confirm that the MZR resides similar to 0.3 dex lower in metallicity than local galaxies and is consistent with the fundamental metallicity relation if the low-mass slope varies with SFR. At lower redshifts (z similar to 0.5) our sample reaches similar to 0.5 dex lower in SFR than current calibrations and we find enhanced metallicities that are consistent with extrapolating the MZR to lower SFRs. Finally, we detect only an similar to 0.1 dex difference in the metallicities of galaxies in groups versus isolated environments. These results are based on robust calibrations and reach the lowest masses and SFRs that are accessible with HST, providing a critical foundation for studies with the Webb and Roman Space Telescopes.