The Mass-Metallicity Relation and its Observational Effects at z~3-6

The correlation between galaxy stellar mass and gas-phase metallicity, known as the mass-metallicity relation (MZR), gives key insights into the processes that govern galaxy evolution. However, unquantified observational and selection biases can result in systematic errors in attempts to recover the intrinsic MZR, particularly at higher redshifts. We characterize the MZR at z~3-6 within a fully Bayesian framework using JWST NIRSpec spectra of 193 galaxies from the RUBIES survey. We forward model the observed mass-metallicity surface using prospector-generated spectra to account for two selection biases: the survey selection function and success in observing high signal-to-noise emission lines. We demonstrate that the RUBIES selection function, based on F444W magnitude and F150W-F444W color, has a negligible effect on our measured MZR. A correct treatment of the non-Gaussian metallicity uncertainties from strong-line calibrations lowers the derived MZR normalization by 0.2 dex and flattens the slope by ~20%; forward-modeling the effect of emission line observability steepens the slope by ~15%. Both of these biases must be taken into account in order to properly measure the intrinsic MZR. This novel forward modeling process motivates careful consideration of selection functions in future surveys, and paves the way for robust, high-redshift chemical enrichment studies that trace the evolution of the mass-metallicity relation across cosmic time.