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

TL;DR

This study addresses the observational biases that distort measurements of the mass-metallicity relation (MZR) at z~3–6. Using a fully Bayesian forward-modeling framework, the authors combine RUBIES JWST/NIRSpec spectra withProspector-generated synthetic spectra to propagate uncertainties and selection effects—specifically the survey selection function and line-detectability—into the inference of the intrinsic MZR. They show that non-Gaussian metallicity uncertainties and emission-line observability biases significantly alter the observed MZR, flattening the low-mass slope and lowering the normalization by about 0.2 dex, while emission-line measurability can steepen the slope. The resulting intrinsic MZR at high redshift remains flatter and offset below the local relation, emphasizing the importance of forward modeling for comparing high-redshift chemical enrichment to simulations and across cosmic time. This framework sets the stage for robust, bias-aware studies of galaxy metallicities with upcoming deep, wide surveys.

Abstract

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.

Figures (8)

• Figure 1: The emission line and continuum fits for RUBIES ID 37791. The raw spectrum is shown in black, the emission line fits in blue, and the fit reduced to the observed resolution in orange. The four panels correspond to the permutations of grating (PRISM and G395M) and complex (H$\beta$-[O$\;$] and H$\alpha$-[N$\;$]$\lambda 6548,6584$-[S$\;$]$\lambda 6717,6731$). The [N$\;$]$\lambda 6548,6584$ lines are fixed to a 1:2.94 ratio. In the PRISM spectra, the [S$\;$]$\lambda 6717,6731$ doublet is fit with a single Gaussian, and H$\alpha$ is blended with [N$\;$]$\lambda 6548,6584$. We do not use this blended H$\alpha$ measurement for any of our science cases. Subplots below each panel show residuals. Due to an absolute flux offset between measured PRISM and G395M fluxes, we adjust the measured G395M H$\alpha$ flux when comparing with PRISM [S$\;$]$\lambda 6717,6731$ fluxes; see Sec. \ref{['subsec:line_ratios']}. We find that the fitting mechanism is able to successfully reproduce the observed data.
• Figure 2: Metallicity MCMC posterior for RUBIES object 37791. The use of multiple diagnostic metallicity relations does not always completely break the metallicity degeneracy; the double-Gaussian nature of the converged posterior is evident in this figure. We sample from the entire metallicity posterior in our fitting procedure as opposed to assigning a single metallicity value to preserve this uncertainty. The double-branched R3 solutions and the S2 solution are shown in blue and orange, respectively.
• Figure 3: In red we show the RUBIES mass--metallicity points at $z=3-6$. We take the peak of the metallicity posterior distribution as the fixed metallicity for each galaxy. In grayscale we show the RUBIES MZR surface. Each galaxy is sampled 100 times from the metallicity posterior and Gaussian stellar mass uncertainties. The surface exists in two components: a flatter portion below log(M$_\star$/M$_\odot$)$\sim$9, and a positively-sloped portion above that, more akin to the expected behavior of low-redshift MZRs. The local Universe SDSS MZR from curti2020 is shown in blue.
• Figure 4: Our process of modeling the RUBIES selection function. The left panel shows the fraction of galaxies that have confirmed spectroscopic redshifts in bins of F444W and F150W-F444W space that were selected from a parent photometric catalog (weibel2024) for RUBIES targeting on a normalized scale. The middle panel shows our fit to this surface, linear in both magnitude and color. Both the left and middle panel are colored on a normalized scale (yellow being 1, dark blue being 0). The right panel shows the residuals from this fit, with no evidence of structure in the heavily-populated regions, suggesting that we have accurately parameterized the RUBIES selection function to first order. Fitting the selection function plane as opposed to using the raw fraction enables us to assign a weight to the regions of parameter space in which no RUBIES objects were targeted (e.g., the bottom left corner of the first panel).
• Figure 5: This figure illustrates the process by which the prospector matrix is sampled in order to compare to the RUBIES mass--metallicity surface. Each panel is shown on a normalized scale, such that yellow corresponds to 100% of objects in that cell being selected, and dark blue 0%. The first panel shows the initial prospector sample after star formation rate sampling. The second panel shows an example posited MZR in the form of Eqn. \ref{['eqn:mzr_fit']} with mass-independent Gaussian scatter. The third panel shows the effect of the RUBIES selection function applied to the posited MZR, which is to prefer massive galaxies given RUBIES preferential targeting of bright objects. Finally, the fourth panel shows the effect of our ability to measure metallicity; namely emission line strength: dim galaxies with less luminous emission lines are undersampled. In our process, the selection function and metallicity measurability sampling happens prior to the MZR iteration; this figure shows the impact on the shape on a hypothetical given MZR.