An Investigation into the Low-Mass Fundamental Metallicity Relation in the Local and High-z Universe

TL;DR

To establish a local, low-mass baseline for the Fundamental Metallicity Relation, the authors perform a meta-analysis of approximately 700 [OIII]$\lambda4363$ emitters at $z\sim0$ with $\log(M_{\star}/M_{\odot}) \lesssim 9$. Across minimization, parametric, and non-parametric FMR tests, they find no evidence for a steady FMR below $\log(M_{\star}/M_{\odot}) \lesssim 9$, instead revealing large intrinsic $12+\log(\mathrm{O/H})$ scatter, diverse effective yields $y_{\rm eff}$, and gas-rich, non-equilibrated reservoirs; they further show high-$z$ $[$OIII$]\lambda4363$ systems are about $0.3$ dex more metal-poor at fixed $M_{\star}$ than local counterparts. The study finds extremely high gas fractions and metallicity variations that correlate with star formation and enriched outflows rather than steady inflows, consistent with non-equilibrium gas-regulation models (e.g., Dalcanton 2007). High-$z$ samples ($z\gtrsim 2$) are metal-poor at fixed mass and exhibit stronger FMR offsets, but with comparable ranges in $y_{\rm eff}$, suggesting that non-equilibrium processes dominate metallicity evolution across cosmic time in the low-mass regime. Overall, the low-mass local universe does not support a universal low-mass FMR, providing a critical baseline for interpreting JWST-era high-$z$ metallicities within non-steady gas-regulation frameworks.

Abstract

Recent JWST/NIRSpec observations have revealed high-$z$ star-forming galaxies depart from the Fundamental Metallicity Relation (FMR), yet the $z = 0$ FMR has not been well-characterized in the low-mass regime ($\rm log(M_{\star}/M_{\odot}) \lesssim 9$) for an appropriate comparison of low- and high-$z$ systems. We attempt to rectify this limitation through a meta-analysis, providing a local, observational comparison for future high-$z$ FMR studies. We analyzed common FMR fitting methods for $\sim 700$ [OIII]$λ4363$ emitters with $\rm log(M_{\star}/M_{\odot}) \lesssim 9$ at $z \sim 0$. We find no evidence of the FMR below $\rm log(M_{\star}/M_{\odot}) \lesssim 9$ through any method, suggesting that slowly-evolving, quasi-steady state gas reservoirs are not yet established. We simultaneously find a weak positive correlation between metallicity and star formation, and that these systems are gas-rich with substantial diversity in effective yields ($y_{\rm eff}$) spanning $\rm \sim 3~dex$. We demonstrate increasing $y_{\rm eff}$ correlates with decreasing FMR offsets, which in the context of the analytical and non-equilibrium gas models of Dalcanton et al. (2007), indicates a scenario where star formation bursts rapidly return and eject metals from the ISM before subsequent gas-balancing. Pristine infall diluting the ISM metal-content cannot lead to the $y_{\rm eff}$ diversity we measure, and thus is not the primary process behind FMR deviations. Our results suggest low-$\rm M_{\star}$ systems, regardless of redshift, depart from a steady-state gas reservoir shaping the canonical FMR, in which metallicity variations are primarily driven by star formation and enriched outflows. With this characterization, we demonstrate $z \gtrsim 3$ [OIII]$λ4363$ systems are indeed more metal-poor than $z \sim 0$ counterparts ($\rm Δ12+log(O/H) = 0.3~dex$) at fixed $\rm M_{\star}$.

Figures (7)

• Figure 1: Panel A: The low-$\rm M_{\star}$ MZR with $\rm SFR_{10}$ residuals. The FMRs from Andrews_2013 and Curti_2020 are presented as well, color-coded by the respective $\rm SFR_{10}$ at fixed $\rm log(M_{\star})$. Low-$\rm M_{\star}$ systems demonstrate a gradual decrease in $\rm SFR_{10}$ with $\rm log(M_{\star})$ with large O/H scatter ($\rm \sim 1dex$). We also include an inset normalized histogram of high-$z$ stellar masses from JADES, demonstrating that high-$z$ studies have been extrapolating the locally sampled FMR well over a dex to lower $\rm M_{\star}$. Panel B: Same as panel A, but with $\rm sSFR_{10}$ residuals instead. We include the MZRs from Andrews_2013 and Berg_2022 (CLASSY). Panel C: The SFMS for our low-$\rm M_{\star}$ sample, including the low-$\rm M_{\star}$ SFMS from Popesso_2023 and $\rm 12+log(O/H)$ residuals.
• Figure 2: Panel A: The Curti_2020 minimization with our low-$\rm M_{\star}$ sample overlaid with $\rm SFR_{10}$ residuals. Panel B: Our attempt at minimizing $\rm SFR_{10}$ residuals in the low-$\rm M_{\star}$ regime. We derive $\rm \alpha = -0.1$, which is in distinct contrast to the Curti_2020 ($\alpha = 0.65$) and Andrews_2013 ($\alpha = 0.66$). Our minimization fails to decrease MZR O/H dispersion based on $\rm SFR_{10}$ residuals as $\rm \sigma_{MZR} \approx \sigma_{Min}$. Panel C: System deviations from the Curti_2020 FMR per $\rm log(M_{\star})$ with $\rm sSFR_{10}$ residuals.
• Figure 3: Panel A: A 3D projection of the parameterized Curti_2020 FMR (both calibrated and extrapolated) with our low-$\rm M_{\star}$ fit and sample. The parametrized Curti_2020 FMR clearly intersects our sample distribution, which is relatively uniform at fixed $\rm M_{\star}$ and $\rm SFR_{10}$. Panel B: The same distribution and relations from panel A but in a different projection. Our decreasing parameterized fit is more evident, which explains the $\rm 12+log(O/H)$ residuals within $\rm \Delta FMR$. Panel C: $\rm sSFR_{10}$ relation with $\rm \Delta FMR$ with $\rm 12+log(O/H)$ residuals.
• Figure 4: The non-parametric FMR as proposed by Salim_2014, given by $\rm \Delta sSFR-12+log(O/H)$ (Top Row) and $\rm \Delta sSFR-\Delta MZR$ (Bottom Row). We parse our sample into $\rm 0.5~dex$ bins with respect to $\rm M_{\star}$, as well as including $\rm \Delta FMR$ residuals. We take $\rm \Delta sSFR$ and $\rm \Delta MZR$ relative to the low-$\rm M_{\star}$ SFMS from Popesso_2023 and the CLASSY MZR from Berg_2022, respectively. We include Pearson r and p coefficients per bin to indicate the degree of linearity. The canonical FMR is seen as an inverse correlation that steepens with decreasing $\rm M_{\star}$, but we find uniform distributions in the low-$\rm M_{\star}$ regime, given by low r-values and high p-values. These results are simply a different parameterization of the results of Figures \ref{['MZR']}-\ref{['3d_scatter']}, further indicating a departure from a quasi-steady state gas reservoir in low-$\rm M_{\star}$ systems.
• Figure 5: Panel A: The MZR with $f_{\rm gas}$ residuals. Similar to the MZR with $\rm SFR_{10}$ and $\rm sSFR_{10}$ residuals, there is no correlation between $f_{\rm gas}$ at fixed $\rm M_{\star}$ with $\rm 12+log(O/H)$, which is contrast to the canonical FMR. Panel B: $\rm \Delta FMR$ correlation with $f_{\rm gas}$ with $\rm 12+log(O/H)$ residuals. The majority of our low-$\rm M_{\star}$ sample is extremely gas rich, as expected; we include the median $f_{\rm gas}$ ($\rm 0.95$) as a vertical line. We find no correlation between $f_{\rm gas}$ and $\rm \Delta FMR$, though the strong relationship between $\rm \Delta FMR$ and $\rm 12+log(O/H)$ is present. Panel C: $\rm SFR_{10}$ correlation with $f_{\rm gas}$ with $\rm 12+log(O/H)$ residuals.