Both Stellar Mass and Gravitational Potential Shape the Gas-Phase Metallicity

TL;DR

This work tackles the origin of the galaxy gas-phase metallicity by distinguishing whether metallicity tracks integrated metal production or retention in the gravitational potential. Using MaNGA and SDSS data, the authors apply Random Forest regression and Partial Correlation Coefficients to a broad set of galaxy properties, including photometric and spectroscopic stellar masses, gravitational potential proxies, SFR, and dynamical quantities. They find that the primary drivers are the photometric stellar mass $M_{*,\mathrm{phot}}$ and the stellar baryonic potential $\Phi_* = M_*/R_e$, with their relative importance exhibiting a clear radial dependence: $M_{*,\mathrm{phot}}$ dominates inside $\sim0.7R_e$ while $\Phi_*$ dominates beyond $\sim0.9R_e$. The SFR acts as a secondary factor (7–15% influence) and the sign of its correlation with metallicity depends on radius and mass, consistent with a nuanced version of the Fundamental Metallicity Relation. The study reconciles prior conflicting results by highlighting the critical roles of measurement definitions and spatial scale, and provides a local benchmark for interpreting metallicity evolution in galaxies and at high redshift.

Abstract

The relation between metallicity and galaxy mass (the so-called mass-metallicity relation) is the strongest and most prominent among scaling relations between chemical enrichment and galactic properties. However, it is unclear whether this relation primarily traces metal retention or the integrated production of metals, as past studies have obtained contrasting results. We investigate this issue through an extensive Random Forest and Partial Correlations analysis of spectral cubes of 4,500 galaxies from the MaNGA survey. We find that stellar mass ($\rm M_*$) and baryonic gravitational potential ($\rm Φ_* = M_*/R_e$) are the two most important quantities determining gas metallicity in galaxies. However, their relative roles strongly depend on the galactocentric radius -- the metallicity within 0.7~$\rm R_e$ depends primarily on the stellar mass, while the metallicity at radii beyond 0.9~$\rm R_e$ depends primarily on the gravitational potential. This finding can be interpreted in terms of metals in the central region ($\rm R\leq 0.7~R_e$) being mostly bound, regardless of the global gravitational potential and, therefore, the metallicity is determined primarily by the cumulative production of metals (hence the integrated star formation history, i.e. $\rm M_*$); by contrast, in the galactic peripheries the retention of metals depends more critically on the gravitational potential, hence the stronger dependence of the metallicity on $\rm Φ_*$ at large radii. Our finding reconciles apparent discrepancies between previous results. Finally, we find that the Star Formation Rate is the third most important parameter (after $\rm M_*$ and $\rm Φ_*$) in determining the metallicity, as expected from the Fundamental Metallicity Relation.

Figures (12)

• Figure 1: Bar-chart representing the results from random forest regression of the MaNGA sample for our 14 input features in driving the gas-phase metallicity. The error bars represent the 16th and 84th percentiles from 100 bootstrap random samples. The parameters are described in detail in Table \ref{['tab:manga_rf_parameters']}. The figure shows that the photometric stellar mass is the main driver of the gas-phase metallicity, with secondary, significant dependences only coming from the baryonic gravitational potential and SFR.
• Figure 2: Importances in driving the gas-phase metallicity in annuli (of width $\rm 0.2 R_e$), as a function of Galactocentric radius of the annulus, of the photometric stellar mass $\mathrm{M_{*,phot}}$, photometric baryonic gravitational potential $\mathrm{\Phi_{*,phot}}$, global $\mathrm{SFR}$ from all star-forming spaxels from the pyPipe3D catalogue sanchez_sdss-iv_2022, and integrated $\mathrm{SFR}$ obtained by taking the sum of selected star-forming spaxels within the same annuli. The x-axis corresponds to the radial position of the centre of each $\rm 0.2 R_e$ annulus. The results indicate a spatial variation: at smaller radii, the stellar mass dominates over the baryonic gravitational potential, but this flips toward larger radii ($\mathrm{\gtrsim 0.9 R_e}$).
• Figure 3: Results for the random forest regression for our SDSS sample. As there are no dynamical or spectroscopic mass measurements available, we only include the following parameters: photometric stellar mass $\mathrm{M_{*,phot}}$, $\mathrm{SFR}$, velocity dispersion $\mathrm{\sigma}$, baryonic gravitational potential $\mathrm{\Phi_{*,phot}}$, effective radius $\mathrm{R_e}$, and a random uniform control variable. The error bars represent the 16th and 84th percentiles from 100 bootstrap random samples. Our results again indicate that the gas-phase metallicity is most dependent on the stellar mass.
• Figure 4: 2D histogram of the effective radius versus photometric stellar mass, colour-coded by the gas-phase metallicity for the MaNGA survey. The data is plotted in hexagonal bins, and the grey density contours highlight the distribution of galaxies, with the outer contour corresponding to $90 \%$ the data. The colour coding of each bin gives the average metallicity of the galaxies in that bin; left is for the metallicity within $\rm 1R_e$, while right is for the metallicity within $\rm 2R_e$. The dashed lines indicate the locii at constant $\rm \Phi_*$. The arrow angles are defined in Eq.\ref{['eq:arrow_angle']} and indicate the direction of the average gradient.
• Figure 5: Partial Correlation Coefficients (PCC) between the gas-phase metallicity and several galaxy properties from the MaNGA survey: photometric stellar mass $\mathrm{M_{*,phot}}$, SFR, effective radius $\mathrm{R_e}$, dynamical mass $\mathrm{M_{dyn}}$, dynamical gravitational potential $\mathrm{\Phi_{dyn}}$, velocity dispersion $\mathrm{\sigma_e}$, and a uniform random variable (Random). Left is for the metallicities within $\rm 1R_e$, and right is for the metallicities within $\rm 2R_e$. Blue histograms are for the full sample, while violet histograms are limited to galaxies within $\mathrm{\log{(M_*/M_\odot)}<10.5}$.