What Sets the Metallicity of Ultra-Faint Dwarfs?

TL;DR

This work addresses why ultra-faint dwarfs (UFDs) around Milky Way–like hosts have their characteristic metallicities. It combines IGM metallicity distributions from state-of-the-art cosmological simulations with a GRUMPY regulator-type semi-analytic model to evolve UFDs in MW-like environments, testing whether external IGM enrichment or internal processes dominate. The key finding is that IGM pre-enrichment cannot explain the observed metallicities or their scatter; instead, internal enrichment regulated by feedback-driven outflows—captured by a maximum wind mass loading factor $\eta_{\rm max}$—sets the metallicities, with $200 \lesssim \eta_{\rm max} \lesssim 2000$ reproducing the observed plateau and scatter. Pop III enrichment of the IGM has little impact on the results, underscoring the central role of outflow physics and motivating further study of $\eta$ in the lowest-mass galaxies and the implied $M_*- M_{\rm h}$ relation.

Abstract

We use intergalactic medium (IGM) metallicity distributions from several state-of-the-art cosmological simulations of Milky Way analogs and a semi-analytic model of ultra-faint dwarf galaxy (UFD) formation to model the stellar metallicities of UFDs in MW-like environments. We study simulations with different treatments of star formation, stellar feedback, and Population III enrichment, and in all cases, we find that only a few percent of the IGM accretable by UFD progenitors is enriched to metallicities $\rm [Fe/H]\ge-4$. When the metallicity of accreted IGM in the semi-analytic galaxy formation model is set using these IGM metallicity distributions, the model underpredicts UFD metallicities and their scatter compared to the observed luminosity--metallicity relation. Our results indicate that IGM enrichment is not the dominant mechanism setting metallicities of UFD stars. Instead, UFD stellar metallicity is determined primarily by the interplay between internal enrichment and metal loss through feedback-driven outflows. We examine models with different values of the maximum outflow mass loading factor $η_{\rm max}$ and show that the full range of average stellar metallicities of UFDs at $M_V<-7$ can be reproduced if the maximum mass loading factor varies in the range $200\lesssimη_{\rm max}\lesssim 2000$. We also consider stellar metallicity distribution functions (MDFs) within individual model galaxies with different assumptions about IGM enrichment and $η_{\rm max}$. We find that all considered models are in reasonable agreement with observed UFD MDFs, with model differences less than the uncertainties of current metallicity measurements.

Figures (7)

• Figure 1: Cumulative distributions of the physical distance to the MW host progenitor (left), virial mass (center), and virial temperature (right) at a redshift $z$ (see legend) of the Caterpillar+GRUMPY UFD progenitors. The properties of mock UFD halos used to sample $Z_{\rm IGM}$ in cosmological simulation are drawn from these distributions. $T_{200}$ is derived from $M_{200}$, but is included to illustrate the temperature range of gas UFD progenitors may accrete.
• Figure 2: Cumulative distributions of the metallicity of gas available for accretion by UFD progenitor halos in the environment around simulated MW analogs at several redshifts. Average stellar metallicities in the GRUMPY model are taken to be defined by the mass of metals and total mass in stars relative to solar. Note that the axis limits vary from panel to panel, however in all model families, only a small fraction of enriched gas is available at the highest and most impactful redshifts. Left: All 8 FIRE-2 m12 simulations, where model-to-model variation in gas availability is sufficiently low that the sample data from all models are combined to create this distribution. These models impose a metallicity floor of $\mathrm{[Fe/H]} \simeq -3.9$. Center: The S25 ART model. Unlike FIRE-2 models, no metallicity floor imposed in the model. The lower [Fe/H] limit of this figure is selected for convenience of visualization to show the distribution in a region below $\mathrm{[Fe/H]} = -4$, however the majority of available gas resides at significantly lower metallicities. Proportionally more gas than for other MW-like models is enriched above $\mathrm{[Fe/H]}=-2$ as this model evolves, however at $z=10$ it is the least enriched. Right: Several MEGATRON models with different feedback or star formation prescriptions are shown with different line styles. Distributions for $z=10$ and $z=8.5$ are shown with the same color scheme as FIRE-2 legend. Lower redshift data is not yet available at the time of writing. Unlike other models shown, MEGATRON models include explicit Pop III stellar prescriptions in addition to no imposed metallicity floor. In general, increasing feedback strength or changing the IMF leads to more available metals in gas near the host galaxy progenitor compared to the fiducial (Efficient SF) model. Similar to the center panel, the majority of available gas resides at significantly lower metallicity than shown.
• Figure 3: Average stellar metallicity vs V-band magnitude for observed and model galaxies in this study. Lines are the median, and shaded or hatched regions contain $68\%$ of model galaxies for a given $M_V$. Red points are observed MW dwarf galaxies reported in Pace_lvdb which have mean spectroscopic metallicities derived using $>5$ stars. All model parameters other than $Z_{\rm IGM}$ are the fiducial values of MK22. For models informed by cosmological simulations, shown in violet, $Z_{\rm IGM}$ is drawn from the distribution categorized in Section \ref{['subsec:accretable gas']}. The MK22 and $Z_{\rm IGM}$$=-4$ models use a constant value. All simulation-informed models, which have very little enriched gas available to UFDs, possess lower average metallicity than observed UFDs, and the intrinsic scatter in all models is significantly less than the intrinsic scatter of observed galaxies. $Z_{\rm IGM}$$=-4$ is included to demonstrate the behavior of a typical metallicity floor, and all simulation-informed models very closely follow this behavior in both the average and scatter regardless of metallicity floor or prescription.
• Figure 4: Metallicity vs $V$-band absolute magnitude relation of galaxies in the models that use S25 and FIRE-2 IGM metallicity distributions and in the model with constant $Z_{\rm IGM}=10^{-4}\, Z_\odot$. Lines show the medians of model galaxies in bins of absolute magnitude and shaded bands contain $95\%$ of galaxies in a particular model; galaxies outside the 95% bands are shown as individual dots. This figure shows that the luminosity--metallicity relation is generally insensitive to the form of $Z_{\rm IGM}$ distribution for $Z_{\rm IGM}<10^{-4}\, Z_\odot$. However, the simulation-informed models produce a tail of galaxies enriched considerably more than the median for their luminosity, which is lacking in the constant $Z_{\rm IGM}=10^{-4}\, Z_\odot$ model. Likewise, the S25-informed model produces a larger fraction of galaxies in the high-metallicity tail than the FIRE-2 informed model because $Z_{\rm IGM}$ in the former is wider and extends to higher metallicities (see Figure \ref{['fig:zigm_cdf']}).
• Figure 5: Same as Figure \ref{['fig:mag-metal_mw-like']}, however the GRUMPY model galaxies shown now vary $\eta_{\rm max}$ with fixed $Z_{\rm IGM}=10^{-4}\, Z_\odot$, a value which produces outputs consistent with the $Z_{\rm IGM}$ distributions categorized in all cosmological simulation-informed models studied in previous sections. Varying $\eta_{\rm max}$ has a profound effect on the location of the plateau, and $200<\eta_{\rm max}<2000$ is sufficient to bracket the entire observed range in average metallicity. Reducing $\eta_{\rm max}$ from the fiducial value of $2000$ to $1000$ almost exactly recovers the same plateau position as the $Z_{\rm IGM}=10^{-3}\, Z_\odot$ model, and the plateau of the $\eta_{\rm max} = 650$ model is well aligned with the median observed UFD metallicity of $\mathrm{[Fe/H]}=-2.48$.