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arxiv: 2606.13124 · v1 · pith:CV5A3B4Anew · submitted 2026-06-11 · 🌌 astro-ph.GA

Beyond the Fundamental Metallicity Relation: galaxy sizes encode the link between inflow and metallicity

N. F. Boardman , V. Wild , D. Scholte , K. Wang , N. Vale Asari , A. Saintonge This is my paper

Pith reviewed 2026-06-27 06:40 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords galaxy metallicitymass-metallicity relationfundamental metallicity relationgalaxy sizegas inflowstar-forming galaxiesMaNGA surveychemical evolution
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The pith

At fixed stellar mass, galaxy size encodes the link between long-term gas inflow history and present-day metallicity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines why some galaxies at the same stellar mass have different gas-phase metallicities even after accounting for the fundamental metallicity relation with star-formation rate. It finds that inner gas mass is the strongest secondary predictor of metallicity, and that inner gas mass itself correlates tightly with optical galaxy size. Compact galaxies therefore show lower current gas reservoirs and higher metallicities. Chemical evolution models indicate this pattern arises because compact galaxies experienced their main gas inflows earlier, so their gas supply has been declining for longer. Galaxy size at fixed mass thus serves as a proxy for differences in halo assembly and inflow timing that shape chemical evolution.

Core claim

More compact galaxies at fixed stellar mass have lower dynamical masses, lower inner gas masses, and higher metallicities. The strong observed correlation between inner gas mass and size rules out short-term inflow fluctuations as the cause of the residuals. Instead, chemical evolution models show that earlier long-term inflow histories in compact systems produce more rapidly declining gas reservoirs at late times, yielding higher metallicities today. Stellar metallicities and N/O ratios follow the same trends, confirming the link to long-term histories.

What carries the argument

The correlation between inner gas mass (estimated from HI-MaNGA and MaNGA data) and optical size, interpreted through chemical evolution models as a signature of differing long-term inflow histories.

If this is right

  • Compact galaxies have lower dynamical masses than extended galaxies at the same stellar mass.
  • Inner gas mass is the dominant secondary parameter after stellar mass in predicting gas, stellar, and N/O metallicities.
  • Long-term differences in inflow timing produce the observed anti-correlation between size and metallicity at fixed mass.
  • Halo assembly history differences are encoded in present-day galaxy size through their effect on gas reservoir evolution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If size really traces inflow timing, then size-selected samples at fixed mass should show systematic differences in gas depletion timescales that can be checked with future HI and CO observations.
  • The result suggests that semi-analytic models or simulations should reproduce the size-gas mass correlation as a direct consequence of earlier assembly for compact systems.
  • Extending the analysis to higher redshifts could test whether the size-metallicity link strengthens or weakens as average inflow rates change.

Load-bearing premise

The correlation between inner gas mass and optical size is strong enough to exclude short-term inflow fluctuations as the driver of metallicity residuals, and chemical evolution models can be used to attribute the pattern exclusively to differences in long-term inflow timing.

What would settle it

A large sample of star-forming galaxies at fixed stellar mass showing no correlation between optical size and inner gas mass, or showing that short-term inflow variations reproduce the observed metallicity residuals without needing differences in long-term inflow timing.

Figures

Figures reproduced from arXiv: 2606.13124 by A. Saintonge, D. Scholte, K. Wang, N. F. Boardman, N. Vale Asari, V. Wild.

Figure 1
Figure 1. Figure 1: Star-forming sequence (SFS) for our star-forming galaxy samples. Blue points indicate galaxies in our main sample, while purple points indicate galaxies that are also within the MDyn subsample. In the histograms, blue bars indicate the main sample and the red bars the MDyn subsample. We also show galaxies without reliable HI masses with gray points and bars. The dashed line indicates where SFR reaches 1 de… view at source ↗
Figure 2
Figure 2. Figure 2: Top: gas metallicity as a combined function of stellar mass (M∗) and half-light radius (Re), for the MDyn subsample with smoothing applied. We also show the direction of maximum metallicity increase (black arrow). Bottom: as above, but for MDyn. We find MDyn to rise with both increasing M∗ and increasing Re. This suggests that Φe (= M∗/Re) is not a good proxy for the gravitational potential depth, and that… view at source ↗
Figure 3
Figure 3. Figure 3: Top: global HI gas mass (MHI) plotted as a combined function of stellar mass (M∗) and half-light radius (Re) with LOESS smoothing applied. We also show the direction of maximum MHI increase (black arrow), com￾puted using partial correlation coefficients. Middle: as above, but for the HI mass within galaxies’ 90% light radii (MHI,in). We find MHI to rise with both increasing M∗ and increasing Re, consistent… view at source ↗
Figure 4
Figure 4. Figure 4: Spearman correlation coefficients (ρ) between gas metallicity (O/H) and various parameters as indicated in the legend, with p represent￾ing an arbitrary power. We find Mgas,in to yield the highest ρ peak and thus the strongest metallicity correlation, suggesting this parameter to be the most fundamentally connected to metallicity after the stellar mass. We obtained consistent results in this case, meaning … view at source ↗
Figure 5
Figure 5. Figure 5: As in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mass–metallicity relation colored by the three most constraining parameters after M∗ according to our correlation coefficient analysis: Mgas,in (top), MHI,in (middle) or Re (bottom), with LOESS smoothing applied in each case. The error bars show the median errors in stellar mass and metallicity, and the arrows show directions of maximum increase. We find Re to move across the mass-metallicity space in a ne… view at source ↗
Figure 7
Figure 7. Figure 7: Feature importances for determining gas metallicity from a random forest analysis, reported as means and standard deviations across 50 random forest realisations with importances normalised such that they sum to 1. We find M0.7 gas,in/M∗ to be by far the most informative parameter for determining the metallicity. Φe holds little importance by comparison, despite the existence of a tight Φe-metallicity rela… view at source ↗
Figure 8
Figure 8. Figure 8: M0.7 gas,in/M∗ vs. Φe, colored by gas metallicity with smoothing ap￾plied. We also show the direction of maximum increase, computed from par￾tial correlation coefficients. We find the metallicity to vary almost entirely with M0.7 gas,in/M∗, explaining the low importance ascribed to Φe by the ran￾dom forest in [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Inner gas mass vs stellar mass, colored by light-weighted stel￾lar ages at 1 Re with smoothing applied. The arrow shows the direction of maximum increase computed from partial correlation coefficients. Lower gas masses are associated with older ages at fixed M∗, supporting a link between inner gas masses and broad star-formation histories. older at fixed stellar mass. Earlier (later) SFHs can in turn be re… view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of VICE models in terms of inflow rate (left), gas mass (middle) and gas metallicity (right). From models 1-4, p′ and ϵ increase and the total accreted mass decreases (see [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 12
Figure 12. Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: Final states of the twelve VICE models in terms of inner gas mass vs stellar mass (top) and the mass-metallicity relation (bottom). The MaNGA galaxy sample is shown as small gray points. The models show a good coverage of the data, as well as an inverse trend between gas mass and metallicity at fixed M∗ as indicated by the opposite positions of the triangles in upper and lower plots. beyond which effectiv… view at source ↗
Figure 13
Figure 13. Figure 13: Top: effective yield vs gas fraction, plotted for our MaNGA sam￾ple. Bottom: inner effective yield vs inner gas fraction, plotted for the data and for the twelve VICE models with symbols as in [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: N/O–metallicity relation for our twelve models with the J23 yields (top) and tuned yields (bottom) for our twelve VICE models and for the MaNGA sample. Symbols are as in [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The physical interpretation of our results for the chemical evolution of extended and compact star-forming galaxies. Extended galaxies contain more dark matter within their optical extents, resulting in steady late-time accretion of cold metal-poor gas (blue clouds); this results in more massive gas reservoirs and lower present-day metallicities. Compact star-forming galaxies possess less dark matter with… view at source ↗
read the original abstract

Gas-phase chemical abundances are key observable consequences of galaxy evolution, being intrinsically tied to galaxy formation histories. Gas metallicity rises with increasing stellar mass ($\mathrm{M_*}$), forming the well-known mass-metallicity relation (MZR). MZR residuals have separately been shown to anti-correlate with star-formation rate (the ``fundamental'' metallicity relation), with gas mass and with optical size, but no single analysis has considered all trends together. We thus perform a combined analysis of all three trends, utilizing optical MaNGA integral field spectroscopy, HI-MaNGA gas masses, and MaNGA DynPop dynamical masses. We estimate inner gas masses for $\sim$1500 star-forming galaxies, finding this to be the most important parameter after $\mathrm{M_*}$ in predicting gas metallicities. We obtain equivalent results for stellar metallicities and gaseous N/O, suggesting that current inner gas masses are intrinsically linked to long-term chemical evolution histories. We show that more compact galaxies have lower dynamical masses, challenging suggestions that deeper gravitational potentials confer higher metallicities. We find a strong correlation between inner gas mass and galaxy size, meaning that short term inflow fluctuations cannot be responsible for the MZR residuals. With chemical evolution models, we show that our results can instead be explained by differences in long-term inflow histories. The earlier inflow histories of compact galaxies lead to lower gas masses and more rapidly declining gas reservoirs at late times, leading to higher metallicities. At fixed stellar mass, galaxy size therefore encodes the link between halo assembly histories, long-term gas inflow histories, current gas reservoirs and metallicity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript analyzes ~1500 star-forming galaxies using MaNGA integral-field spectroscopy, HI-MaNGA gas masses, and DynPop dynamical masses. It reports that inner gas mass is the strongest predictor of gas-phase metallicity after stellar mass M_*, that inner gas mass correlates strongly with optical size at fixed M_*, and that more compact galaxies exhibit lower dynamical masses. Chemical-evolution models are invoked to interpret the size–metallicity residual correlation as arising from differences in long-term inflow timing rather than short-term fluctuations or deeper potentials, leading to the claim that galaxy size encodes the connection between halo assembly history, long-term gas inflow, current gas reservoirs, and metallicity.

Significance. If the central observational correlations are robust, the work offers a unified empirical picture of MZR residuals that ties an easily measured structural parameter (size) to assembly and accretion history. The combined treatment of SFR, gas mass, and size trends on the same sample is a clear strength, as is the use of public survey data. The result would be of broad interest to galaxy-evolution studies if the exclusion of short-term inflow scenarios can be placed on a quantitative footing.

major comments (2)
  1. [Abstract] Abstract: the assertion that the observed inner-gas-mass versus size correlation 'meaning that short term inflow fluctuations cannot be responsible for the MZR residuals' is presented as a direct logical consequence of the correlation strength. No quantitative test (e.g., forward-modelled mock catalogs with stochastic short-term accretion bursts, selection effects, and measurement uncertainties) is described that demonstrates incompatibility with the data; this step is load-bearing for the central claim that long-term inflow timing is the sole explanation.
  2. [Chemical evolution models] Chemical-evolution-model section: the models invoked to attribute the trends exclusively to long-term inflow history differences must have their parameters (inflow timescales, efficiencies, etc.) shown to be fixed by independent constraints or prior literature rather than tuned to the present MaNGA sample; otherwise the interpretation carries a circularity risk that affects the physical conclusion.
minor comments (1)
  1. [Methods] Methods: the manuscript should explicitly state the precise criteria used to select the ~1500 star-forming galaxies, the aperture definition for 'inner' gas mass, and the full error-propagation procedure for the dynamical-mass and metallicity measurements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback. We respond point by point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the observed inner-gas-mass versus size correlation 'meaning that short term inflow fluctuations cannot be responsible for the MZR residuals' is presented as a direct logical consequence of the correlation strength. No quantitative test (e.g., forward-modelled mock catalogs with stochastic short-term accretion bursts, selection effects, and measurement uncertainties) is described that demonstrates incompatibility with the data; this step is load-bearing for the central claim that long-term inflow timing is the sole explanation.

    Authors: We agree a forward-modeling test with mocks would provide additional support. However, the observed tight correlation between inner gas mass and size at fixed M_* is difficult to produce via short-term stochastic inflows alone, since size is a long-term structural property while short-term fluctuations would primarily add uncorrelated scatter. We will revise the abstract wording to indicate that the correlation supports (rather than directly proves) the long-term interpretation and add a clarifying sentence on this reasoning. revision: partial

  2. Referee: [Chemical evolution models] Chemical-evolution-model section: the models invoked to attribute the trends exclusively to long-term inflow history differences must have their parameters (inflow timescales, efficiencies, etc.) shown to be fixed by independent constraints or prior literature rather than tuned to the present MaNGA sample; otherwise the interpretation carries a circularity risk that affects the physical conclusion.

    Authors: The model parameters (inflow timescales and efficiencies) are taken from standard values in the prior literature on galaxy chemical evolution and are not adjusted to the MaNGA sample. We will revise the section to explicitly cite the independent sources of these parameters and state that they were not tuned to the present data. revision: yes

Circularity Check

0 steps flagged

No significant circularity; observational correlations independent of interpretive models

full rationale

The paper reports direct observational correlations (inner gas mass vs. size at fixed M_*, metallicity trends) from MaNGA/HI-MaNGA data that do not reduce to prior fits or self-definitions. The assertion that the correlation excludes short-term fluctuations and the subsequent use of chemical evolution models for long-term inflow interpretation constitute model-based explanation rather than a derivation that collapses to the inputs by construction. No equations, self-citations, or ansatzes are shown that would make any 'prediction' tautological with the fitted quantities. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the analysis rests on standard survey data reduction and chemical evolution modeling whose internal assumptions are not detailed here.

pith-pipeline@v0.9.1-grok · 5843 in / 1175 out tokens · 30684 ms · 2026-06-27T06:40:56.504669+00:00 · methodology

discussion (0)

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Reference graph

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