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REVIEW 4 major objections 5 minor 81 references

Unveiling the galactic baryon cycle process by an empirical model

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read An empirical model anchored to observed scaling relations finds that galaxies recycle 25–75% of their wind ejecta, with the share rising from dwarf to Milky Way-mass halos.

desk verdict A clearly written empirical gas regulator model that derives a mass-dependent recycle fraction from the z=0 MZR, but the headline numbers are fit-dependent and the zero-metallicity accretion assumption is load-bearing. read the letter →

arxiv 2507.12209 v1 pith:FT5NAJIJ submitted 2025-07-16 astro-ph.GA

Yaoxin Chen , Xi Kang , Hong Guo , Hou-Zun Chen , Jiafeng Lu This is my paper · ORCID
classification astro-ph.GA
keywords galaxyevolutionbaryoncyclegasrecyclinggalacticwindscircumgalacticmediummass-metallicityrelationstarformationhistoryempiricalmodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish how much of the gas a galaxy blows out in winds eventually falls back in, and how that fraction depends on dark matter halo mass. The authors build an empirical model in which a galaxy's star formation history is fixed by the observed stellar mass–halo mass relations and its cold gas content is fixed by a calibrated empirical model for atomic and molecular hydrogen, so the only free pieces are the recycling and accretion of gas. Requiring the model to reproduce the observed gas-phase mass–metallicity relation at $z=0$ yields the central result: the recycled fraction rises from about 25% in halos near $10^{10.4}\,M_\odot$ to about 75% in halos near $10^{12}\,M_\odot$, peaking near $10^{11.8}$. If correct, the same feedback law produces very different long-term fuel retention simply because massive halos recycle more of their outflows.

What carries the argument

The machine is the metal budget equation of the chemical evolution model (Equation 10): with fresh accretion assumed metal-free, the interstellar medium metal content is set only by star formation, outflow, and recycled outflow, so the observed mass–metallicity relation fixes the recycle fraction $f_{\rm REC}(M_h)$. The companion gas budget (Equation 7) then fixes the IGM accretion fraction $\epsilon(M_h)$. These two equations are fed by star formation histories from abundance-matching stellar mass–halo mass relations plus mean halo growth histories, cold gas from the NeutralUniverseMachine model, the FIRE-2 mass loading factor, and a simulation-calibrated recycle timescale $t_{\rm REC}(M_h)$.

What would settle it

Measure the metal abundance of gas flowing into galaxies at $z=0$ across the mass range $10^{10.4}$–$10^{12}M_\odot$, for example through ultraviolet absorption-line observations of inflowing gas around isolated galaxies; if inflow metallicities above even a few percent of solar are common, the zero-metallicity accretion assumption fails and the fitted $f_{\rm REC}(M_h)$ curve is not unique.

Watch

Extended reading notes

Core claim

The central claim is that gas recycling is mass-dependent and is the missing ingredient that makes the local mass–metallicity relation come out right. In the fiducial model the recycle fraction $f_{\rm REC}(M_h)$ grows from roughly 25% at $M_h \sim 10^{10.4}M_\odot$ to roughly 75% at $M_h \sim 10^{12}M_\odot$, with a plateau or downturn above that mass. The same fit favors the FIRE-2 mass loading factor, the ratio of outflow rate to star formation rate, over the earlier FIRE-1 value. Extrapolations then yield a halo-level baryon accretion efficiency near 70% and an escape fraction near 80% for non-recycled outflow, with the prediction that circumgalactic medium metallicity rises then flattens at large halo mass.

Load-bearing premise

The result stands or falls on the assumption, stated in Section 2.4, that all gas a galaxy accretes from the intergalactic medium is metal-free; if even mildly enriched gas is coming in, the metal budget no longer isolates recycling, and the inferred recycle and accretion fractions become degenerate with the metallicity of the inflow.

Editorial extensions

If this is right

  • Low-mass halos eject most of their wind gas permanently, while Milky Way-mass halos recycle about three quarters of it, so the gas retention efficiency of a galaxy is largely set by halo mass.
  • The local gas-phase mass–metallicity relation can be reproduced by mass-dependent recycling with the FIRE-2 mass loading factor, without needing a strongly mass-dependent outflow efficiency.
  • The model's quantitative predictions—roughly 70% of the universal baryon supply reaching the halo and 80% of non-recycled outflow escaping into the IGM—give semi-analytic models concrete functions $f_{\rm REC}(M_h)$ and $\epsilon(M_h)$ to adopt.
  • At $M_h(z=0)=10^{12}M_\odot$, metals end up more than half in stars and only a few percent in gas still recycling, while the ISM keeps about 30% at all masses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If even mildly enriched IGM accretion is common at low redshift, the low-mass end of the inferred $f_{\rm REC}$ should be read as an upper limit, because part of the metal budget would enter with the fresh gas rather than with recycled outflows.
  • The model's $z=2$ mass–metallicity overshoot, which the paper attributes to either missing physics or calibration systematics, could be turned into a test: re-fit $f_{\rm REC}$ separately to the $z=2$ MZR. A significantly different curve would indicate redshift evolution of recycling, while no change would point to metallicity-calibration offsets.
  • A natural extension is to let $f_{\rm REC}$ and $t_{\rm REC}$ depend on redshift as well as halo mass; the current data only constrain their mass dependence, and the paper's own CGM/IGM discussion notes that the exchange rates between those reservoirs remain unconstrained.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper presents an empirical 'baryon cycle' model for galaxies at z=0 with halo masses in the range roughly 10^11 to 10^12 M_sun. Star formation histories are constructed by assuming that galaxies always sit on the Girelli et al. (2020) stellar mass-halo mass relation, with halo growth taken from Fakhouri et al. (2010) and cold gas masses taken from the NeutralUniverseMachine of Guo et al. (2023). A gas-regulator chemical evolution model (Eqs. 7-10) is then used, with the z=0 gas-phase mass-metallicity relation as calibration, to fit a halo-mass-dependent recycling fraction f_REC(Mh) and an accretion efficiency epsilon(Mh). With a FIRE-2 mass loading factor the authors obtain f_REC rising from roughly 25% at Mh ~ 10^10.4 M_sun to roughly 75% at Mh ~ 10^12 M_sun, compare epsilon with NIHAO/C16 results, and make predictions for the z=2 MZR, the stellar MZR, the CGM baryon fraction and metallicity, and the metal budget. The abstract advances the 25-75% recycling relation and the CGM values (epsilon_halo ~ 0.7, X ~ 0.8) as the main results.

Significance. If the derived f_REC(Mh) relation is robust, it would provide a rare empirical constraint on wind recycling, a process that is usually accessible only in hydrodynamical simulations, and the preference for the FIRE-2 mass loading factor over FIRE-1 is an interesting, potentially testable conclusion. The paper is transparent in its construction, uses publicly available empirical relations, and its predicted gas fractions agree well with TNG50 (Fig. 3). The high-redshift MZR and CGM predictions are falsifiable in principle, and the authors are candid about the model's limitations. However, the central quantitative claims are currently contingent on a calibration loop, on the zero-metallicity IGM accretion assumption, and on post-hoc choices of epsilon_halo and X, so the significance of the results is conditional on whether these issues can be addressed convincingly.

major comments (4)
  1. [§3.2, Fig. 4, Eq. (10)] The z=0 MZR agreement shown in the lower panel of Fig. 4 is a calibration check, not an independent validation. In Section 3.2 the free function f_REC(Mh) is tuned by MCMC to reproduce the Maiolino et al. (2008) MZR, so the perfect match in the figure is guaranteed by construction rather than being evidence that the model has effectively constrained the recycling process. The text should label Fig. 4 explicitly as a fit, and an out-of-sample statistic (e.g., an independent z=0 metallicity calibrator not used in the fit, or a scatter/yield sensitivity test) is needed before claiming that the MZR imprints f_REC.
  2. [§2.4, Eq. (10)] The zero-metallicity IGM accretion assumption is the load-bearing step, and the paper itself states that the parameter constraints critically rely on it. Dropping the term Z_gas,acc * Mdot_gas,acc attributes the entire metal budget to recycling, outflow, and star formation. Since the time-integrated accreted gas mass is comparable to the stellar mass, even accreted gas with Z_acc ~ 0.1 Zsun would supply a non-negligible fraction of the total metal budget and would change the inferred f_REC(Mh). The authors should add a sensitivity run with nonzero Z_acc or an enriched-accretion model and report the corresponding f_REC(Mh); without that, the quoted 25-75% range is conditional on an assumption that the paper itself identifies as fragile.
  3. [§3.4.1, Fig. 7] The model's main out-of-sample test is currently not passed: with f_REC(Mh) fixed by the z=0 fit, the predicted z=2 gas-phase MZR lies systematically above the Maiolino et al. (2008) z=2.2 and Sanders et al. (2021) z=2.3 measurements. The authors acknowledge this tension but defer it to future work. Because the offset is exactly the signature of f_REC(Mh) absorbing missing physics (enriched accretion, redshift-dependent f_REC, or evolving outflow metallicity), the paper should either quantify how much of the offset can be explained by known metallicity calibration systematics or present the headline f_REC(Mh) relation as provisional.
  4. [§3.4.3, Figs. 9-10, Eq. (15)] The CGM numbers are not predictions in the same sense as the rest of the paper. The choices epsilon_halo = 0.7 and X = 0.8 are selected in Section 3.4.3 specifically because they bring the model into agreement with the halo baryon fractions from Christensen et al. (2016), Tollet et al. (2019), and Hafen et al. (2019), and with the FIRE-2 CGM metallicity from Pandya et al. (2023). The agreement in Figs. 9 and 10 is therefore by construction. The abstract's statement that the model predicts that on average 70% of baryon accretion enters the halo and 80% of non-recycled outflow escapes should be reframed as consistency requirements imposed by simulation constraints, and the degeneracy between epsilon_halo and X should be explored rather than quoting a single pair.
minor comments (5)
  1. [§2.3, Eq. (5)] The text lists the H2 model parameters as ζ0, ζ1, ζ2, µ, and η, but the equation uses ν for the stellar-mass slope and µ is not otherwise defined; the symbol list should be corrected.
  2. [§2.3] There is a typo in 'redshfit' in the sentence defining the halo formation time; it should read 'redshift'.
  3. [§3.4.2, Eq. (14)] The acronym MZR is used for both the gas-phase and stellar mass-metallicity relations; after Eq. (14) it would be helpful to introduce MZR_gas and MZR_* explicitly to reduce ambiguity.
  4. [Abstract, §3.2, §3.4.3] The headline numbers (25-75% recycle fraction, 70% halo accretion, 80% escape) are quoted without uncertainties; showing the MCMC credible intervals for f_REC(Mh) and epsilon(Mh) would put these central claims on a firmer statistical footing.
  5. [Fig. 9] The claim that the epsilon_halo = 1.0 model is 'significantly higher' than the simulation results is made visually; a simple quantitative comparison (e.g., residuals or a goodness-of-fit value) would make the choice of epsilon_halo = 0.7 more transparent.

Circularity Check

2 steps flagged · score 6.0 of 10

The z=0 MZR 'prediction' is the calibrating data refit, and the 70%/80% baryon-cycle numbers are selected grid parameters reported as predictions; the genuinely out-of-sample z=2 and stellar MZR tests remain.

  1. fitted input called prediction [Section 3.4.1, Figure 7 (cf. Section 3.2)]
    "Our MZR prediction at z= 0 shows excellent agreement with the local universe observations of Maiolino et al. (2008), as expected since these data were used to calibrate our model parameters."

    Section 3.2 explicitly uses the observed z=0 gas-phase MZR as the constraint to fit f_REC via Equation 10 and MCMC. The 'prediction' shown in Figures 4 and 7 at z=0 is the same observable used in the likelihood, so perfect agreement is guaranteed by the fit, not by the model's physics. The paper's own wording 'as expected' confirms that this is a calibration check rather than an independent prediction. This does not invalidate the fitted f_REC(Mh) relation, but the agreement cannot be counted as independent support for the model.

  2. fitted input called prediction [Section 3.4.3, Figures 9/10; Abstract]
    "In this study, we test a few cases for ϵhalo and X with ϵhalo = 1.0, ϵhalo = 0.7 and X= 0.0,0.5,0.8. ... It is found from the right panel that a model with ϵhalo = 0.7 and X= 0.8 agrees better with the simulation results."

    These values are chosen from a small grid by comparing with the hydrodynamical-simulation baryon fractions in Figure 9; the Abstract then reports 'our model predicts that on average 70% ... and 80% ...' as if they were outputs. For the quantity used in the selection (total baryon fraction within the halo), agreement is by construction. The CGM metallicity comparison in Figure 10 is a partly independent check, and the paper openly says these are constraints, so this is a labeling/framing circularity rather than a hidden one, but the headline numbers are calibrated inputs, not out-of-sample predictions.

full rationale

Most of the derivation chain is self-contained: SFHs come from SHMR plus halo growth, cold gas comes from NeutralUniverseMachine, and the chemical evolution equations (9/10) are stated explicitly. The central f_REC(Mh) result is a fit, not a prediction, and the paper is transparent about this. Genuinely out-of-sample tests exist: the z=2 gas-phase MZR is not used in calibration and is actually in tension with observations, and the stellar MZR is not used in calibration and lies within the spread of simulations. The main circularity is framing: Figure 4's z=0 MZR agreement and the 70%/80% CGM numbers are fit/selection outputs presented as predictions. The zero-metallicity-accretion assumption, explicitly flagged by the authors in Section 2.4, does not by itself create circularity but does make the f_REC constraints degenerate if it is relaxed. No load-bearing self-citation chain was found: Chen et al. (2023) and Guo et al. (2023) supply method/inputs with independent external calibrations. Hence partial circularity (score 6) from the two fitted-as-prediction items, with real independent content remaining.

Assumptions & free parameters 8 free parameters · 10 assumptions · 0 invented entities

The paper's four own free choices are f_REC(Mh), epsilon(Mh), epsilon_halo, and X. The first two are MCMC-fitted to the z=0 MZR and gas bookkeeping; the last two are selected from a small grid to match simulation CGM constraints. The remaining entries are adopted fits from prior work (SHMR, NeutralUniverseMachine, FIRE mass loading, and the authors' own t_REC fit to simulation recycling times) that the derivation depends on but does not re-fit. This counts what the paper pulls from the literature.

free parameters (8)
  • f_REC(Mh) recycle fraction = 25% at 10^10.4 Msun, 75% at 10^12 Msun, peak near 10^11.8 Msun
    Free parameter fitted via MCMC to reproduce the z=0 gas-phase MZR (Maiolino et al. 2008) using Equation 10; the shape of f_REC(Mh) is the central result of the paper.
  • epsilon(Mh) accretion fraction = about 40% at Mh ~ 10^11.5 Msun, with a peak around 10^11.6 Msun
    Free parameter obtained from Equation 7 after f_REC is fixed; controls the fresh gas accretion rate in Equation 13. It is effectively fitted to the cold gas evolution from the NeutralUniverseMachine model.
  • epsilon_halo = 0.7 (also tested 1.0)
    Chosen to match the baryon fraction-halo mass relation from hydro simulations (Christensen et al. 2016; Tollet et al. 2019; Hafen et al. 2019) in Section 3.4.3. Not fitted by MCMC but selected from a small grid.
  • X = 0.8 (also tested 0.0 and 0.5)
    Fraction of non-recycled outflow escaping the halo; chosen so that predicted CGM metallicity matches FIRE-2 (Pandya et al. 2023). This is a tuned parameter, presented as a prediction in the abstract.
  • t_REC(Mh) recycle time = alpha0=4.02, alpha1=-0.28 (Equation 12)
    Fitted to recycle time results from NIHAO, EAGLE, FIRE, C16, and Auriga simulations; used as input to the gas cycle model. This is the paper's own fit to external simulation data.
  • NeutralUniverseMachine parameters (15) = See Guo et al. (2023), Equations 17-22
    The cold gas content and its evolution are taken from the empirical NeutralUniverseMachine model, which has 15 parameters fitted to HI and H2 observations across 0<z<6. These are prior fitted inputs, not fitted here, but the baryon cycle constraints depend on them.
  • SHMR parameters (A, MA, beta, gamma as functions of z) = Best-fit from Girelli et al. (2020) Table 4, linearly extrapolated to lower masses
    The SHMR is used to derive SFHs by assuming galaxies always lie on the relation. These are external fits, adopted as inputs; extrapolation to lower mass is an unvalidated extension.
  • eta_m mass loading factor = FIRE-2 fitting relation (Pandya et al. 2021); FIRE-1 as test
    Input adopted from simulations; the choice of FIRE-2 over FIRE-1 is based on better agreement with observations (Figure 1), and the model results depend on this input.
assumptions (10)
  • domain assumption Galaxies always follow the mean SHMR at every redshift
    SFHs are computed by differentiating the SHMR along each halo growth track (Section 2.1-2.2); any lag or scatter around the relation changes the SFH and every downstream cycle constraint.
  • domain assumption Mergers are negligible for Mh < 10^12 Msun
    Section 2.1 assumes stellar mass growth is entirely from star formation; if mergers contribute, inferred SFRs and outflow rates are biased high.
  • domain assumption IGM accretion is primordial, Z_gas,acc ~ 0
    Section 2.4 states parameters 'critically rely' on this; it isolates the recycling term in the metal equation. Enriched accretion introduces degeneracies between f_REC and epsilon.
  • domain assumption Outflow metals follow outflow gas exactly
    Recycling of metals is assumed to have the same fraction and timescale as gas (Section 2.5, 3.4.3); if outflows are metal-enriched or have different fates, CGM metallicity predictions and X change.
  • domain assumption f_REC and t_REC depend only on halo mass
    Section 2.5 sets both as functions of Mh alone; the authors acknowledge redshift dependence is ignored, which may explain the z=2 MZR tension.
  • domain assumption NeutralUniverseMachine cold gas model is accurate
    HI and H2 masses are taken from Guo et al. (2023) with 15 fitted parameters (Section 2.3); errors in that empirical model propagate into epsilon and f_REC.
  • domain assumption Mean halo mass accretion rate of Fakhouri et al. (2010) applies to all model halos
    Halo growth tracks come from integrating Equation 2; individual assembly histories scatter around the mean and are ignored.
  • domain assumption Chabrier IMF, R=0.44, y_Z=0.06
    Adopted from Vincenzo et al. (2016) (Section 2.2, 2.4); these set the conversion between stellar mass growth and SFR, and the metal production rate.
  • domain assumption Maiolino et al. (2008) MZR is the correct metallicity calibration at z=0
    The model is calibrated to this MZR; Section 3.2 notes other MZRs (Sanders et al. 2021; Andrews & Martini 2013) differ substantially, so the fitted f_REC is calibration-dependent.
  • domain assumption Equation 15 partitions baryons in the halo with constant epsilon_halo and X
    CGM mass and metallicity predictions use a constant halo accretion fraction and a constant escape fraction; simulations find mass-dependent behavior, which the model partly absorbs by tuning.

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Cite this review

Pith. "Pith review of Unveiling the galactic baryon cycle process by an empirical model." pith.science (2026). https://pith.science/paper/FT5NAJIJ

@misc{pith2026250712209,
  author       = {Pith},
  title        = {Pith review of: Unveiling the galactic baryon cycle process by an empirical model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FT5NAJIJ}},
  note         = {Machine review of arXiv:2507.12209}
}
abstract

We propose an empirical model to describe and constrain the baryon cycle process during galaxy evolution. This model utilizes the evolution of star formation rate, derived from the stellar mass-halo mass relations (SHMRs) across different redshifts, and the cold gas content, derived from the NeutralUniverseMachine model, to constrain gas accretion and recycle of gas outflow in the model galaxy. Additionally, through detailed modeling of each cycle process, particularly the recycling process, and utilizing the gas-phase mass-metallicity relation (MZR) at $z=0$ as a constraint, our model establishes a relation between the recycle fraction and halo mass. It is found that the fraction of gas recycled from the outflow is a function of halo mass, with a value of $25\%$ in galaxies with halo mass $\sim10^{10.4}M_{\rm \odot}$, increasing to $75\%$ in halos with mass $\sim 10^{12}M_{\rm \odot}$. We also find that the mass loading factor from the FIRE-2 simulation matches well with the constraints from both observational data and our model. Furthermore, using the gas content and metallicity of the circumgalactic medium (CGM) obtained from hydrodynamical simulations as constraints, our model predicts that on average $70\%$ of universal baryon accretion is accreted to the halo and $80\%$ of the non-recycled gas in the outflow has escaped from the galaxy, entering the intergalactic medium (IGM). However, we note that future observational data are needed to finally constrain the mass and metal exchange between the CGM and the IGM.

Figures

Figures reproduced from arXiv: 2507.12209 by the authors.

Figure 1
Figure 1. The input mass loading factor ηm(M∗) adopted from simulations (black lines). The dashed black and solid black lines are the fitting relations from the FIRE-1 simula￾tion (Muratov et al. 2015) and FIRE-2 simulation (Pandya et al. 2021), respectively. All scattered dots represent the data from observations, including Chisholm et al. (2017), McQuinn et al. (2019), Kado-Fong et al. (2024). It is seen that result from th… view at source ↗
Figure 2
Figure 2. The input recycle time tREC(Mh) adopted from simulations (black line). The black line represents the fitting result across multiple hydrodynamic simulations, including NIHAO simulation (Tollet et al. 2019), EAGLE simulation (Mitchell et al. 2020a), FIRE simulation (Angl´es-Alc´azar et al. 2017), C16 simulation (Christensen et al. 2016) and Auriga simulation (Grand et al. 2019). two parameters may indeed depend on re… view at source ↗
Figure 3
Figure 3. The prediction of cold gas for ten model galax￾ies obtained by NeutralUniverseMachine model (Guo et al. 2023). The evolutions of both gas mass and gas fraction are presented in the top and middle panel, respectively. Bottom panel: the gas fraction as a function of stellar mass at z = 2 and z = 0 (the µgas − M∗ relation). The model predictions are shown as filled color circles connected by the solid black line (z = 0… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: The best-fit results for parameter fREC(Mh) and the corresponding predicted gas-phase mass-metallicity rela￾tion (MZR) at z = 0. Upper panel: the best fitting results for parameter fREC(Mh) for two different mass loading factors (black lines). The solid line represents…
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: We find that for our model galaxies, the gen￾eral trend of accumulate accretion fraction with the halo mass at z = 0 agree with results from a few simulations. Specifically, the accumulative accretion fraction gradu￾ally increases as the halo mass at z = 0 increases fr…
Figure 7
Figure 7. Figure 7: The gas-phase mass-metallicity relation (MZR) at z = 2. Model prediction: The MZRs predicted by our fiducial model are shown as colored scatter points. Different shapes represent different redshifts, such as circles for z = 0 and triangles for z = 2. Observations: The …
Figure 8
Figure 8. Figure 8: The stellar mass-metallicity relation (MZR∗) at z = 0. The prediction of our fiducial model for MZR∗ at z = 0 is shown as color circles connected by the solid black line. The light color lines correspond to results from Garcia et al. (2024) for Illustris simulation (bl…
Figure 9
Figure 9. Figure 9: The total baryon fraction within halo (scaled by the cosmic baryon fraction) as a function of halo mass at z = 0. The prediction of our model are presented by colored scatters in both panels, but with different parameters (detailed in text). The result of simulations i…
Figure 10
Figure 10. Figure 10: The metallicity in the circumgalactic medium (CGM) as a function of halo mass at z = 0. The pre￾dictions of our model are represented by colored circles (ϵhalo = 0.7, X = 0.0), crosses (ϵhalo = 0.7, X = 0.5) and stars (ϵhalo = 0.7, X = 0.8) connected by various lines,…
Figure 11
Figure 11. Figure 11: Amount of metals in each component at z = 0 for model galaxies in fiducial model, including the metal locked in stars (orange), in ISM (blue), undergoing recycle process (red) and that will never re-accreted into the galaxy again (gray). the metal content into four co…

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