Metallicity of stars formed throughout the cosmic history based on the observational properties of star forming galaxies

Gijs Nelemans; Martyna Chruslinska

arxiv: 1907.11243 · v1 · pith:ZCGVCKSRnew · submitted 2019-07-25 · 🌌 astro-ph.GA

Metallicity of stars formed throughout the cosmic history based on the observational properties of star forming galaxies

Martyna Chruslinska , Gijs Nelemans This is my paper

Pith reviewed 2026-05-24 15:51 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords metallicitystar formation rate densitymass-metallicity relationcosmic star formation historygalaxy scaling relationsstellar populations

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The pith

The fraction of stellar mass formed at low and high metallicities since redshift 3 differs by 18 to 26 percent depending on the mass-metallicity relation chosen.

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

This paper assembles empirical scaling relations from star-forming galaxies to build the distribution of cosmic star formation rate density across metallicities and redshifts. It shows that the share of stellar mass formed below 10 percent solar metallicity since z=3 changes by roughly 18 percent between extreme model choices, while the share above solar metallicity changes by 26 percent. These spreads come mostly from how different methods set the mass-metallicity relation. The resulting model is compared directly to local core-collapse supernova data. The distribution supplies the input needed to calculate rates of stellar-evolution transients such as compact-object mergers.

Core claim

We combine empirical scaling relations and other observational properties of star-forming galaxies to construct the distribution of the cosmic star formation rate density at different metallicities and redshifts; the fraction of stellar mass formed at metallicities below 10 percent solar (above solar) since z=3 varies by about 18 percent (26 percent) between the extreme cases considered, with the spread driven primarily by differences among mass-metallicity relations obtained with different methods.

What carries the argument

The cosmic star formation rate density distribution versus metallicity and redshift, assembled from galaxy scaling relations including the mass-metallicity relation.

If this is right

Rates of stellar-evolution transients such as double compact object mergers and gamma-ray bursts inherit an 18-26 percent uncertainty from the metallicity distribution.
The largest contribution to that uncertainty comes from the choice of mass-metallicity relation.
The publicly released model supplies a concrete input for any calculation that needs the metallicity history of star formation.
Comparison with core-collapse supernova observations provides an external consistency check on the constructed distribution.

Where Pith is reading between the lines

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

Improved absolute calibration of the metallicity scale could shrink the reported spread without changing the underlying galaxy data.
The same framework can be used to propagate the uncertainty into predicted event rates at higher redshifts where direct observations remain sparse.
Future surveys that tighten the low-mass end of the galaxy mass function would mainly affect the low-metallicity tail of the distribution.

Load-bearing premise

The chosen empirical scaling relations, especially the mass-metallicity relations from different methods, correctly capture the true cosmic distribution of star formation across redshifts without major unaccounted systematic offsets.

What would settle it

A measurement of the metallicity distribution among local core-collapse supernovae that falls outside the range spanned by the extreme model cases would show the uncertainty estimate is too narrow.

read the original abstract

Metallicity is one of the crucial factors that determine stellar evolution. To characterize the properties of stellar populations one needs to know the fraction of stars forming at different metallicities. Knowing how this fraction evolves over time is necessary e.g. to estimate the rates of occurrence of any stellar evolution related phenomena (e.g. double compact object mergers, gamma ray bursts). Such theoretical estimates can be confronted with observational limits to validate the assumptions about the evolution of the progenitor system leading to a certain transient. However, to perform the comparison correctly one needs to know the uncertainties related to the assumed star formation history and chemical evolution of the Universe. We combine the empirical scaling relations and other observational properties of the star forming galaxies to construct the distribution of the cosmic star formation rate density at different metallicities and redshifts. We address the question of uncertainty of this distribution due to currently unresolved questions, such as the absolute metallicity scale, the flattening in the star formation--mass relation or the low mass end of the galaxy mass function. We find that the fraction of stellar mass formed at metallicities <10% solar (>solar) since z=3 varies by ~18% (~26%) between the extreme cases considered in our study. This uncertainty stems primarily from the differences in the mass metallicity relations obtained with different methods. We confront our results with the local core-collapse supernovae observations. Our model is publicly available.

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.

Desk Editor's Note private letter to a colleague

This paper stitches together published galaxy scaling relations to produce a metallicity-dependent star-formation distribution with an explicit uncertainty range driven mainly by different MZR calibrations.

read the letter

The useful part is the public model that turns observed mass-metallicity relations, star-formation-mass relations, and the galaxy mass function into a redshift-dependent distribution of star formation across metallicity. They run several published MZRs through the same machinery and report that the stellar mass fraction formed below 0.1 solar since z=3 shifts by roughly 18 percent and the super-solar fraction by 26 percent; most of the spread traces to the absolute scale and low-mass slope of the MZR. They also compare the local end of the model to core-collapse supernova host metallicities, which is a straightforward sanity check. Making the code available is the right move for anyone who needs to fold this into merger-rate or GRB calculations. The construction itself is not a first-principles calculation; it inherits the systematic uncertainties of the input fits. They do vary the low-mass end of the mass function and the SFR-mass flattening, but the paper does not appear to test alternative functional forms for redshift evolution or selection biases in the high-redshift samples that anchor the relations. That keeps the uncertainty estimate tied to the current empirical scatter rather than a broader exploration. The work is aimed at modelers who need a ready-to-use metallicity distribution with error bars for stellar-evolution population synthesis. It is solid enough on its own terms to go to referees; the main value is the quantified envelope rather than any new observational result.

Referee Report

2 major / 3 minor

Summary. The manuscript constructs the distribution of cosmic star formation rate density as a function of metallicity and redshift by combining empirical scaling relations (mass-metallicity relation, star-formation rate-mass relation, galaxy stellar mass function) drawn from observations of star-forming galaxies. It quantifies the uncertainty in the integrated fractions of stellar mass formed since z=3 at metallicities <0.1 Z_⊙ and >Z_⊙ by varying the absolute scale, low-mass slope, and SFR-mass flattening across published calibrations, reporting spreads of ~18% and ~26% respectively; the model is released publicly and compared to local core-collapse supernova metallicity distributions.

Significance. If the central result holds, the work supplies a concrete, observationally anchored envelope on the systematic uncertainty in the metallicity-dependent cosmic star-formation history. This envelope is directly relevant for population-synthesis predictions of metallicity-sensitive transients (compact-object mergers, GRBs). The explicit variation of multiple published relations and the public code release constitute clear strengths that increase reproducibility and allow downstream users to propagate the reported range.

major comments (2)

[§4] §4 (results on fractional stellar-mass contributions): the assertion that 'this uncertainty stems primarily from the differences in the mass metallicity relations' requires a quantitative decomposition (e.g., a table or figure showing the fractional contribution of each varied ingredient—MZR scale, MZR slope, SFR-mass flattening, mass-function low-mass end—to the final 18%/26% envelopes). Without it the 'primarily' qualifier is not demonstrated.
[§3.2] §3.2 (integration over the galaxy mass function): the procedure for extrapolating the adopted MZR below the completeness limit of the observational samples and above z=3 is described only qualitatively; a concrete statement of the functional form used for extrapolation and a sensitivity test to the adopted cutoff mass would strengthen the load-bearing integration step that produces the quoted fractions.

minor comments (3)

[Figure 1] Figure 1 caption: the legend should explicitly list which published MZR calibrations correspond to each colored curve rather than referring only to 'different methods'.
[§2.1] §2.1: the adopted solar metallicity value (Z_⊙) should be stated numerically once, together with the reference, to avoid ambiguity when readers compare the <0.1 Z_⊙ and >Z_⊙ thresholds.
[abstract, §5] The public-model repository link in the abstract and §5 should include the exact commit hash or version tag used for the results presented in the paper.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive recommendation of minor revision. We address each major comment below.

read point-by-point responses

Referee: [§4] §4 (results on fractional stellar-mass contributions): the assertion that 'this uncertainty stems primarily from the differences in the mass metallicity relations' requires a quantitative decomposition (e.g., a table or figure showing the fractional contribution of each varied ingredient—MZR scale, MZR slope, SFR-mass flattening, mass-function low-mass end—to the final 18%/26% envelopes). Without it the 'primarily' qualifier is not demonstrated.

Authors: We agree that the current text does not quantitatively demonstrate the relative contributions. In the revised version we will add a table (or supplementary figure) that isolates the effect of each varied ingredient on the final 18 % and 26 % envelopes, thereby substantiating the statement that MZR variations dominate. revision: yes
Referee: [§3.2] §3.2 (integration over the galaxy mass function): the procedure for extrapolating the adopted MZR below the completeness limit of the observational samples and above z=3 is described only qualitatively; a concrete statement of the functional form used for extrapolation and a sensitivity test to the adopted cutoff mass would strengthen the load-bearing integration step that produces the quoted fractions.

Authors: We will revise §3.2 to state explicitly the functional form adopted for extrapolation (linear in log-metallicity versus log-mass below the completeness limit, and constant metallicity for z>3). We will also include a brief sensitivity test varying the cutoff mass by ±0.5 dex and report the resulting change in the integrated fractions. revision: yes

Circularity Check

0 steps flagged

Empirical synthesis from external scaling relations; no internal circularity

full rationale

The paper constructs the cosmic metallicity distribution of star formation by integrating published empirical relations (MZR variants, SFMS, GSMF) taken from the literature. The quoted fractions and their ~18%/26% spreads are explicit consequences of varying those external calibrations; no step reduces a claimed prediction to a fitted parameter by construction, nor relies on a self-citation chain for a uniqueness theorem or ansatz. The work is a transparent sensitivity study rather than a derivation that is definitionally equivalent to its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on empirical scaling relations that are themselves derived from observational fits; no new entities are postulated.

free parameters (1)

mass-metallicity relation parameters
Different observational methods supply different fitted relations that are adopted as extreme cases for the uncertainty range.

axioms (1)

domain assumption Star-forming galaxies obey the observed scaling relations at all redshifts from z=3 to the present
Invoked to map galaxy properties onto the cosmic star-formation distribution.

pith-pipeline@v0.9.0 · 5790 in / 1119 out tokens · 27524 ms · 2026-05-24T15:51:23.855399+00:00 · methodology

discussion (0)

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