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arxiv: 2604.11885 · v1 · submitted 2026-04-13 · 🌌 astro-ph.HE · astro-ph.GA· astro-ph.SR

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Distinct First-to-Second Peak Yield Ratios and Timescales Reveal a Sub-dominant Prompt Channel

Kenta Hotokezaka, Paz Beniamini, Yossef Zenati

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:55 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.GAastro-ph.SR
keywords r-processchemical evolutionneutron star mergersstellar abundancess-processfirst peak elementseuropiumyield ratios
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The pith

Stellar [Y/Eu] trends require a prompt first-peak channel, dominant delayed r-process, and late AGB s-process

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

Stellar observations show non-monotonic evolution in [Y/Eu] and [Sr/Eu]: the ratios decline with increasing [Eu/H] at low metallicity, reach a minimum near [Eu/H] ~ -0.3, then rise at higher metallicity. This pattern demands at least three separate neutron-capture sources with distinct timescales. A one-zone chemical-evolution model reproduces all features when a prompt channel supplies most first-peak elements with little europium, a delayed r-process channel (most likely binary neutron-star mergers) supplies nearly all europium, and a delayed AGB s-process supplies the late upturn in yttrium and strontium after 0.3-0.6 Gyr. The model fixes the prompt yield ratio at [Y/Eu] ~ -0.3 and the delayed r-process ratio at ~ -0.8 while matching the full 0.6 dex amplitude and the location of the minimum.

Core claim

Reproducing the observed [Y/Eu] and [Sr/Eu] sequences requires a delayed r-process channel dominating Eu production (≳95% of total Eu), a prompt channel preferentially producing first-peak elements with minimal Eu, and delayed AGB s-process enrichment with delays greater than t_min = 0.3-0.6 Gyr. The first-to-second peak yield ratios correspond to [Y/Eu] ≈ -0.3 (prompt) and ≈ -0.8 (BNS mergers). The observed Δ[Y/Eu] amplitude establishes a model-independent lower limit on the first to second peak yield ratio ≳3.4 between the prompt and delayed channels.

What carries the argument

A one-zone chemical-evolution model that superposes three sources with fixed yield ratios and characteristic delay times to track the buildup of first- and second-peak elements.

If this is right

  • The prompt channel must have a first-to-second peak yield ratio at least 3.4 times higher than the delayed r-process channel.
  • Binary neutron-star mergers dominate europium production across the Galaxy.
  • AGB s-process enrichment begins only after a minimum delay of 0.3-0.6 Gyr.
  • All quantitative constraints including the 0.6 dex amplitude and the location of the minimum at [Eu/H] ~ -0.3 are simultaneously satisfied.

Where Pith is reading between the lines

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

  • The same three-channel structure should produce analogous non-monotonic trends in other first-peak to second-peak ratios such as [Sr/Eu] or [Zr/Eu].
  • The prompt channel is likely a rare, short-timescale event such as certain core-collapse supernovae or magnetorotational supernovae whose yield patterns can be tested against metal-poor star data.
  • Extending the model to include inhomogeneous mixing would test whether the observed scatter at low metallicity is consistent with the well-mixed assumption.
  • The derived rates and delay-time distributions can be compared directly to binary population synthesis predictions for neutron-star mergers.

Load-bearing premise

The observed non-monotonic abundance trends are produced solely by the superposition of three sources with fixed yield ratios and characteristic delay times inside a one-zone, well-mixed interstellar medium.

What would settle it

Spectroscopic measurements showing that [Y/Eu] does not increase below [Eu/H] ≲ -2.5 or that the amplitude of the variation between the minimum and late-time rise is substantially smaller than 0.6 dex would falsify the required separation in yield ratios and delay times.

Figures

Figures reproduced from arXiv: 2604.11885 by Kenta Hotokezaka, Paz Beniamini, Yossef Zenati.

Figure 1
Figure 1. Figure 1: SAGA database T. Suda et al. (2008, 2011, 2017) stellar data (MW stars in grey and dwarf galaxies in color) of [Y/Eu],[Ba/H] vs [Eu/H] (left) and [Y/H] and [Ba/H] vs [Eu/H] (right). We over-plot (blue lines) the fiducial three-channel model presented in this work with r, s process contributions as given in Tab.B1. With these observational indications of a prompt channel producing mostly first-peak elements… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic overview of the enrichment channels included in our fiducial one-zone model and how they map onto the abundance trends analyzed in this work. We in￾clude a prompt, primarily first-peak producing, channel (A), and a delayed BNS-merger channel (B). First-peak enrich￾ment additionally receives a delayed AGB s-process (chan￾nel C) component with long delays compared to channel B. The prompt channel s… view at source ↗
Figure 3
Figure 3. Figure 3: [Y/Eu] versus [Y/Ba] for MW (gray) and dwarf galaxies (color), overlaid with the fiducial one-zone chemical-evolution track. Markers indicate cosmic time along the model trajectory. Early times reflect increased prompt contribution (channel A) to first peak production, intermediate times move toward a more Eu-rich mixture as the delayed BNS channel B becomes important, and late times deviate as AGB s-proce… view at source ↗
read the original abstract

Stellar abundances reveal non-monotonic [Y/Eu] and [Sr/Eu] evolution, a systematic decline with increasing [Eu/H] at low metallicity, a minimum at $[\rm{Eu/H}] \sim -0.3$ and then a rise at high metallicity. This behavior requires at least three distinct neutron-capture sources operating on different timescales. We develop a one-zone chemical-evolution model constraining their typical delay-times, rates, and yield ratios. Reproducing the observed $\rm{[Y/Eu]}$ and $\rm{[Sr/Eu]}$ sequences requires, a delayed $r$-process channel (most likely binary neutron-star mergers) dominating Eu production ($\gtrsim 95\%$ of total Eu). A prompt channel preferentially producing first-peak elements with minimal Eu, explaining the increasing [Y/Eu] at decreasing [Eu/H] below $[\rm{Eu/H}] \lesssim -2.5$; and delayed AGB $s$-process enrichment with delays greater than $t_{min} = 0.3-0.6$\,Gyr reproducing the late-time upturn in Y (Sr). Our model quantitatively reproduces all constraints, including the large $\Delta[\rm{Y/Eu}] \approx 0.6$ dex variation between the late-time rise [Eu/H] and the minimum value, the location of the minimum at [Eu/H] $\sim -0.3$ and late-time rise. The first-to-second peak yield ratios correspond to $[\rm{Y/Eu}] \approx -0.3$ (prompt) and $\approx -0.8$ (BNS mergers). The observed $\Delta[\rm{Y/Eu}]$ amplitude establishes a model-independent lower limit on the first to second peak yield ratio $\gtrsim 3.4$ between the prompt and delayed channels, ruling out models with similar prompt and delayed yield ratios. These results demonstrate that explaining the observed heavy-element abundance patterns requires multiple channels with distinct nucleosynthetic signatures and operational timescales, providing constraints on the relative rates, delay times, and yield patterns of candidate production sites.

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

3 major / 2 minor

Summary. The paper develops a one-zone chemical-evolution model to explain the observed non-monotonic trends in [Y/Eu] and [Sr/Eu] versus [Eu/H], which show a decline at low metallicity, a minimum near [Eu/H] ≈ −0.3, and a late-time rise. It argues that reproducing these sequences requires three distinct neutron-capture channels: a prompt first-peak channel with minimal Eu, a delayed r-process channel (likely BNS mergers) supplying ≳95 % of Eu, and a delayed AGB s-process channel with minimum delay 0.3–0.6 Gyr. The model is stated to quantitatively match the 0.6 dex amplitude, the location of the minimum, and the late upturn, while also providing a model-independent lower limit ≳3.4 on the first-to-second peak yield ratio between prompt and delayed channels.

Significance. If the central claim holds, the work supplies useful constraints on the relative rates, delay times, and yield patterns of candidate r-process and s-process sites. The model-independent lower limit on the yield-ratio amplitude is a clear strength that does not rely on the details of the one-zone fit and directly rules out scenarios with similar prompt and delayed yields. The explicit separation of prompt and delayed contributions also offers a concrete target for future nucleosynthesis calculations and rate estimates.

major comments (3)
  1. [Abstract and §4] Abstract and §4 (model results): the assertion that the model “quantitatively reproduces” the observed sequences and the 0.6 dex amplitude is made without any description of the fitting procedure, goodness-of-fit metric, or exploration of alternative parameter choices. The four free parameters (prompt [Y/Eu], BNS [Y/Eu], t_min, and Eu fraction from BNS) are adjusted until the model matches the data, so the reproduction reduces to a consistency check rather than an independent test.
  2. [§2] §2 (one-zone model): the necessity of a distinct prompt channel with fixed high [Y/Eu] rests on the assumption of a well-mixed, homogeneous ISM with linear superposition of sources. At [Eu/H] ≲ −2 the enrichment is dominated by individual events; the manuscript does not demonstrate that stochastic enrichment or modest metallicity dependence in the delayed-channel yields cannot produce comparable non-monotonic trends, which would weaken the claim that three fixed-yield channels are required.
  3. [§4 and abstract] §4 and abstract: while the model-independent lower limit ≳3.4 on the first-to-second peak yield ratio is robust, the specific quoted values ([Y/Eu] ≈ −0.3 prompt, ≈ −0.8 BNS, 95 % Eu from BNS) are obtained by construction from the same fit that is used to claim reproduction; this circularity should be stated explicitly when presenting the “quantitative” match.
minor comments (2)
  1. [Figures] Figure captions and text should explicitly state whether the plotted model curves include any uncertainty bands arising from parameter variations or data errors.
  2. [Throughout] Notation for abundance ratios should be uniform (e.g., always [Y/Eu] rather than Y/Eu) to avoid ambiguity.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive and detailed comments, which have improved the clarity of our presentation. We respond point-by-point to the major comments below and have made revisions where appropriate to address concerns about parameter exploration and explicit statements on model independence.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (model results): the assertion that the model “quantitatively reproduces” the observed sequences and the 0.6 dex amplitude is made without any description of the fitting procedure, goodness-of-fit metric, or exploration of alternative parameter choices. The four free parameters (prompt [Y/Eu], BNS [Y/Eu], t_min, and Eu fraction from BNS) are adjusted until the model matches the data, so the reproduction reduces to a consistency check rather than an independent test.

    Authors: We agree that the original text did not describe the parameter selection process in sufficient detail. In the revised manuscript we have added a new subsection in §4 that outlines a systematic grid search over the four free parameters, with the combination chosen to simultaneously match the location of the minimum, the 0.6 dex amplitude, and the late-time upturn in both [Y/Eu] and [Sr/Eu]. We have also replaced the phrase “quantitatively reproduces” with “reproduces the principal observed features” to reflect that the exercise is a consistency check within the one-zone framework. The central claim—that no two-channel model reproduces the non-monotonic trend—remains unchanged, as it holds across the explored parameter space. revision: yes

  2. Referee: [§2] §2 (one-zone model): the necessity of a distinct prompt channel with fixed high [Y/Eu] rests on the assumption of a well-mixed, homogeneous ISM with linear superposition of sources. At [Eu/H] ≲ −2 the enrichment is dominated by individual events; the manuscript does not demonstrate that stochastic enrichment or modest metallicity dependence in the delayed-channel yields cannot produce comparable non-monotonic trends, which would weaken the claim that three fixed-yield channels are required.

    Authors: This limitation of the one-zone approximation is valid. We have added a paragraph in §2 that explicitly acknowledges the potential role of stochastic enrichment at the lowest metallicities and notes that the observed trends extend to [Eu/H] ≈ −0.3, where the ISM is expected to be well mixed. While we argue that the specific amplitude and minimum location are most naturally explained by distinct channels, we cannot rule out all stochastic or metallicity-dependent alternatives without new simulations. revision: partial

  3. Referee: [§4 and abstract] §4 and abstract: while the model-independent lower limit ≳3.4 on the first-to-second peak yield ratio is robust, the specific quoted values ([Y/Eu] ≈ −0.3 prompt, ≈ −0.8 BNS, 95 % Eu from BNS) are obtained by construction from the same fit that is used to claim reproduction; this circularity should be stated explicitly when presenting the “quantitative” match.

    Authors: We agree and have revised both the abstract and §4 to state explicitly that the numerical values for the prompt and BNS yield ratios and the 95 % BNS contribution to Eu are taken from the best-fit model, whereas the lower limit ≳3.4 follows directly from the observed 0.6 dex amplitude and does not depend on the particular parameter values adopted. revision: yes

standing simulated objections not resolved
  • A full demonstration that stochastic enrichment or modest metallicity dependence in delayed-channel yields cannot produce the observed non-monotonic trends would require dedicated stochastic chemical-evolution simulations that lie outside the scope of the present one-zone study.

Circularity Check

0 steps flagged

No significant circularity; standard parameter fitting to data

full rationale

The paper builds a one-zone chemical-evolution model with free parameters for delay times, rates, and yield ratios of three channels, then tunes those parameters until the model matches the observed [Y/Eu] and [Sr/Eu] trends. This is ordinary forward modeling and parameter estimation, not a derivation in which any claimed result is definitionally identical to the input data or to a prior self-citation. The model-independent lower-limit statement on the yield-ratio amplitude is presented as arising directly from the observed Δ[Y/Eu] amplitude without further fitting. No equations are shown that equate a fitted quantity to a 'prediction' by construction, and no load-bearing premise rests solely on an unverified self-citation chain. The derivation therefore remains self-contained against external abundance data.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 1 invented entities

The central claim rests on a one-zone mixing assumption, constant per-channel yields, and several parameters whose values are chosen to match the observed abundance trends.

free parameters (4)
  • prompt [Y/Eu] yield ratio = -0.3
    Chosen to reproduce the rise in [Y/Eu] at [Eu/H] ≲ -2.5
  • BNS [Y/Eu] yield ratio = -0.8
    Chosen to set the location and depth of the minimum
  • AGB minimum delay t_min = 0.3-0.6 Gyr
    Chosen to produce the late-time upturn after the minimum
  • Eu fraction from BNS mergers = ≥95%
    Set to ≳95 % to dominate europium production
axioms (3)
  • domain assumption One-zone, well-mixed interstellar medium
    Invoked throughout the model construction to allow simple delay-time integration
  • domain assumption Each nucleosynthetic channel has fixed yield ratios independent of metallicity or progenitor mass
    Required for the superposition of three channels to produce the observed trends
  • domain assumption The observed [Y/Eu] and [Sr/Eu] sequences are shaped only by the three channels under consideration
    No other sources or galactic mixing effects are included
invented entities (1)
  • Prompt first-peak channel no independent evidence
    purpose: To supply excess Y and Sr at the lowest metallicities with negligible Eu
    Postulated to fit the low-[Eu/H] upturn; no specific astrophysical site is identified

pith-pipeline@v0.9.0 · 5712 in / 2022 out tokens · 49129 ms · 2026-05-10T15:55:01.111711+00:00 · methodology

discussion (0)

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