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arxiv: 2606.10648 · v1 · pith:GQJAZAZVnew · submitted 2026-06-09 · 🌌 astro-ph.GA

Star-formation variability on the star-forming main sequence during the Epoch of Reionization

H. T. J. Bevins , S. Tacchella , C. Simmonds This is my paper

Pith reviewed 2026-06-27 12:54 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords star formation variabilitystar-forming main sequenceepoch of reionizationhigh-redshift galaxiespower spectral densitygalactic dynamical timescalesstellar feedback
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The pith

The scatter in high-redshift star-forming main sequence galaxies is set by variability on 10-30 million year timescales.

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

The paper models fluctuations in star formation rates using power spectral density approaches fitted to measurements of scatter across six different averaging timescales from 10 to 100 million years. It tests two models on data from about 17000 galaxies at redshifts 3 to 8 and finds that the data prefer models with characteristic variability times of 10-30 million years. These times align with the orbital and feedback cycles inside galaxies rather than slower processes such as gas accretion over longer periods. The results also indicate stronger variability in lower-mass galaxies and only weak signs of a change in the character of the variability at the highest redshifts. This points to galactic dynamics as the main driver of the observed scatter during the epoch of reionization.

Core claim

Using estimates of intrinsic scatter in main-sequence star-formation rates at six averaging timescales from a catalogue of roughly 17000 galaxies at z=3-8, both the single-component Simple Harmonic Oscillator model and the dynamical component of the Extended Regulator model are constrained to characteristic variability timescales of approximately 10-30 Myr. These timescales match expected galactic dynamical and stellar feedback times, showing that the observed 10-100 Myr scatter is governed primarily by short-timescale variability. At least in the SHO model the power on 10 Myr timescales decreases with stellar mass, and there is weak evidence in the lowest-mass bin for a shift from a two-com

What carries the argument

Power spectral density (PSD) models of star-formation rate fluctuations, specifically the Simple Harmonic Oscillator (SHO) model and the dynamical component of the Extended Regulator (ExtReg) model, fitted via nested sampling to scatter measurements at multiple averaging timescales.

If this is right

  • The regulator component of the ExtReg model remains poorly constrained by current data.
  • In the SHO model, power on approximately 10 Myr timescales decreases with increasing stellar mass, implying more rapid variability in lower-mass galaxies.
  • There is only weak evidence for a transition from a two-component ExtReg-like PSD to a single-component SHO-like PSD at higher redshift in the lowest stellar-mass bin.
  • The observed scatter on 10-100 Myr scales is explained primarily by variability on galactic dynamical timescales.

Where Pith is reading between the lines

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

  • Galaxy formation simulations would need to resolve orbital and feedback timescales to reproduce the measured scatter rather than assuming smoother, longer-term accretion.
  • Lower-mass galaxies would contribute more bursty ionizing output during reionization if the mass dependence of variability holds.
  • Repeating the same PSD analysis on lower-redshift samples with comparable scatter measurements could test whether the dominance of short-timescale variability evolves with cosmic time.

Load-bearing premise

The estimates of intrinsic scatter in main-sequence star-formation rates at six averaging timescales from the Simmonds et al. 2025 catalogue accurately reflect variability without major biases from selection effects, measurement errors, or other contaminants.

What would settle it

A measurement of scatter that stays flat or rises when star-formation rates are averaged over timescales shorter than 10 Myr would show that short-timescale variability does not dominate the observed scatter.

Figures

Figures reproduced from arXiv: 2606.10648 by C. Simmonds, H. T. J. Bevins, S. Tacchella.

Figure 1
Figure 1. Figure 1: The intrinsic scatter around the main sequence on timescales between 10 and 100 Myr for redshifts between 3 and 8 (shown in panels) and stellar masses between 108 and 1010 M⊙ (indicated by colours). The error bars shown are estimated from bootstrapping and are later floored at 3% in our analysis. The bottom right panel shows the number of galaxies in each stellar mass and redshift bin analysed in this work… view at source ↗
Figure 2
Figure 2. Figure 2: Example of the data generation pipeline described in Section 3 using the ExtReg PSD (Iyer et al. 2024). For each 𝜃PSD we calculate a corresponding power spectral density (top left) and auto correlation function (top middle). For the PSD we show the dynamical and regulator components as dashed and dotted lines respectively. The dynamical component dominates on short time scales for this particular PSD model… view at source ↗
Figure 3
Figure 3. Figure 3: The upper bound on the incorrect information inferred when per￾forming inference with each of the 37 emulators trained in this paper in nats. The top panel corresponds to the ExtReg emulators and the bottom to the SHO emulators. The ExtReg is a more complex model and the forecast uncer￾tainties in the emulated posteriors are higher for this model than for the SHO model as a result. To account for the emula… view at source ↗
Figure 4
Figure 4. Figure 4: Parameter recovery for mock data in the stellar mass bin log 𝑀∗/𝑀⊙ = 8 − 8.5 and redshift 𝑧 = 4 − 5 emulator for the SHO model (left) and ExtReg model (right). The prior is shown in grey, the posterior in blue and the true values as red dashed lines [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The posteriors on the PSDs for mock observations in the log 𝑀∗/𝑀⊙ = 8 − 8.5 and redshift 𝑧 = 4 − 5 bin for the SHO model (left) and ExtReg model (right). Prior samples are shown as grey lines, one and two sigma posterior contours are shown as dark and light shaded red areas, the average of the PSD posterior is shown as the black solid line and the true PSD is shown as the red dashed line. The two vertical … view at source ↗
Figure 6
Figure 6. Figure 6: Predicted main sequence scatter (𝜎MS) as a function of averaging timescale for the SHO model (left) and ExtReg model (right). Each row shows results for one stellar mass bin, at three different averaging timescales over the redshift range 3-8. Dashed black lines show the average of the functional posteriors, while shaded regions indicate 68% (dark) and 95% (light) posterior confidence intervals. Prior samp… view at source ↗
Figure 7
Figure 7. Figure 7: The posterior distributions on the PSD constraints for all four stellar mass bins at redshifts 3 − 4. The top row corresponds to the SHO PSD, the middle row to the ExtReg model and the bottom row to the log of the ratio between them. The vertical dashed lines in all panels correspond to timescales of 10 and 100 Myr. Prior samples are shown as grey lines in the top two rows. One sigma and two sigma confiden… view at source ↗
Figure 8
Figure 8. Figure 8: Bayesian model comparison between the ExtReg and SHO models across the different stellar mass and redshift bins. Logarithmic evidence differences Δ log Z = log ZExtReg − log ZSHO are shown with positive values indicating a preference for the ExtReg model and negative values for the SHO model. A log Bayes ratio of 3 nats (equivalently ≈ 1.3 in base 10) corresponds to betting odds of 20:1 and is regarded as … view at source ↗
Figure 9
Figure 9. Figure 9: The Power Spectral Density at 10 Myrs inferred for each stellar mass (x axis) and redshift (panels from left to right) bin and kernel (SHO￾circles; ExtReg-squares). The colour bar represents the Bayes factor log 𝐾 between the two models (e.g. the ExtReg data points are coloured based on log 𝐾ExtReg−SHO = log 𝑍ExtReg − log 𝑍SHO and the SHO data points are coloured based on − log 𝐾ExtReg−SHO). The error bars… view at source ↗
Figure 10
Figure 10. Figure 10: The constraints on 𝜏0 and 𝜏Dyn as a function of stellar mass and redshift bin and compared to different characteristic timescales. The shaded grey region shows the age of the Universe 𝜏age, the dotted line shows 0.1𝜏age, the solid grey line show the dynamical timescale for the galaxy, the dashed line shows the halo dynamical timescale and the dash dotted line shows the merger timescale inferred from Puská… view at source ↗
read the original abstract

Star formation in galaxies is intrinsically stochastic, driven by physical processes operating across a wide range of scales. The scatter in the star-forming main sequence relation provides a window into this variability, but interpreting this scatter in terms of underlying physical mechanisms remains challenging. We present a study of star-formation variability during reionization (redshift z=3-8) using power spectral density (PSD) models to characterize fluctuations in star formation rates (SFRs). We use estimates of the intrinsic scatter in main sequence SFRs at six averaging timescales (10-100 Myr) from a catalogue of ~17000 galaxies presented in Simmonds et al. 2025 to constrain two PSD models, the Simple Harmonic Oscillator (SHO) and the Extended Regulator (ExtReg), with nested sampling and neural network emulators. We find that the regulator component of the ExtReg model is poorly constrained by the present data. However, both the dynamical component of the ExtReg model and the single-component SHO model favour characteristic variability timescales of ~10-30 Myr, comparable to expected galactic dynamical and stellar feedback timescales. At least in the SHO model, and most clearly at z~3-4, the inferred PSD power on ~10 Myr timescales decreases with stellar mass, indicating more bursty, rapidly varying star formation in lower-mass galaxies than in higher-mass systems. We find weak evidence for a transition from a two-component ExtReg-like PSD at lower redshift to a single-component SHO-like PSD at higher redshift in the lowest stellar-mass bin, log M*/M$\odot$ = 8-8.5, although the Bayes factors are small and selection effects at high redshift prevent strong conclusions. Overall, our results suggest that the observed 10-100 Myr scatter of the high-redshift star-forming main sequence is governed primarily by short-timescale variability, consistent with galactic dynamical timescales.

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 manuscript analyzes star-formation variability during the Epoch of Reionization (z=3-8) by fitting Simple Harmonic Oscillator (SHO) and Extended Regulator (ExtReg) power spectral density models to estimates of intrinsic scatter in the star-forming main sequence at six averaging timescales (10-100 Myr) drawn from the Simmonds et al. 2025 catalogue of approximately 17,000 galaxies. Using nested sampling and neural network emulators, the authors constrain the models and infer that characteristic variability timescales are 10-30 Myr, consistent with galactic dynamical timescales. They report mass-dependent behavior in the SHO model and weak evidence for a transition in PSD form with redshift in the lowest mass bin, while noting that the regulator component in ExtReg is poorly constrained and that selection effects limit conclusions at high redshift.

Significance. If the scatter estimates accurately reflect intrinsic variability, this work offers important constraints on the stochasticity of star formation at high redshift, suggesting that short-timescale processes dominate the observed scatter on 10-100 Myr scales. The application of PSD modeling with efficient emulators represents a useful methodological approach for interpreting main-sequence scatter in terms of physical timescales. The explicit use of nested sampling and neural network emulators for model fitting is a methodological strength.

major comments (3)
  1. [Methods (data input from Simmonds et al. 2025)] Methods section (description of scatter inputs from Simmonds et al. 2025): The six scatter values at 10-100 Myr averaging timescales are adopted directly without a reported dedicated quantification of biases from selection effects, measurement errors, or dust systematics, although the text acknowledges that selection effects at high redshift limit conclusions. Since these values are the sole observational inputs constraining the PSD parameters and the inferred 10-30 Myr timescales, an explicit test (e.g., via mock catalogues or error budget decomposition) is needed to confirm they trace intrinsic SFR fluctuations rather than contaminants.
  2. [Results (ExtReg model constraints)] Results section (ExtReg model): The regulator component of the ExtReg model is stated to be poorly constrained by the present data, yet the headline claim that variability is governed primarily by short-timescale dynamical processes relies on the dynamical component; additional analysis showing the robustness of the 10-30 Myr inference when marginalizing over the unconstrained regulator parameter would strengthen the central interpretation.
  3. [Discussion (redshift evolution)] Discussion section (redshift evolution claim): The reported weak evidence for a transition from a two-component ExtReg-like PSD at lower redshift to a single-component SHO-like PSD at higher redshift in the log M*/M⊙ = 8-8.5 bin rests on small Bayes factors; given the acknowledged selection effects at high z, a quantitative assessment of how those effects could produce or mask such a transition is required before the claim can be considered load-bearing.
minor comments (2)
  1. [Abstract] The abstract states '~17000 galaxies' but the full text uses 'approximately 17,000'; consistent phrasing would improve precision.
  2. [Methods] Notation for the dynamical versus regulator components in the ExtReg model would benefit from an explicit equation reference when first introduced in the methods to aid reader clarity.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive review and for highlighting the methodological strengths of the work. We address each major comment below and have revised the manuscript to incorporate additional analysis and discussion where feasible.

read point-by-point responses

  1. Referee: Methods section (description of scatter inputs from Simmonds et al. 2025): The six scatter values at 10-100 Myr averaging timescales are adopted directly without a reported dedicated quantification of biases from selection effects, measurement errors, or dust systematics, although the text acknowledges that selection effects at high redshift limit conclusions. Since these values are the sole observational inputs constraining the PSD parameters and the inferred 10-30 Myr timescales, an explicit test (e.g., via mock catalogues or error budget decomposition) is needed to confirm they trace intrinsic SFR fluctuations rather than contaminants.

    Authors: We agree an explicit error budget would strengthen the presentation. Simmonds et al. (2025) already quantifies several of these systematics; we have added a new subsection in Methods that decomposes the reported scatter uncertainties into measurement, dust, and selection contributions based on that work. A full mock-catalogue test is not possible without the underlying simulation data, but the expanded discussion now makes the limitations more quantitative. revision: partial

  2. Referee: Results section (ExtReg model): The regulator component of the ExtReg model is stated to be poorly constrained by the present data, yet the headline claim that variability is governed primarily by short-timescale dynamical processes relies on the dynamical component; additional analysis showing the robustness of the 10-30 Myr inference when marginalizing over the unconstrained regulator parameter would strengthen the central interpretation.

    Authors: We have performed the requested robustness test by drawing the regulator parameter from a broad prior, re-running the nested sampling, and confirming that the dynamical timescale posterior remains peaked between 10-30 Myr with only modest broadening. The new results are shown in an updated figure and text in the revised Results section. revision: yes

  3. Referee: Discussion section (redshift evolution claim): The reported weak evidence for a transition from a two-component ExtReg-like PSD at lower redshift to a single-component SHO-like PSD at higher redshift in the log M*/M⊙ = 8-8.5 bin rests on small Bayes factors; given the acknowledged selection effects at high z, a quantitative assessment of how those effects could produce or mask such a transition is required before the claim can be considered load-bearing.

    Authors: We have added a quantitative estimate in the Discussion using a simplified incompleteness model that increases with redshift for the lowest-mass bin. This shows that selection can modestly enhance the apparent trend in Bayes factors but is unlikely to create it entirely. We have also toned down the language to stress that the evidence remains weak. A full end-to-end selection simulation on the PSD inference is beyond current scope. revision: partial

standing simulated objections not resolved
  • A complete mock-catalogue validation of the input scatter values and of the redshift-evolution claim would require the full simulation outputs and selection functions from Simmonds et al. (2025), which are not available to us.

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent scatter inputs to fit PSD parameters

full rationale

The paper takes six scatter values at 10-100 Myr averaging timescales from the Simmonds et al. 2025 galaxy catalogue as fixed inputs, then fits SHO and ExtReg PSD models via nested sampling to extract characteristic timescales. This is a standard parameter inference step with no reduction by construction: the output timescales are not equivalent to the input scatters, nor are they a renamed fit. The Simmonds citation supplies processed observational data rather than a self-cited theorem or ansatz that justifies the central claim. No self-definitional equations, fitted-input predictions, or uniqueness imports appear in the derivation chain. The result remains falsifiable against external data and is therefore scored 0.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that scatter measurements at different averaging timescales can be directly mapped to PSD model parameters, plus the validity of the two chosen PSD functional forms; no invented entities are introduced.

free parameters (1)
  • SHO and ExtReg model parameters
    Parameters of the simple harmonic oscillator and extended regulator PSD models are fitted to the scatter data at six timescales.
axioms (1)
  • domain assumption Scatter in SFRs at different averaging timescales reflects intrinsic star-formation variability driven by physical processes on galactic dynamical and feedback timescales.
    Invoked when using the catalogue scatter values to constrain the PSD models.

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discussion (0)

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Reference graph

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