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REVIEW 4 major objections 5 minor 136 references

Granulation's spectral fingerprint is set by line strength: weak lines carry the largest velocity wobble (up to 40–50 m/s), strong lines the largest width changes, and width tracks velocity—a handle for removing stellar noise.

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2026-08-04 10:50 UTC pith:LQTYLOJF

load-bearing objection A careful, useful extension of the granulation parametrisation to 72 lines, but the headline RV–EW correlations are partly baked into the construction and the summary contains a direct contradiction. the 4 major comments →

arxiv 2608.02240 v1 pith:LQTYLOJF submitted 2026-08-03 astro-ph.SR

Towards understanding stellar variability at the sub m/s level: granulation-induced variability across the optical spectrum

Cis Lagae , Ginger Frame , Heather M. Cegla , Veronika Witzke , Ren\'e Holzreuter , Sergiy Shelyag , Christopher Watson , Alexander Shapiro This is my paper
classification astro-ph.SR
keywords granulationradial velocity variabilitysolar spectral linesequivalent widthline depthcentre-to-limb variationstellar noise mitigationsolar-type stars
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to isolate how surface granulation—the churning of hot rising and cool sinking gas on a solar-type star—changes spectral lines over time. Using a 3D hydrodynamic simulation of the Sun and radiative-transfer synthesis, it reconstructs p-mode-free timeseries for 72 unblended lines in two optical bands, from disc centre to the limb. The central claim is that line strength controls the granulation fingerprint: weak lines show the largest radial-velocity scatter (up to 40 m/s at disc centre, 50 m/s at the limb), while strong lines show the largest equivalent-width variability. The paper further claims that a line's instantaneous equivalent width and depth are strongly anti-correlated with its granulation-induced velocity, and since planets shift velocity but not width, this opens a path to subtract granulation noise. Finally, most lines—especially Fe I and Ca I—wobble coherently in time, so line blends preserve the granulation signal and many lines can share a single parametrisation for building disc-integrated spectra.

Core claim

The discovery is a systematic, differential map of granulation's effect across 72 unblended lines in the 5500–5600 Å and 6100–6200 Å regions. RV scatter from granulation anti-correlates with line depth (Spearman r ≈ −0.8 at disc centre) and correlates with lower excitation potential; weak lines reach σ_RV ≈ 40 m/s at disc centre and 50 m/s at the limb. Equivalent-width scatter does the opposite, correlating with line depth (r ≈ 0.87), with strong saturated lines varying most. Instantaneously, equivalent width is linearly anti-correlated with RV for all lines (r < −0.6), and line depth joins it for strong lines (r < −0.75); these correlations strengthen toward the limb. The RV and equivalent

What carries the argument

The engine is a three-component parametrisation of the stellar surface. Each pixel is classified—via regularised logistic regression on continuum intensity, line velocity, and equivalent width—into granular tops, outer-granular regions, and intergranular lanes. Time-averaging the three template line profiles removes p-modes; the granulation signal is carried entirely by the time-varying surface filling factors. Each reconstructed line profile is the weighted sum I_recon = f_GT·I_GT + f_OGR·I_OGR + f_IgL·I_IgL, which both produces p-mode-free timeseries and, by sampling filling factors, generates new disc-integrated spectra. A Wasserstein-distance selection of similar filling-factor distribut

Load-bearing premise

The load-bearing premise is that all granulation-induced line variability is captured by the time-varying filling factors of three fixed template components—if a component's own line shape changes over time, the reconstruction and every correlation built on it miss that signal.

What would settle it

Synthesise the granulation timeseries for a weak line such as Fe I 6183 Å directly from the full 3D simulation, skipping the three-template reconstruction, and compare its RV rms and EW-RV correlation to the reconstructed values; a disagreement larger than the reported few m/s would show the fixed-template assumption loses real variability.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Line masks for exoplanet RV work should be depth-aware: weak lines carry the largest granulation jitter, so including them raises RV rms.
  • Strong lines are the best targets for granulation mitigation via line-shape diagnostics, because their equivalent-width–RV correlation is tightest.
  • Granulation moves most lines coherently, so line blends shift absolute RV and EW values without distorting the temporal granulation pattern.
  • The 48 coherent Fe I and Ca I lines can be parametrised chunk-by-chunk with shared filling factors, enabling multi-line disc-integrated synthetic spectra.
  • P-mode contamination changes the centre-to-limb behaviour entirely; p-mode-free reconstructions are needed to measure the granulation component alone.

Where Pith is reading between the lines

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

  • Beyond the paper: if a few hundred strong coherent lines are co-added, equivalent-width precision could reach the sub-0.01 mÅ level needed to use EW as a live granulation monitor for RV data.
  • Beyond the paper: the three limb outliers (V I, Ti I, Co I) hint that a minority of species are phase-incoherent; a line-selection step should test whether excluding them improves multi-line masks.
  • Beyond the paper: the same filling-factor decomposition could be applied to magnetised simulations; if magnetic regions also produce EW–RV correlations, the method might separate granulation from spot/facula noise rather than only removing p-modes.
  • Beyond the paper: the coherence result predicts line-by-line RV extraction should beat full-spectrum cross-correlation for granulation mitigation, a claim that can be tested on existing disc-resolved solar spectra.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper uses a 3D MURaM hydrodynamic solar model and MPS-STOKES-ATLAS spectrum synthesis to generate 72 unblended spectral lines in two 100 Å optical windows, at five disc positions (μ=1.0 to 0.2). Building on the parametrisation framework of Frame et al. (2025), the authors classify each pixel into granular tops, outer-granular regions, and intergranular lanes, construct time-averaged component templates, and use time-dependent filling factors to reconstruct p-mode-free line-profile time series (Eq. 1). From these reconstructed time series they report: (i) weak lines have the largest granulation-induced RV rms, up to 40 m/s at disc centre and 50 m/s at the limb; (ii) strong lines have the largest equivalent-width rms; (iii) equivalent width and line depth are strongly correlated with instantaneous RV; (iv) most lines, especially Fe I and Ca I, vary coherently in time, enabling a multi-line parametrisation. The paper also compares RV measurement methods and discusses implications for exoplanet RV surveys.

Significance. If the results are robust, the paper is a valuable systematic extension of granulation-variability studies from the usual handful of Fe I lines to a diverse 72-line sample with tabulated atomic data, and it provides useful scaling relations between line strength, excitation potential, and granulation-induced RV/EW variability. The explicit treatment of RV-measurement dependencies and the cautionary noise budgets for equivalent-width observability are strengths. The validation against F25 and the IAG atlas for Fe I 6151/6173 gives confidence in the mean reconstructed line shapes. However, the central quantitative claims rest on a reconstruction ansatz whose temporal variability is validated for only one or two lines and on correlations that are partly imprinted by the classification features; no uncertainties are given for the headline numbers. These issues must be addressed before the conclusions can be taken as established.

major comments (4)
  1. [§3, Eq. (1); §3.2; App. B] The reconstruction assumes that all granulation-induced variability is carried by the three component filling factors, while the component templates are time-averaged. The validation in §3.2 and App. B compares temporal means, VPSD, and mean bisectors of Fe I 6151/6173, and mean bisectors of other lines; it does not test the temporal variability of the 70 non-validated lines. Since §4.1–4.3 measure all rms and correlations on the reconstructed time series, a line-depth-dependent intra-component line-shape variability would bias the central weak/strong dichotomy. Agreement with F25 does not resolve this, because F25 used the same reconstruction ansatz. Please add a direct check, e.g., reconstruct a subset of weak lines without template averaging, or quantify the fraction of variance captured by Eq. (1).
  2. [§3.1 and §4.3] The pixel classification uses RVcog (Eq. 2) and equivalent width as features, and Eq. (1) makes the filling factors the only time-dependent quantities. The EW–RV and depth–RV correlations in §4.3 are therefore partly constructed rather than independently measured: any decomposition built from those features will produce correlated time series. The paper should state this explicitly and test independence, e.g., by classifying on continuum intensity only, or by verifying that the correlations survive when RV and EW are computed from reconstructions with independently determined filling factors. The phrase 'opening the door to new granulation-mitigation methods' overstates the present evidence.
  3. [§4.1–4.3] No uncertainties are reported for the rms values (Figs 5–8), Spearman coefficients, or the F25 comparisons. The time series contain 129 snapshots from one 65-minute simulation, and the three filling-factor series are smooth, so the effective number of independent samples is small. Bootstrap or other confidence intervals are needed before the r≈0.87 and r≈−0.8 correlations and the 20–50 m/s rms values can be assessed. This is particularly important because the paper uses these numbers to recommend observing strategies and mitigation methods.
  4. [§7] The summary states 'Without p-modes, strong lines exhibit larger variability in both RV and equivalent width across all limb angles.' This contradicts §4.1 and Fig. 8, where weak lines have the largest RV rms at disc centre and at μ=0.4 (r=−0.8 and −0.77 with line depth), and is inconsistent with the abstract. Please correct this internal inconsistency; as written it will confuse readers about the paper's main result.
minor comments (5)
  1. [Abstract / §4.3] The abstract states that 'the equivalent width and line depth of a spectral line are strongly linearly correlated with its radial velocity,' but §4.3 shows that depth–RV correlations are weak for many lines with depth<0.5 at disc centre (−0.6<r<0.05). Please qualify the claim.
  2. [Fig. 10] The right panel shows only regression lines without scatter; given the stated wide range of Spearman coefficients for weak lines, adding shaded intervals or error bars would make the plot informative.
  3. [App. B] The poor bisector matches for Fe I 5503/5555/5567/6171 and Si I 6125/6155 are attributed to blends in the IAG atlas, but no synthetic test with a more complete line list is made. A sentence acknowledging this as a limitation would be appropriate.
  4. [§4] Eq. (5) introduces a sign convention opposite to Bouchy et al. (2001); it would help to state explicitly in the text that blueshift corresponds to negative RV.
  5. [§3.2] The Harvey-function fit parameters are compared with F25 values obtained with different power-law slopes (α=2 versus α=3.3). This makes the comparison difficult to interpret; please present a single consistent fit or clearly explain the change.

Circularity Check

0 steps flagged

No direct circular reduction found: Eq. 1 is a generative ansatz, and the reported RMS/CLV/correlation values are computed outputs rather than refitted inputs; the main concern is a validation-coverage gap, not circularity.

full rationale

The derivation chain is: MURaM 3D HD snapshots -> MPS-ATLAS spectrum synthesis -> pixel classification into GT/OGR/IgL -> time-averaged component templates -> Eq. 1 reconstruction -> RV/EW/depth diagnostics. No step equates the target result to an input by construction. Eq. 1 defines the reconstructed line as a linear mixture of three time-averaged templates with time-dependent filling factors; the filling factors are obtained from a classifier whose features include RV_cog and equivalent width. This creates a partial overlap between model construction and the measured diagnostics, but it is not a logical circle: the reported quantities (e.g., sigma_RV_Bouchy ~ 20-40 m/s, Spearman coefficients, CLV trends, the weak/strong dichotomy) are not set by the classifier; they emerge from the radiative-transfer templates and the actual time evolution of the filling factors. The same EW-RV anti-correlation is also independently supported by previous work (Cegla et al. 2019; Frame et al. 2026) and by the LARS/IAG comparisons for Fe I 6151/6173. The honest limitation is that the static-template ansatz is directly validated only for two Fe I lines, and the paper explicitly notes that future PoET observations 'will enable more detailed validation of our work'. That is an assumption/validation gap, not a self-consistent reduction. Self-citation of Frame et al. (2025) is load-bearing for the method, but F25 is peer-reviewed and the present paper repeats external comparisons (VPSD vs LARS, bisectors vs IAG), so it does not reduce to an unverified self-citation chain.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

No new physical particles, forces or conserved quantities are introduced. The three surface components (granular tops, outer-granular regions, intergranular lanes) are established phenomenological categories, not new entities. The main external inputs are the MURaM model, the LTE radiative-transfer approximation, the VALD atomic data, and the p-mode-removal assumption; these are the things the reader pays for upstream.

free parameters (3)
  • Template percentile for classification = 2% brightest, 2% faintest, 2% most uncertain pixels
    Chosen in the logistic-regression classification (Sec. 3.1). This choice defines which pixels seed the GT/IgL/OGR components and therefore directly affects all reconstructed RV and EW variability values.
  • Coherent-subsample Wasserstein cutoff = 0.4 (normalised 1-Wasserstein distance)
    Hand-chosen threshold in Sec. 5 used to define the 48-line Fe I/Ca I subsample. It determines the claimed feasibility of multi-line parametrisation, though the central weak/strong line results do not depend on it.
  • Harvey function parameters for granulation PSD = A_g = (1.21 ± 0.21) × 10^-3 m^2 s^-2 Hz^-1; τ = 34 ± 9 s with α = 3.3 refit
    Fit to the reconstructed RV power spectral density in Sec. 3.2 for validation against F25. Not part of the central science claims, but it is a fitted quantity used in the method-comparison narrative.
axioms (5)
  • domain assumption The non-magnetic 3D MURaM HD model (9×9×5 Mm, T_eff ≈ 5787 K, log g = 4.44) faithfully represents solar granulation for line-formation studies.
    Invoked in Sec. 2.1; all synthetic spectra and derived variability are conditional on this model representing the real Sun.
  • domain assumption MPS-STOKES-ATLAS 1.5D LTE spectrum synthesis including 3D local velocity fields produces accurate Stokes-I line profiles.
    Stated in Sec. 2.1; the radiative-transfer treatment sets the absolute line shapes and bisectors, and is not independently benchmarked for all 72 lines.
  • domain assumption Time-averaging the component template profiles removes p-modes while preserving granulation; all remaining temporal variability is encoded in the filling factors.
    Core of Eq. 1 in Sec. 3. This assumption is validated only for Fe I 6151 and 6173 against F25/LARS/IAG, and is extended to the other 70 lines without individual validation.
  • domain assumption Using per-line RVcog, equivalent width and continuum intensity as classification features yields a physically meaningful three-component decomposition.
    Introduced in Sec. 3.1; because the outputs (RV and EW) are also classification features, this assumption carries some circularity burden.
  • domain assumption VALD atomic data and the curated unblended line list are accurate enough for the 72 lines studied.
    The line list in Appendix A is compiled from VALD; errors in gf-values, damping parameters or line lists would propagate into the synthetic line strengths and variability.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Towards understanding stellar variability at the sub m/s level: granulation-induced variability across the optical spectrum." pith.science (2026). https://pith.science/paper/LQTYLOJF

@misc{pith2026260802240,
  author       = {Pith},
  title        = {Pith review of: Towards understanding stellar variability at the sub m/s level: granulation-induced variability across the optical spectrum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LQTYLOJF}},
  note         = {Machine review of arXiv:2608.02240}
}
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read the original abstract

Detecting the radial velocity signal of Earth-mass exoplanets requires the characterisation and removal of granulation-induced radial velocity variability from spectroscopic observations. By coupling three-dimensional (3D) hydrodynamic (HD) simulations to a radiative transfer code, we can isolate and study the effect of granulation on stellar lines. In this study we isolated the impact of granulation on spectral line shapes and shifts for the largest and most diverse synthetic spectral line sample to date. Our aims were twofold. First, we quantified how granulation affects the temporal evolution of shapes and shifts of 72 unblended spectral lines in two wavelength regions: 5500-5600 {\AA} and 6100-6200 {\AA}, from disc centre to the stellar limb. Second, we investigated if spectral lines behave coherently in their line shape variability. We find that weak lines show the largest radial-velocity variability due to granulation, up to 40 m/s at disc centre and 50 m/s at the stellar limb. On the other hand, strong lines exhibit larger variability in equivalent width than weak lines across the stellar disc. In addition, the equivalent width and line depth of a spectral line are strongly linearly correlated with its radial velocity. While granulation affects all three of these quantities, planetary Doppler shifts only affect radial velocities, opening the door to new granulation-mitigation methods. Lastly, we find that the radial velocity and equivalent width of most spectral lines in our sample evolve coherently in time, with the Fe I and Ca I lines behaving the most similarly. Due to the coherency, line blends will not significantly affect the temporal behaviour of RV and line shape, as induced by granulation. Besides, the coherency between spectral lines offer the opportunity to create disc-integrated spectra of many lines simultaneously, which will be explored in future work.

Figures

Figures reproduced from arXiv: 2608.02240 by Alexander Shapiro, Christopher Watson, Cis Lagae, Ginger Frame, Heather M. Cegla, Ren\'e Holzreuter, Sergiy Shelyag, Veronika Witzke.

Figure 1
Figure 1. Figure 1: Histograms of the three features: continuum intensity, mean radial velocity and mean equivalent width over all lines, used in the spectral classification process of a single 3D model at disc centre. Each component is colour-coded: granular tops (orange), outer-granular regions (purple), intergranular lanes (black). In this paper, we used the parametrisation technique developed by Cegla et al. (2018) and Fr… view at source ↗
Figure 2
Figure 2. Figure 2: RV timeseries of the reconstructed spectra from Frame et al. (2025) (solid black) and this work (dashed red), for the Fe i 6151 and 6173 Å lines at disc centre. Both timeseries are shifted by ±100 m/s for visualisation purposes. defined as the mean of 𝑅𝑉line cog over all lines, where each line RV has been centered by its spatial mean ⟨𝑅𝑉line cog ⟩. 𝑅𝑉cog = 1 𝑁lines ∑︁ line [PITH_FULL_IMAGE:figures/full_fi… view at source ↗
Figure 3
Figure 3. Figure 3: Top panel: power spectral density of the RV timeseries of the original (including p-modes, grey) and the reconstructed (only granulation, blue) Fe i 6173 Å line at disc centre. The best joint-fit of the granulation and p-mode components from Frame et al. (2025) are overplotted as an orange line. The best fit of the granulation component from this work is shown in red. Bottom panel: power spectral density o… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of line bisectors for the Fe i 6151 and 6173 Å lines between Frame et al. (2025) (blue), spatially resolved IAG atlas at disc centre (red) and the current work (orange). The spectra from IAG and F25 are downgraded to the resolution used in this work 𝑅 = 500 000. The line bisectors (dashed lines) are shifted by their mean value to zero to compare their shape, and are zoomed in for scale, see the … view at source ↗
Figure 5
Figure 5. Figure 5: RMS of the temporal evolution of 𝑅𝑉Bouchy at disc centre, for reconstructed lines in the wavelength region 5500 − 5600 Å and 6100 − 6200 Å . From left to right, 𝜎𝑅𝑉,Bouchy is plotted, and colour coded, against mean line depth, lower excitation potential and element + ionisation stage. The Spearman correlation coefficient (r-value) is shown at the top of the left and middle panel. comparing the true RV rms … view at source ↗
Figure 6
Figure 6. Figure 6: RMS of the temporal evolution of the equivalent width at disc centre, for reconstructed lines in the wavelength region 5500−5600 Å and 6100−6200 Å . From left to right, equivalent width (𝑊) is plotted, and colour coded, against mean line depth, lower excitation potential and element + ionisation stage. The Spearman correlation coefficient (r-value) is shown at the top of the left and middle panel [PITH_FU… view at source ↗
Figure 7
Figure 7. Figure 7: RMS of the temporal evolution of line depth at disc centre, for reconstructed lines in the wavelength region 5500 − 5600 Å and 6100 − 6200 Å . From left to right, 𝜎𝑅𝑉,linedepth is plotted, and colour coded, against mean line depth, lower excitation potential and element + ionisation stage. & Ludwig 2023), although the absolute values of their RV rms ranges from 𝜎𝑅𝑉 = 100−250 m s−1 , from limb to disc-centr… view at source ↗
Figure 8
Figure 8. Figure 8: Centre-to-limb variation of the rms in 𝑅𝑉Bouchy, equivalent width and line depth, for a strong (solid) and weak (dashed) Fe i line. The values obtained from the reconstructed spectra (only granulation) and the original spectra (including p-modes) are shown in black and red, respectively. that weak lines have larger variability in RV, but smaller in equiva￾lent width, than strong lines. Regarding line depth… view at source ↗
Figure 9
Figure 9. Figure 9: Equivalent width as a function of 𝑅𝑉Bouchy for each point in the reconstructed timeseries at disc centre. A subset of five lines are shown in the left panel, with their best fitting linear regression model shown as a solid line. In the right panel, the best fitting linear regression model for all lines are shown, offset by the intercept for ease of comparison. All linear regressions in the right panel are … view at source ↗
Figure 10
Figure 10. Figure 10: Spectral line depth as a function of 𝑅𝑉Bouchy for each point in the reconstructed timeseries at disc centre. A subset of five lines are shown in the left panel, with their best fitting linear regression model shown as a solid line. In the right panel, the best fitting linear regression model for all lines are shown, offset vertically by the intercept for ease of comparison. All linear regressions in the r… view at source ↗
Figure 11
Figure 11. Figure 11: Temporal evolution of the RV computed for each spectral line plus an arbitrary offset of ±30 m s−1 to visualise the coherency between lines. The lines are sorted and colour coded by mean line depth. explored in Salzer et al. (2025). In order for such analysis to work, we will need to measure the equivalent width to a higher precision than its predicted variability. We can estimate the error on the measure… view at source ↗
Figure 12
Figure 12. Figure 12: , and is at most ≈ 2.5 m s−1 . The absolute difference be￾tween the instantaneous 𝑅𝑉CCF and 𝑅𝑉Bouchy measurements is at most ⪅ ±7.5 m s−1 , with the majority of points having a difference less than ⪅ ±2.5 m s−1 . The largest absolute differences occur when the spectral lines reach their largest line shifts ( 𝑅𝑉Bouchy ≈ 100 m s−1 , see the x-axis of [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.