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The Fe I 4377 Å line reveals facular coverage from disc-integrated sunlight.

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2026-08-03 06:40 UTC pith:TKCHOWE6

load-bearing objection A solid, honest SRA-to-filling-factor inversion for the Sun—the MURaM correlations are convincing for a relative activity indicator, but the facular-specific quantitative claim is not uniquely established and needs a network/spot sensitivity test. the 4 major comments →

arxiv 2607.29455 v1 pith:TKCHOWE6 submitted 2026-07-31 astro-ph.SR astro-ph.EPastro-ph.IM

The Fe I 4377 {AA} Line as a Solar Faculae Indicator: Insights from Spectral Ratio Analysis

Katlyn L. Hobbs (1) , Christopher A. Watson (1) , Jean C. Costes (1) , Yvonne Unruh (2) , Dana Clarice Yaptangco (2) , Krishnamurthy Sowmya (3) , Mitchell E. Young (1) , Ernst J. W. de Mooij (1)
show 27 more authors
Alexander G. M. Pietrow (4) P\'al V\'aradi Nagy (5) Alexander I. Shapiro (3 6) Veronika Witzke (3) Federica Rescigno (7) Ryan A. Rubenzahl (8) Megan Bedell (8) Andrew Collier Cameron (9) Xavier Dumusque (10) Sean M. O'Brien (1) Benjamin M. J. Cadell (1) Baptiste Klein (11) Niamh Mallaghan (1) Niamh K. O'Sullivan (11) Toby Rodel (1) Sara Tavella (10) ((1) Queen's University Belfast (2) Imperial College London (3) University of Graz (4) Leibniz-Institut f\"ur Astrophysik Potsdam (5) Independent Researcher (6) Max-Planck-Institut f\"ur Sonnensystemforschung (7) University of Birmingham (8) Flatiron Institute (9) University of St Andrews (10) University of Geneva (11) University of Oxford)
This is my paper
classification astro-ph.SR astro-ph.EPastro-ph.IM
keywords spectral ratio analysisfaculaesolar activitySun-as-a-starradial velocity noisephotospheric activity indicatorFe I 4377 Å
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.

Faculae are bright magnetic patches that dominate stellar activity noise in radial-velocity searches for Earth-like exoplanets, but their low contrast makes them hard to track in disc-integrated light. This paper argues that a single photospheric iron line, Fe I 4377 Å, carries a strong and coherent facular signal when high-activity spectra are divided by a low-activity template (Spectral Ratio Analysis). By fitting the residual feature with composite synthetic spectra — either temperature-perturbed or magnetically enhanced — the paper recovers fractional facular coverage whose time evolution matches disc-resolved solar images (Pearson R ≈ 0.59–0.93) over two multi-rotation epochs. If the claim holds, this provides a photospheric activity indicator that directly probes the regions responsible for RV noise, complementing chromospheric proxies like log R'HK.

Core claim

The paper's central claim is that the Fe I 4377 Å line's Spectral Ratio Analysis residual is dominated by faculae, and that its amplitude can be inverted, using forward models of composite spectra, to estimate the fractional area of the solar disc covered by faculae. Two complementary synthetic frameworks are used: one approximates faculae as LTE atmospheres 200–400 K hotter than the quiet Sun; the other uses radiation-MHD simulations of magnetic regions with ~200 G mean vertical fields. Inferred filling factors rise from ~1.5% to ~5.5% across the two studied activity states and track disc-resolved filling factors with Pearson R = 0.587–0.927. The paper concludes that the line can trace rela

What carries the argument

The central object is the Fe I 4377 Å absorption line and its SRA residual, constructed by dividing a daily high-activity disc-integrated spectrum by a low-activity template. The line's sensitivity to faculae follows from atomic physics: in the quiet photosphere iron is mostly singly ionized, so neutral Fe I is a minority species; the facular temperature enhancement ionizes more Fe I, depletes the ground state (the line's lower level, E_low = 0 eV), and weakens the line. The carrying mechanism of the argument is a forward spectral model: a linear combination of quiet-Sun and facular templates — one family using hotter atmospheres, the other using magnetized convection simulations — is conver

Load-bearing premise

The load-bearing premise is that the 4377 Å SRA residual is produced almost entirely by faculae, so that its amplitude can be converted directly into a facular filling factor; if spots or the magnetic network contribute significantly, every derived filling factor is biased even if the correlations remain high.

What would settle it

A decisive test is to measure the 4377 Å SRA residual during a low-activity period when the solar disc contains magnetic network but essentially no active-region faculae. If the inferred filling factor rises with the network coverage (as measured by non-thresholded magnetogram pixels) while area-thresholded facular coverage stays near zero, the line is not a clean facular tracer and the inversion would need a network component.

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

If this is right

  • Disc-integrated monitoring of the 4377 Å line can recover the rotational modulation and activity-cycle evolution of facular coverage without spatially resolved imaging.
  • The inferred filling factor provides a photospheric, line-profile-based activity indicator directly tied to the regions responsible for radial-velocity noise, potentially improving RV decorrelation in exoplanet surveys.
  • The same fitting framework can in principle be applied to high-resolution spectra of other Sun-like stars, giving a stellar facular filling factor without resolved disc imaging.
  • The recovered facular temperature contrasts of roughly 200–400 K are consistent with the range used in solar activity modelling, supporting the interpretation of the residual as a temperature-sensitive photospheric signal.
  • The inferred coverage tracks the non-thresholded filling factor (faculae plus network) at high activity and the area-thresholded one at low activity, indicating where the line's sensitivity begins.

Where Pith is reading between the lines

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

  • A multi-line extension of the SRA fit, using several iron lines with different sensitivities, could break the degeneracy between filling factor and temperature contrast and recover limb-angle information that the single-line fit cannot.
  • If the facular-only interpretation survives on the Sun, the same line could serve as a spectral template for correcting transmission spectroscopy of exoplanets, where unocculted faculae bias inferred planetary radii at short wavelengths.
  • On more active stars, spot contamination could bias the filling-factor inversion; calibrating the method against solar epochs with substantial spot coverage would quantify that bias.
  • The systematic offset between inferred and thresholded coverage at low activity suggests the line may be a tunable tracer of the network-to-faculae ratio, a parameter otherwise hard to observe in disc-integrated light.

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 / 4 minor

Summary. The paper uses Spectral Ratio Analysis (SRA) on HARPS-N Sun-as-a-star spectra from two ~3-rotation windows (2016 June–August and 2022 May–July) to isolate the Fe I 4377 Å residual feature and model it with composite PHOENIX spectra (facular temperature contrast 200–400 K) and MPS-ATLAS spectra from MURaM simulations with imposed vertical magnetic fields of 100, 200, and 300 G. The inferred facular filling factors are compared with SDO/HMI filling factors, with reported Pearson R values of 0.587–0.927 depending on model, epoch, and SDO definition (thresholded vs non-thresholded). The paper concludes that the Fe I 4377 Å line can trace relative variations in facular filling factors, offering a photospheric activity diagnostic for RV exoplanet work. The workflow is clearly described, the external SDO comparison is a strength, and the limitations are candidly discussed; however, the central quantitative claim that the fitted single-component coverage is specifically the facular filling factor is weakened by admitted mixing with the magnetic network and by post-hoc data selection in the PHOENIX correlations.

Significance. If the central claim holds, the paper provides a direct, disc-integrated spectroscopic tracer of photospheric facular coverage that could be applied to other stars and improve activity mitigation in RV surveys and transmission-spectroscopy analyses. The manuscript has genuine strengths: it uses public HARPS-N and SDO data, documents the SRA and model-fitting pipeline in detail, validates against an independent disc-resolved dataset, and uses two complementary synthetic frameworks (1D PHOENIX and 3D MURaM). The clear statement of caveats, including the temperature–filling-factor degeneracy and the limb-angle insensitivity, is commendable. However, the quantitative identification of the inferred coverage as the facular filling factor is not uniquely established, because the model attributes all residual amplitude to a single facular-like component while the comparison in Section 5.1 shows that the inferred quantity tracks network-inclusive and area-thresholded SDO curves differently at different activity levels. This weakens the main quantitative claim, though the qualitative conclusion that the line is a useful activity proxy may still survive with reframing or additional modelling.

major comments (4)
  1. [§5.1, Fig. 9] The claim that the fitted alpha is specifically the facular filling factor is not uniquely established. Section 5.1 states that in the high-activity period the inferred coverage mainly tracks the non-thresholded SDO curve (which includes the magnetic network), while in the low-activity period it tracks the area-thresholded curve. Because the model contains only one active component, alpha is an effective coverage of whatever bright magnetic features the line responds to, not necessarily photospheric faculae alone. The paper should either include a network/spot component (or otherwise demonstrate insensitivity to such contamination) or reframe the central claim as measuring the coverage of magnetically bright photospheric features. This is load-bearing for the abstract and conclusions, which state specifically that facular filling factors are recovered.
  2. [§5.1, Table 1] The reported improvement in the PHOENIX 2022 correlations from R=0.640 to R=0.795 after removing several days is not reproducible as written. The manuscript does not state how many points were removed, which days, or the selection criterion beyond 'larger errors bars ... pulling the reduced chi2 fit into the continuum.' Since these correlations are a key validation of the method, the removal must be pre-specified or fully transparent. Please provide the removed dates, the number of points, and an analysis showing the result is not driven by post-hoc selection. Also report p-values or confidence intervals for all correlation coefficients, given the modest number of days.
  3. [§4.1, Fig. B1] The temperature–filling-factor degeneracy is acknowledged in Section 5.2, but the reported alpha values are presented without uncertainties. The reduced-chi2 maps in Figure B1 show broad, correlated minima, so the daily alpha estimates in Figure 9 likely have substantial uncertainties that are not propagated into the SDO correlations. Please provide confidence intervals or posterior bounds for the best-fit alpha (and for the MURaM fits), and account for this uncertainty when quoting Pearson R values.
  4. [§4.2, Fig. 6] The selection of the 200 G MURaM model as the adopted facular proxy is not fully supported by the model comparison. The text notes that the 300 G models give the lowest reduced chi2 but that 'little difference' is seen between 200 G and 300 G, and 100 G models were removed post hoc because they underestimate the amplitude. The conclusion that 'the best estimates of faculae filling factor are given by magnetic field strengths of approximately 200G' is therefore based on an external canonical value rather than on the data. Please either present the comparison as a choice with motivation (e.g., Schrijver & Harvey 1994) rather than a fit result, or provide model-selection statistics (e.g., AIC/BIC or chi2 differences) that justify preferring 200 G over 300 G.
minor comments (4)
  1. [Abstract] The abstract states that SRA offers a means to 'reliably track surface magnetic activity in disc-resolved spectra.' The observations are disc-integrated Sun-as-a-star spectra; 'disc-resolved' should be 'disc-integrated' (or the sentence should be reworded) to avoid confusion with SDO-style resolved imaging.
  2. [Eq. (1)] The ripple model uses a Lomb-Scargle periodogram to identify the frequency f, but the text does not specify the wavelength range over which the periodogram is computed or the units of f. Please clarify, since the wavelength-scaled term lambda_med/lambda changes the effective frequency.
  3. [§3] Typo: 'further investigiation' should be 'further investigation.' Also, 'MP-ATLASMURaMmodels' in the same section appears to be a spacing error for 'MPS-ATLAS MURaM models.'
  4. [§5.1, Table 1] The table is referred to in the text as 'Table 5.1'; it should be 'Table 1.' The caption should also state the number of days in each period and the uncertainty on R.

Circularity Check

1 steps flagged

Absolute filling-factor scale is anchored to the SDO values used for validation; the central relative-tracking claim remains independent.

specific steps
  1. other [Section 4.1 (PHOENIX model construction, Eq. 2); validated in Section 5.1 and abstract]
    "We began by creating a low-activity model spectrum, where the faculae coverage was set to 1%, similar to the solar faculae coverage as determined from SDO images (see Section 5 for details) of our low activity template on the day of 2017 July 23."

    The zero-point of the filling-factor fit is set to the SDO-derived 1% coverage of the reference day. The absolute values reported (e.g., 'rising from ~1.5% to ~5.5%, consistent with SDO-measured filling factors') therefore inherit their scale from the same SDO data used as the Section 5 ground truth, so the absolute 'agreement' is partly fixed by construction. The relative temporal variations and Pearson R values are not forced by this anchor, making the circularity partial rather than total.

full rationale

The central derivation is largely self-contained: HARPS-N residuals are fit with synthetic PHOENIX/MURaM composites without using the SDO filling-factor time series as a fitting target, and the temporal correlations (R=0.587-0.927) are an external, non-forced validation. The line choice relies partly on self-citations (Thompson et al. 2020; Costes et al. 2026), but this is not load-bearing because the paper adds independent Sol'Ex spectroheliograms and physical line-formation arguments. The one genuine circular element is the absolute filling-factor zero-point: the low-activity model template is set to 1% facular coverage based directly on SDO, so the reported absolute scale inherits its calibration from the same data later used as ground truth. This does not force the relative variations or the correlation coefficients, so the circularity is partial and the central claim of tracking relative facular variations stands.

Axiom & Free-Parameter Ledger

9 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical entities; it relies on prior model frameworks (PHOENIX, MURaM/MPS-ATLAS) and an external SDO benchmark. The main free parameters—temperature, filling factor, log g, magnetic field strength, limb angle, and RV shift—encode the simplified facular model. The absolute filling-factor scale is anchored to SDO via the 1% low-activity template, and the 200 G choice is partly justified by canonical values rather than derived from the new data.

free parameters (9)
  • Low-activity template facular filling factor = 1%
    Set to 1% based on SDO-derived coverage for 2017-07-23 (Section 4.1). Anchors the absolute filling-factor scale of all inferred values; not independently derived.
  • PHOENIX facular temperature contrast = 200–400 K (6000–6200 K vs 5800 K quiet Sun)
    Fitted per day via grid search over 5800–6300 K in 50 K steps (Section 4.1).
  • PHOENIX facular surface gravity log g = 4.0
    Chosen from grid 3.5/4.0/4.5 as lowest reduced chi-squared; used as proxy for pressure broadening changes in faculae (Section 4.1).
  • Facular filling factor alpha = 1–10% per day
    Fitted per day via grid search with 0.2% steps for both PHOENIX and MURaM models (Sections 4.1–4.2).
  • MURaM imposed vertical magnetic field = 200 G
    100 G excluded because it underestimates feature amplitude; 200 G vs 300 G similar; 200 G chosen as canonical facular field from Schrijver & Harvey 1994; Carlsson et al. 2019 (Section 4.2).
  • MURaM limb angle mu = Best-fit 0.3–0.5
    Fitted per day over mu grid 0.1–1.0; authors later conclude they are insensitive to limb angle (Section 5.1).
  • Facular radial-velocity shift = Free, no significant signal
    Grid search over ±2.5 km/s in 0.25 km/s steps; recovered RVs show no coherent signal and are not analyzed further (Section 4.1).
  • Ripple model parameters (A, f, T0, k) = Fitted per residual spectrum
    Equation 1 is fit to remove etaloning ripples; frequency varies with wavelength. Affects residual spectra before the model fitting.
  • SDO/HMI facular classification thresholds = B > 24 G; I > 0.89 * I_quiet; area threshold 2 μHem
    Adopted from Haywood et al. 2016 and Milbourne et al. 2019; changing these thresholds changes the benchmark filling factors (Section 5).
axioms (6)
  • domain assumption PHOENIX LTE model atmospheres can represent faculae as hotter, lower-gravity non-magnetic spectra.
    Stated in Section 4.1 as an approximation; the authors note it is an incomplete representation of facular structure.
  • domain assumption MURaM small-scale dynamo plus an imposed mean vertical field of 200 G produces realistic facular analogues.
    Section 4.2 relies on prior MURaM studies; the authors note this is a simplified parametrization and does not reproduce all observed line-profile features.
  • domain assumption SDO/HMI pixel classification with B > 24 G and I > 0.89 I_quiet gives ground-truth facular filling factors.
    Section 5 adopts thresholds from Haywood et al. 2016 and Milbourne et al. 2019; varying these criteria directly changes the comparison values.
  • domain assumption Fe I 4377 Å weakening in faculae is driven by increased ionization and ground-state depopulation.
    Section 3 gives a physical explanation for the line's temperature sensitivity; treated as known stellar-atmosphere physics.
  • domain assumption HARPS-N DRS 3.2.0 reductions, quality cuts, heliocentric corrections, and daily averaging preserve the line-profile information used in SRA.
    Section 2.1–2.2 describes the data processing; the reliability of the method depends on these calibrations.
  • domain assumption Rotational broadening with v sin i = 2 km/s and linear limb darkening 0.4, plus Gaussian instrumental broadening, adequately model the disc-integrated synthetic spectra.
    Section 4.1; authors later acknowledge this does not capture the exact physics of rotational line broadening.

pith-pipeline@v1.3.0-daily-deepseek · 22842 in / 16412 out tokens · 171609 ms · 2026-08-03T06:40:33.224760+00:00 · methodology

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read the original abstract

Faculae are a dominant source of stellar activity noise in radial velocity measurements, yet their low contrast and broad surface distribution make them difficult to track in disc-integrated observations. We apply Spectral Ratio Analysis (SRA) to HARPS-N Sun-as-a-star observations to isolate and characterize the spectral imprint of facular regions over rotational timescales. The resulting SRA spectra show coherent, line-dependent variability sensitive to surface magnetic activity, with the Fe I 4377 Angstrom line exhibiting a particularly strong diagnostic response to facular coverage. We interpret the observed signatures using two complementary synthetic frameworks: composite PHOENIX spectra, from which we derive best-fit facular temperature contrasts in the range 200-400 K, and MPS-ATLAS spectra synthesized using MURaM simulations of the quiet Sun including a small-scale dynamo and magnetically-enhanced facular analogues with initial mean vertical magnetic fields of 100G, 200G, and 300G. Both approaches are benchmarked against facular filling factors measured from Solar Dynamics Observatory (SDO) disc-resolved images. We find good agreement between SDO-measured and SRA-inferred filling factors using the Fe I 4377 Angstrom line, with Pearson R coefficients of 0.587-0.927 across models and timescales. The estimated filling factors track the solar activity cycle, rising from ~1.5% at lower activity to ~5.5% at higher activity, consistent with SDO-measured filling factors. These results demonstrate that SRA offers a means to reliably track surface magnetic activity in disc-resolved spectra, which is necessary for mitigating the effects of activity on RV characterization of exoplanet masses and atmospheres at modern precision.

Figures

Figures reproduced from arXiv: 2607.29455 by (10) University of Geneva, (11) University of Oxford), (2) Imperial College London, (3) University of Graz, (4) Leibniz-Institut f\"ur Astrophysik Potsdam, (5) Independent Researcher, 6), (6) Max-Planck-Institut f\"ur Sonnensystemforschung, (7) University of Birmingham, (8) Flatiron Institute, (9) University of St Andrews, Alexander G. M. Pietrow (4), Alexander I. Shapiro (3, Andrew Collier Cameron (9), Baptiste Klein (11), Benjamin M. J. Cadell (1), Christopher A. Watson (1), Dana Clarice Yaptangco (2), Ernst J. W. de Mooij (1), Federica Rescigno (7), Jean C. Costes (1), Katlyn L. Hobbs (1), Krishnamurthy Sowmya (3), Megan Bedell (8), Mitchell E. Young (1), Niamh K. O'Sullivan (11), Niamh Mallaghan (1), P\'al V\'aradi Nagy (5), Ryan A. Rubenzahl (8), Sara Tavella (10) ((1) Queen's University Belfast, Sean M. O'Brien (1), Toby Rodel (1), Veronika Witzke (3), Xavier Dumusque (10), Yvonne Unruh (2).

Figure 1
Figure 1. Figure 1: Time series of the disc-integrated solar chromospheric activity log 𝑅 ′ HK index, measured from HARPS-N Sun-as-a-star observations between 2015 and 2025. Blue points show daily averaged values, while the pink star indicates the low-activity reference day used throughout this work. The long-term evolution traces the solar magnetic cycle, with a clear minimum around 2019–2020 and rising activity toward the s… view at source ↗
Figure 2
Figure 2. Figure 2: Top panel: observed low activity template Sun-as-a-star HARPS-N Solar spectrum, continuum normalized and shown over a select wavelength range for clarity of individual lines. Bottom: the ratio spectra across five different activity levels, over the same selected wavelength range. Various prominent features are highlighted here: The Fe i lines at 4377 Å and 4381 Å change in amplitude, with the first showing… view at source ↗
Figure 3
Figure 3. Figure 3: Trailed spectrum of the Fe i 4377 Å feature as a function of time. Carrington rotation periods and half-periods are indicated by dashed and dot￾ted lines, respectively. The colour scale traces the evolution of the residual line profile and the variation in its amplitude is consistent with rotational modulation. The slanted morphology of each emergent residual feature re￾flects the expected blue-to-red shif… view at source ↗
Figure 4
Figure 4. Figure 4: Top row: solar disc observed with Sol’Ex tuned to the line core of the 4377 Å feature (left), the outer wing of the same line (middle), and their ratio (right), which highlights enhanced contrast in facular regions. Bottom row: comparison between the Sol’Ex spectrum and the corresponding HARPS-N spectrum. The pink and purple markers indicate the wavelengths corresponding to the line-core and wing images sh… view at source ↗
Figure 5
Figure 5. Figure 5: Example residual spectra of the HARPS-N data (purple points) in comparison to PHOENIX models of varying surface gravity values (3.5 in green, 4.0 in pink, 4.5 in blue.) Modelled residual spectra are created by dividing a linear combination of quiet Sun spectrum plus faculae spectrum (normalized by filling factor, here set to 4.5%) by a low activity reference (1% filling factor). See text for further detail… view at source ↗
Figure 6
Figure 6. Figure 6: Example spectra of the HARPS-N data (purple) in comparison to MURaM models of varying magnetic field strengths. 100 G model as a green dashed line, 200 G as a pink solid line, and 300 G as a dash-dotted blue line. Faculae coverage level is set to 4.5%, matching SDO values for this particular day (2022 June 13). Variations in the residuals seen here are representative of changes caused by varying magnetic f… view at source ↗
Figure 7
Figure 7. Figure 7: Various examples of the Fe i 4377 Å feature are shown for different observation days, with HARPS-N data displayed as dark blue points, PHOENIX best-fit models as green dashed lines, and MURaM models in as a red solid line. The left column corresponds to dates during the 2016 period, and the right column shows examples from the 2022 period. Dates were chosen to demonstrate the variation in amplitude of the … view at source ↗
Figure 8
Figure 8. Figure 8: Top row: SDO images of the solar surface for two example days of 2016 June 16 and 2022 June 18. Blue shows pixels defined as faculae with the area threshold applied, orange shows all magnetically active bright points (not visible due to scale), and red shows areas identified as spots. Concentric circles mark limb angles as given by SDO. Bottom row: Histograms of the limb angles calculated by SDO for each p… view at source ↗
Figure 9
Figure 9. Figure 9: Results of faculae filling-factor estimates using each synthetic stellar model in comparison to HARPS-N solar data. The markers show faculae coverage for each day as predicted by each model, with the top row showing PHOENIX results in 2016 and 2022, and the bottom row showing the respective results with MURaM. The colour bars show the best-fit temperature and best-fit 𝜇 angle for PHOENIX and MURaM, respect… view at source ↗
Figure 10
Figure 10. Figure 10: MURaM model residuals computed with a 1% faculae filling-factor of the 200 G injected magnetic field model. Left panel shows residuals at disc centre, middle panel shows residuals at 𝜇 = 0.5, and the right panel shows residuals at the limb. These residuals highlight the change in amplitudes between the 4377 Å and 4381 Å features, showing how their relative strengths vary considerably with limb angle and, … view at source ↗

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