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REVIEW 2 major objections 7 minor 171 references

Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars

T0 review · 2 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Doppler Imaging, a technique built for rapidly rotating stars, can map the Sun's surface from high-stability spectra and filter its radial-velocity activity down to 0.58 m/s, opening a wavelength-domain route to long-period low-mass…

desk verdict Brightness DI of the Sun from disk-integrated HARPS-N CCFs is a solid proof of concept, validated against SDO images, and the joint DI+planet fit recovers injected signals as well as 2D GP; the caveats are the cited GP baseline and mildly circular priors. read the letter →

arxiv 2508.12963 v1 pith:AZ3YXVJB submitted 2025-08-18 astro-ph.EP astro-ph.IMastro-ph.SR

Baptiste Klein , Suzanne Aigrain , Michael Cretignier , Xavier Dumusque , Khaled Al Moulla , Jean-François Donati , Niamh K. O'Sullivan , Haochuan Yu
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Andrew Collier Cameron Oscar Barragán Annelies Mortier Alessandro Sozzetti
This is my paper · ORCID
classification astro-ph.EPastro-ph.IMastro-ph.SR
keywords DopplerimagingstellaractivityradialvelocitiesSunasastarlow-massplanetsearchGaussianprocessregressioninjection-recoveryfiltering
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to prove that Doppler Imaging can be moved from fast rotators to Sun-like stars and act as a stellar-activity filter for planet hunting. It reconstructs the Sun's relative surface brightness every 27 days from HARPS-N spectra, finds that the maps agree with large-scale SDO Dopplergrams when activity is strong enough, and reports RV residuals of 0.58 m/s after subtracting the DI model. In planet injection-recovery tests, DI recovers long-period, low-mass planet signals as accurately as Gaussian-process regression when the planet fit is run jointly with the imaging. If true, this gives planet hunters a physically motivated, wavelength-domain way to remove stellar noise that does not rely on time-domain covariance assumptions.

What carries the argument

The central object is the Doppler Imaging inversion itself: a maximum-entropy reconstruction of relative surface brightness from a time series of cross-correlation functions. The surface is divided into roughly 10,000 cells, each with a brightness and a local line profile computed from an assumed radiative-transfer model; synthetic disc-integrated profiles are matched to the observed CCFs by conjugate-gradient iteration. Two adaptations make this work for the slow-rotating Sun: an iterative self-calibration of the unknown intrinsic line profile (subtract the median observed-minus-model CCF, re-fit, repeat until flat), and division of the two-year dataset into 27-day chunks over which active regions are assumed static. The planet search is an extension of the same code: shift the CCFs by a trial Keplerian signal, re-run the inversion, and map $\chi^2$ over the planet grid, following the joint-fit method.

What would settle it

Repeat the joint DI-plus-planet injection-recovery on a star with a known transiting planet and semi-amplitude near 0.4 m/s, or on the Sun with the true local line profile measured from disc-resolved spectroscopy; if the joint fit is biased beyond its 1-sigma uncertainties, or if using the true profile instead of the iteratively flattened one changes the maps or residuals, the slow-rotator self-calibration is absorbing signal and the central claim fails.

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Extended reading notes

Core claim

The paper's central claim is that a maximum-entropy Doppler Imaging inversion of observed cross-correlation functions can serve as an activity model for Sun-like stars. Applied chunk-by-chunk to two years of HARPS-N solar spectra, DI reconstructs brightness maps with an angular resolution of about 36 degrees, matching large-scale SDO Dopplergrams (modelled to spherical-harmonic degree $\ell_{\max}=5$) with a median absolute correlation of 0.63 at the phase of maximum profile distortion, provided the disc-integrated RV exceeds about 2 m/s. The RVs read off the best-fit profiles reproduce the observed solar RV curve with 0.58 m/s residuals, and no power remains at the rotation period or its harmonics. The same inversion, run blindly, preserves the period and phase of an injected planet but underestimates its semi-amplitude by roughly 40 percent; when the planet fit is folded directly into the inversion by Doppler-shifting the CCFs, the recovered semi-amplitudes match the injected values within $1\sigma$, with uncertainties comparable to a two-dimensional Gaussian-process fit. The paper concludes that DI is not yet an operational planet-search tool, but it is a credible physical, wavelength-domain alternative for suppressing activity around slowly rotating solar twins.

Load-bearing premise

The load-bearing premise is that the Sun's local line profile can be replaced by an assumed model and then fixed by iteratively subtracting the median data-minus-model difference until flat; if that step absorbs axisymmetric activity or part of a planet's Doppler shift, the reconstructed maps and the 0.58 m/s correction are biased.

Editorial extensions

If this is right

  • DI removes the rotationally modulated activity signal from Sun-like-star RVs, leaving 0.58 m/s RMS residuals with no periodicity at the rotation period or its harmonics.
  • DI brightness maps agree with disc-resolved SDO Dopplergrams on scales of about 36 degrees only when the activity-induced RV is above about 2 m/s; quieter epochs yield unreliable maps.
  • Blind DI gives unbiased orbital periods and phases but underestimates injected low-mass planet semi-amplitudes by about 40 percent; the paper's joint DI-plus-planet fit is required for accurate masses.
  • With the joint fit, DI recovers injected planet semi-amplitudes as accurately as a two-dimensional Gaussian-process model, with comparable 1-sigma uncertainties.
  • Injection-recovery completeness reaches 100 percent for injected planets with orbital period above 100 days and semi-amplitude above 0.4 m/s, and 67 percent below 0.4 m/s, while planets with periods near the rotation period and its harmonics are lost.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, a multi-cycle Sun-like dataset could test whether DI's wavelength-domain filtering stays stable while Gaussian-process hyperparameters drift over a magnetic cycle; the two-year baseline here cannot address that.
  • Beyond the paper, using CCF masks built from lines with different formation temperatures should separate convective-bluesshift inhibition from brightness contrast, potentially yielding simultaneous intensity and velocity maps from one spectral time series.
  • Beyond the paper, a hybrid pipeline suggests itself: run blind DI to supply period and phase priors, then switch to a joint DI-plus-planet fit for unbiased masses, avoiding the 40 percent blind bias while keeping DI's long-period sensitivity.
  • Beyond the paper, the 2 m/s threshold implies DI will be noise-dominated for very quiet stars, so a sensitivity-floor test on synthetic quiet-star spectra would show where DI should yield to time-domain methods.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. This paper presents a proof-of-concept application of traditional maximum-entropy Doppler Imaging (DI) to Sun-as-a-star observations, using HARPS-N CCFs collected between December 2021 and January 2024. The data are split into 23 independent 27-day chunks, and for each chunk a relative brightness map is inverted from the CCF time series, after an iterative self-calibration of the unknown intrinsic line profile (Sec 2.2.1) and assuming non-evolving active regions (Sec 2.2.2). Three lines of evidence are presented. First, RVs extracted from the best-fit CCFs reproduce the observed activity-driven RVs with a residual RMS of 0.58 m/s, and a GLS periodogram of the residuals shows no remaining power at the rotation period or its harmonics. Second, the DI brightness maps correlate with large-scale (ell_max = 5) SDO/HMI dopplergrams at epochs of strong line-profile distortion: the median absolute Pearson correlation is about 0.63 at the phase of maximum |RV| per chunk, with correlations above roughly 0.5 only when |RV| exceeds about 2 m/s. Third, in planet injection-recovery tests, blind DI preserves the orbital period and phase of injected planets but underestimates K by about 40%, whereas a joint DI+planet fit recovers K within 1 sigma of the injected values for periods of 6 and 100 d, with uncertainties comparable to those from 1D and 2D Gaussian process regression.

Significance. The potential significance of this work is genuine: it appears to be the first demonstration that classic DI, designed for rapidly rotating stars, can be applied to a Sun-like slow rotator observed with a stable spectrograph, and that the reconstructed maps carry spatially resolved information grounded against independent, disc-resolved SDO observations. Several aspects of the paper are strengths that should be credited. The planet injection-recovery tests are built on the actual solar CCFs and include multiple phase realisations; the SDO comparison provides an external validation that is rare in this literature; the authors explicitly report the blind-DI K underestimate (about 40%) rather than hiding it; and the robustness tests in Sec 4.3 characterise the regime (noise level, number of epochs) in which the inversions are trustworthy. The paper is also appropriately hedged about map realism.

major comments (2)
  1. [Sec. 5.2.1-5.2.2, Tables 3-4] The joint activity+planet fit carries the abstract's central claim that DI 'yields planetary mass estimates with an accuracy comparable to, for example, multi-dimensional Gaussian process regression', but its validation has two gaps. First, the fit adopts Gaussian priors on Porb and phi_p that were obtained from the blind DI run on the same data (Sec 5.2.2: 'We thus adopt Gaussian priors for these two parameters, using the best-fit values and uncertainties reported in Tab. 3'), so the K recovery in Table 4 is not a blind validation of the full pipeline. Second, the longest injected period tested is 100 d, while the paper advertises the method for Porb > 100 d. The blind DI run already underestimates K by about 40% (Table 3), which the paper attributes to cross-talk between CCF derivatives; an equally plausible mechanism, acknowledged in Sec 2.2.1 ('could affect axisymmetric structures generating non-modulated profile distortions'), is that the iterative intrinsic-profile self-calibration absorbs the per-chunk mean of a long-period planet signal. For a 27-d chunk (Sec 3.2), a 100-d planet contributes only about 0.4 K of within-chunk RMS; for longer periods that constraint weakens further. I therefore request an additional injection-recovery test in which the joint fit is applied to a planet with Porb of about 200-300 d using wide uniform (or fully marginalised) priors on Porb and phi_p, reporting the recovered K and its credible interval. If K remains unbiased, the claim is supported; if not, the 'accuracy comparable to multi-dimensional GP' statement should be restricted to Porb of about 100 d or less.
  2. [Sec. 4.1, Fig. 3] The headline residual RMS of 0.58 m/s is presented as 'consistent with that obtained with a Gaussian process regression on the RV time series (see Klein et al. 2024)', but the GP residual is not computed on the same 23-chunk dataset in this paper; the comparison rests entirely on a citation. Since the DI-corrected RVs are extracted from the best-fit CCFs to which the DI model was itself fitted (Sec 4.1 reports reduced chi2 = 1), the residual is partly a fit-quality statistic, and the per-chunk self-calibrated intrinsic profile (Sec 2.2.1) gives the model freedom on non-modulated components. To support the abstract's 'comparable with existing state-of-the-art activity correction techniques', I suggest computing a 1D GP regression on the same chunks, with the same noise model and outlier selection, and quoting the resulting residual RMS alongside 0.58 m/s; alternatively, the claim should be reworded to cite the specific Klein et al. 2024 residual and note that it was obtained on the same or a neighbouring time span.
minor comments (7)
  1. [Eq. (4) and Tables 2-3] The units of the orbital phase phi_p are inconsistent: Eq. (4) adds phi_p to 2*pi*(T0 - t)/P as if it were an angle in radians, while the tabulated values (0.0, 0.33, 0.7) read as fractions of an orbital cycle. Please state the units explicitly and write 2*pi*phi_p in the sine argument if cycles are intended.
  2. [Sec. 4.3] The clause 'values consistently larger than 0.5 for relative levels larger or equal to ~10^-4' appears to contradict the preceding statement that the correlation 'decreases roughly linearly with the noise level'; presumably 'smaller than or equal to ~10^-4' is intended.
  3. [Sec. 3.1] 'gosts' in the list of instrumental contamination sources should read 'ghosts'.
  4. [Sec. 4.2] 'intensitigrams' appears twice and should be 'intensitygrams'.
  5. [Fig. 2 caption] The caption states that the color scale depicts the logarithm of the relative surface brightness, but the color bar is labelled 'Relative brightness [%]'; please make the labelling consistent.
  6. [Sec. 4.2, Fig. 5] The '~2 m/s' threshold for a good DI-SDO match is calibrated on only 23 chunks (Pearson rho_RV = 0.85 in Fig. 5) and should be explicitly presented as a tentative, small-sample calibration rather than a general detection criterion.
  7. [Sec. 6.2] Minor wording issues: 'one of the most promising way' should be 'ways', and 'systemtically' in Sec 5.2.2 should be 'systematically'.

Circularity Check

1 steps flagged · score 3.0 of 10

Mild circularity: the joint DI+planet fit reuses period/phase estimates from a blind DI run on the same data, but the SDO comparison and completeness tests remain independent.

  1. other [Section 5.2.2 (Results of joint activity and planet fit)]
    "However, as shown in Section 5.1, the blind CCF modelling with DI has enabled us to accurately estimate the planet's orbital period and phase. We thus adopt Gaussian priors for these two parameters, using the best-fit values and uncertainties reported in Tab. 3."

    The P_orb and phi_p values in Tab. 3 were recovered from the same injected HARPS-N CCFs, after a blind DI activity correction. Feeding those values back as Gaussian priors in the joint DI+planet fit means that the Kp recovery reported in Tab. 4 is conditional on period and phase information already extracted from the same dataset. This does not make Kp itself a fitted input, since it retains a uniform prior, so the circularity is partial rather than an equivalence by construction. The GP comparison is not on exactly the same footing because the GPs use non-informative priors on P_orb and phi_p, whereas DI is given narrow priors derived from the same data.

full rationale

The paper's main derivation chain is not circular: DI maps are inverted from CCF time series, and the primary validation of those maps is an external comparison with SDO/HMI dopplergrams, which is independent of the RV extraction. The planet-sensitivity claims are also tested by injecting synthetic planetary signals with known ground truth, and the blind-DI completeness maps are an independent, well-posed exercise. The one genuinely self-referential element is the joint-fit validation in Section 5.2.2: the Gaussian priors on P_orb and orbital phase are taken from a blind DI analysis of the same dataset, so the Kp accuracy reported for DI in Tab. 4 is not a fully end-to-end blind test and is not on exactly the same footing as the GP comparison, which uses non-informative priors for those parameters. Since Kp remains a free parameter with a uniform prior, this is a validation-circularity issue rather than a case where the predicted quantity is forced by construction. No load-bearing uniqueness theorem, ansatz smuggled in by self-citation, or renaming of a known result was found. The self-calibration limitation in Section 2.2.1 is acknowledged by the authors and is a physical degeneracy that they explicitly discuss, not a circular reduction.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The DI reconstruction relies on a set of modeling choices: a fixed stellar inclination, a self-calibrated intrinsic line profile, static surface brightness within 27-day chunks, and maximum-entropy regularisation. No new physical entities are introduced. The planet injection-recovery tests are grounded in known injected signals, which makes them external benchmarks for the RV recovery rather than fitted outputs.

free parameters (5)
  • Assumed stellar inclination = 80 degrees
    Set to 80 degrees in all inversions to break north-south degeneracy; a chi2 grid later gives 69 +/- 16 degrees, so the maps depend on this choice (Section 4.4.2).
  • Intrinsic local line profile (Unno-Rachkovsky parameters) = unspecified (standard Milne-Eddington values)
    Unknown for slow rotators; the code assumes a Milne-Eddington atmosphere and then self-calibrates via median-difference subtraction (Section 2.2.1).
  • Chunk length = 27.2753 days
    Data are split into one Carrington rotation to limit activity evolution within a chunk (Section 3.2).
  • Chunk selection thresholds = Npt >= 10; phase gap <= 25%
    Chunks with fewer points or larger gaps are excluded, affecting which data enter the analysis (Section 3.2).
  • Map-quality RV threshold = about 2 m/s
    Empirical cutoff above which DI maps correlate with SDO dopplergrams; used to state when the method works (Section 4.2).
assumptions (7)
  • domain assumption Maximum entropy regularisation selects the correct solution to the ill-posed DI inversion
    Used to lift degeneracies (Skilling and Bryan 1984; Section 2.2).
  • domain assumption All CCF distortions are caused by surface brightness inhomogeneities; convective blueshift inhibition in faculae can be approximated by brightness contrast
    Section 2.2.2; if false, DI maps are not physical, though RV filtering may still work.
  • domain assumption Active regions do not evolve within a 27-day chunk
    Section 2.2.2; the Sun's regions do evolve on this timescale, so this is an approximation.
  • ad hoc to paper The intrinsic local line profile can be recovered by iteratively subtracting the median observed-synthetic CCF difference
    Section 2.2.1; this self-calibration may absorb non-modulated signals.
  • standard math Unno-Rachkovsky radiative transfer in a Milne-Eddington atmosphere describes local line profiles
    Section 2.2; standard analytic approximation, but with systematic differences for the Sun.
  • domain assumption Planet orbits are circular in injection-recovery tests
    Section 5; eccentric orbits are not considered.
  • domain assumption Noise is Gaussian and characterised by the CCF continuum dispersion
    Section 4.1; supergranulation and instrument instability are not explicitly modelled.

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Pith. "Pith review of Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars." pith.science (2026). https://pith.science/paper/AZ3YXVJB

@misc{pith2026250812963,
  author       = {Pith},
  title        = {Pith review of: Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AZ3YXVJB}},
  note         = {Machine review of arXiv:2508.12963}
}
read the original abstract

Doppler Imaging (DI) is a well-established technique to map a physical field at a stellar surface from a time series of high-resolution spectra. In this proof-of-concept study, we aim to show that traditional DI algorithms, originally designed for rapidly-rotating stars, have also the ability to model the activity of Sun-like stars, when observed with new-generation highly-stable spectrographs, and search for low-mass planets around them. We used DI to retrieve the relative brightness distribution at the surface of the Sun from radial velocity (RV) observations collected by HARPS-N between 2022 and 2024. The brightness maps obtained with DI have a typical angular resolution of about 36 degrees and are a good match to low-resolution disc-resolved Dopplergrams of the Sun at epochs when the absolute, disc-integrated RV exceeds ~2 m/s. The RV residuals after DI correction exhibit a dispersion of about 0.6 m/s, comparable with existing state-of-the-art activity correction techniques. Using planet injection-recovery tests, we also show that DI can be a powerful tool for blind planet searches, so long as the orbital period is larger than ~100days (i.e. 3 to 4 stellar rotation periods), and that it yields planetary mass estimates with an accuracy comparable to, for example, multi-dimensional Gaussian process regression. Finally, we highlight some limitations of traditional DI algorithms, which should be addressed to make DI a reliable alternative to state-of-the-art RV-based planet search techniques.

Figures

Figures reproduced from arXiv: 2508.12963 by the authors.

Figure 1
Figure 1. Solar-rest-frame RV time series extracted with HARPS-N DRS. The vertical color bands indicate the different subsets of data used in the DI analysis (see Section 3.2). Grey points were not used in the analysis. The number of each chunk as listed in Tab. 1 is indicated in dark blue at the bottom of the figure. as the instrument instability and stellar variability (e.g. supergranu￾lation), not accounted for in the form… view at source ↗
Figure 2
Figure 2. Best-fitting relative brightness distribution of the Sun for each of the 23 chunks listed in Tab. 1 and shown in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Time series of RVs extracted from HARPS-N DRS (black points) and from the best-fitting DI line profiles (red solid lines, top panel), and residuals (bottom panel). phase which maximises the absolute value of the RV in each chunk (see [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: GLS periodogram of the HARPS-N RVs (top black line) and of the RV residuals (bottom yellow line). The false alarm probability of the most prominent peak in the periodogram of the RV residuals, computed using the method of Baluev (2008), is about 0.5. The vertical dotte…
Figure 5
Figure 5. Figure 5: Correlation coefficients between SDO large-scale dopplergrams (DSDO) and DI brightness maps (IDI), against the solar RVs at rotational phase 0, as defined in Eq. 2. The two time series exhibit a Pearson correlation coefficient 𝜌RV of 0.85. not included in our DI framew…
Figure 7
Figure 7. Figure 7: Average Pearson correlation coefficient between the input bright￾ness distribution and the recovered DI maps as a function of the noise level in the continuum-normalised line profiles (left panel), and the number of epochs (right panels). In both panels, the dashed lin…
Figure 8
Figure 8. Figure 8: Correlation between consecutive DI brightness maps averaged over all pairs of chunks with detected solar rotation (top panel) and between chunks 8 and 9 in Tab. 1 (bottom panel), in the (Ωeq,dΩ) space. In both panels the white dashed lines indicate the solar DR values …
Figure 9
Figure 9. Figure 9: GLS periodograms of the HARPS-N solar RVs after the injection of the planet RV signatures listed in Tab. 2. In each case, the top black and bottom yellow lines represent the periodogram of the RV time series before and after applying DI to filter stellar activity signa…
Figure 10
Figure 10. Figure 10: Completeness estimates for the recovery of the 1 000 planet RV signatures injected in the HARPS-N solar CCFs for different activity filtering techniques (see Sec. 5.1.1). The number and the color of each cell both indicate the completeness of the planet injection-reco…
Figure 11
Figure 11. Figure 11: Best estimates of the planet RV semi-amplitude for the three different planets listed in Tab. 2 and retrieved using three different stellar activity models. In each panel, the injected RV semi-amplitude is indicated by the horizontal dashed line. The planet RV semi-am…

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.