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Measuring the Suns radial velocity variability due to supergranulation over a magnetic cycle

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The quiet Sun's supergranulation timescale varies by up to an order of magnitude across the solar cycle, peaking at activity minimum and anti-correlating with sunspot number.

desk verdict Two independent activity corrections agree that the supergranulation timescale in disk-integrated solar RVs anti-correlates with the cycle, but the abstract overstates the amplitude and the injection-recovery test is too thin to fully rule out a modeling artifact. read the letter →

arxiv 2506.23693 v1 pith:DZSUAIVE submitted 2025-06-30 astro-ph.SR astro-ph.EP

Niamh K. O'Sullivan , Suzanne Aigrain , Michael Cretignier , Ben Lakeland , Baptiste Klein , Xavier Dumusque , Nadège Meunier , Sophia Sulis
show 4 more authors
Megan Bedell Annelies Mortier Andrew Collier Cameron Heather M. Cegla
This is my paper · ORCID
classification astro-ph.SRastro-ph.EP
keywords supergranulationsolarradialvelocitiesactivitycycleGaussianprocessregressionSun-as-a-starHARPS-Nstellarnoiseexoplanetvelocitysurveys
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

This paper tries to establish that supergranulation, the Sun's large-scale horizontal convection pattern, produces a radial-velocity noise component whose characteristic timescale is not fixed but changes by roughly an order of magnitude over the 11-year activity cycle, with the longest timescale at activity minimum. Using eight years of Sun-as-a-star observations from HARPS-N, the authors subtract the contribution of magnetically active regions in two independent ways, one image-based and one purely spectroscopic, and model the residual quiet-Sun radial velocities as the sum of two stochastic processes: granulation and supergranulation. Granulation parameters stay stable, but the supergranulation timescale is strongly anti-correlated with the relative sunspot number, and this anti-correlation appears with both correction methods. If true, stellar noise in exoplanet radial-velocity surveys is non-stationary over activity-cycle timescales, and treating it as a fixed, unchanging process needs revision.

What carries the argument

The argument is carried by a two-component Gaussian Process with aperiodic simple-harmonic-oscillator kernels (quality factor $Q=1/\sqrt{2}$), fitted independently to 4-week chunks of quiet-Sun radial velocities, with the supergranulation component forced to have a lower frequency than the granulation component. For each chunk the fit yields amplitude $S_0$ and angular frequency $\omega_0$ for both components, converted to timescale $\tau=2\pi/\omega_0$ and standard deviation; the resulting timescales are then correlated with the mean relative sunspot number over the same chunk. A Fisher-information calculation, based on derivatives of the covariance matrix with respect to $S_0$ and $\omega_0$, translates different observing cadences into the expected fractional uncertainty on the supergranulation timescale, which is used to predict how many nights are needed to characterise supergranulation in other stars.

What would settle it

Re-fit the same 2015-2023 HARPS-N quiet-Sun RVs with a Harvey-style kernel with a free power-law index, or with a quasi-periodic component added, and check whether the $\tau_{\mathrm{SG}}$ anti-correlation with sunspot number survives; alternatively, measure supergranule lifetimes from resolved SDO/HMI Dopplergrams over the same cycle and compare their evolution with the disk-integrated $\tau_{\mathrm{SG}}$.

Watch

Extended reading notes

Core claim

The central discovery is that the disk-integrated quiet-Sun radial-velocity signal attributed to supergranulation carries a cycle-dependent timescale: $\tau_{\mathrm{SG}}$ is longest at solar minimum, drops by a factor of roughly three during the rising and decaying phases, and anti-correlates with the relative sunspot number ($p<10^{-2}$ for the image-corrected data, $p<10^{-4}$ for the spectroscopically corrected data at 3-month chunks). The authors interpret this as a physical property of supergranulation rather than an artefact, because the two correction methods have limitations that would pull in opposite directions, and because their injection tests for reduced daily sampling and for a 13.5-day activity residual do not reproduce the effect. They also find that the supergranulation timescale measured from 4-week chunks shows large scatter that disappears at 3-month and 1-year chunk lengths, and they reconcile their results with the earlier structure-function analysis by converting their Gaussian-process covariance into structure functions.

Load-bearing premise

The analysis assumes that after active regions are removed, the quiet-Sun radial velocities are exactly the sum of two independent aperiodic SHO processes with fixed $Q=1/\sqrt{2}$, so that the fitted supergranulation timescale is an unbiased measure of the true physical timescale rather than a product of the model or of the activity correction.

Editorial extensions

If this is right

  • Radial-velocity noise models for Sun-like stars must allow the supergranulation timescale to vary with activity state; a fixed kernel will misestimate the covariance on multi-year baselines.
  • Exoplanet surveys that deliberately target low-activity stars to reduce spot and facula signals may unintentionally encounter a stronger, longer-timescale supergranulation signal.
  • Characterising supergranulation in other stars requires dedicated campaigns of at least about 23 nights, but rapid switching between targets can monitor up to 10 stars at once to roughly 30% precision in $\tau_{\mathrm{SG}}$.
  • Granulation parameters remain stable over the cycle, so the granulation component can be calibrated once and treated as stationary, while the supergranulation component cannot.
  • The effect disappears when the data are analysed with daily sampling or structure functions, so non-parametric methods on sparsely sampled data can miss the cycle dependence.

Reading between the lines

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

  • A testable consequence the paper leaves implicit: if $\tau_{\mathrm{SG}}$ is activity-dependent, then applying the same Gaussian-process analysis to long-baseline radial-velocity time series of other Sun-like stars, alongside an activity indicator such as the S-index, should reveal a similar anti-correlation between the fitted convective timescale and activity level.
  • The factor-of-two change in timescale is larger than the roughly 10% changes in supergranule size reported in imaging studies, suggesting that the disk-integrated timescale may be modulated by something other than cell size alone, perhaps the distribution of cell lifetimes or the magnetic network; resolved-imaging lifetime measurements over a full cycle would be a discriminating test.
  • Because the spectroscopic correction linearly decorrelates against the S-index, part of the apparent cycle could in principle be caused by activity-dependent removal of supergranulation; the agreement with the image-based correction argues against this, but injecting activity-correlated supergranulation signals into the pipeline would settle it.
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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

3 major / 5 minor

Summary. This paper uses eight years of HARPS-N Sun-as-a-star radial velocities (July 2015 to November 2023) to measure the granulation and supergranulation properties of the quiet Sun after subtracting active-region contributions with two independent methods: an SDO/HMI image-based correction and the YARARA spectral decorrelation. The quiet-Sun RVs are modelled in 4-week, 12-week, and 1-year chunks with a two-component aperiodic simple-harmonic-oscillator Gaussian process plus white noise (Section 3). The paper reports that the supergranulation timescale tau_SG is longest at solar minimum and is strongly anti-correlated with the SILSO relative sunspot number, with Spearman p-values below 1e-2 for SDO and below 1e-4 for YARARA for 3-month chunks, while granulation parameters remain stable. It also uses a Fisher-information approach to argue that a roughly 23-night campaign with rapid target switching can constrain tau_SG to 30% precision for up to 10 stars, and it discusses plausible physical explanations for a supergranulation cycle.

Significance. If the central claim holds, the supergranulation timescale in disk-integrated solar RVs is not stationary over the magnetic cycle, with direct consequences for modelling stellar noise in EPRV surveys and for the interpretation of granulation-driven RV variability. The study's strengths are the use of two independent activity corrections, the explicit reporting of correlation p-values, and the effort to validate the GP model with injection-recovery tests in the appendices. The observing-strategy analysis is concrete and falsifiable, and it provides a useful planning estimate for future campaigns. However, the physical interpretation rests on the assumption that the fitted SHO timescale is an unbiased estimator of the true supergranulation timescale across the activity cycle, and the current validation does not yet establish this. The paper is therefore a potentially valuable contribution whose central claim needs additional support before it can be accepted.

major comments (3)
  1. [Abstract, §4.3, §6] The abstract and the discussion overstate the amplitude of the cycle variation. Table 2 gives mean tau_SG at solar minimum of 1.27 +/- 0.13 d (YARARA) and 1.60 +/- 0.16 d (SDO), versus 0.61 +/- 0.07 d and 0.80 +/- 0.10 d at the beginning of Cycle 25, i.e. a factor of about 2, not an order of magnitude. The order-of-magnitude range appears only in the 4-week-chunk scatter discussed in Section 4.2, which is not the cycle trend; the Discussion's 'factor of three' also exceeds the Table 2 ratios. Please harmonize the abstract, Section 4.3, and Section 6 with the quantitative results.
  2. [§4.3, Appendix B] The injection-recovery test does not rule out activity-dependent contamination of tau_SG. Section 2.2 reports residual power at Prot/2 ~14 d and Prot/3 ~8 d in both corrected datasets, so the actual residuals are not a stationary two-component aperiodic process. Appendix B injects a single quasi-periodic 13.5-day signal at fixed amplitude into one simulated year and finds no bias in the fitted parameters, but it does not scale the injected amplitude with sunspot number, does not reproduce the 4-week/12-week chunking, outlier rejection, and gap patterns, and does not cover the range of activity states present in the real data. If the 8-14 d residual power grows with SSN, the aperiodic SHO kernel and the white-noise term can trade variance, shifting tau_SG; the constant 0.20-0.25 m/s jitter check in Section 6 does not test whether the SHO parameters themselves move. Please add multi-amplitude injection-recovery tests spanning the observed SSN range with the actual chunking and outlier rejection, or otherwise demonstrate that tau_SG is an unbiased estimator of the supergranulation timescale throughout the cycle.
  3. [§3 (Eqs. 6-7), §4.1] The model assumes that the quiet-Sun residuals are exactly described by two independent aperiodic SHO kernels with Q=1/sqrt(2) plus white noise, and the fitted tau_SG is interpreted as the physical supergranulation timescale. This assumption is load-bearing. The agreement between the SDO and YARARA corrections is reassuring but not decisive: both corrections start from the same HARPS-N spectra, both residual sets contain the same 14-day peaks, and the authors themselves note in Section 4.1 that the YARARA S-index decorrelation may remove part of the supergranulation signal. The paper should either validate the two-SHO model against injected signals with activity levels representative of all cycle phases, or test an alternative model that includes a quasi-periodic term and show that the tau_SG-SSN anti-correlation is robust to the model choice.
minor comments (5)
  1. [§2.2] The sentence containing 'weather the activity-correction was done with YARARA or SDO' should read 'whether'; the typo appears in the discussion of the 14-day and 8-day activity residuals.
  2. [Appendix B, Fig. B1 caption] The caption states that the injected activity signal has period = 13.5 hours, while the text says 13.5 days; please correct the inconsistency.
  3. [Table 2] The Al Moulla et al. row lists sigma_G and sigma_SG without uncertainties; please state whether these are central values without published errors or add the uncertainties.
  4. [§4.2] The statement that the 4-week-chunk scatter 'is real' and not an artefact of the limited chunk duration is supported only by a reference to O'Sullivan & Aigrain (2024); please show the relevant injection-recovery result or temper the wording.
  5. [Eq. (13)] The displayed derivative of the SHO kernel with respect to omega appears garbled in the typeset version; please verify the equation and its sign structure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central tau_SG–SSN anti-correlation is an empirical result tested against external SILSO data, not a quantity forced by the GP model or by the paper's own definitions.

full rationale

The paper does not claim a first-principles derivation; it empirically fits a two-component aperiodic SHO Gaussian process (Eqs. 6–7) to quiet-Sun RVs and reads off the supergranulation timescale tau_SG from the fitted angular frequency omega_0 (Eq. 5). The load-bearing result is the anti-correlation between tau_SG and the relative Sunspot number reported in Section 4.3. That comparison uses an external dataset (SILSO; Clette & Lefèvre 2015), and the Sunspot number never enters the GP likelihood, the kernel definition, or the conversion from omega_0 to tau_SG, so the anti-correlation is not imposed by construction. The result is also reproduced with two different activity-correction methods (SDO image-based and YARARA spectroscopic), which start from the same HARPS-N spectra but make different assumptions; the agreement is a consistency check rather than a definitional identity. The self-citations, chiefly to O'Sullivan & Aigrain (2024) for the GP method and to Lakeland et al. (2024) for the SDO correction, are methodological rather than load-bearing: the GP method is validated by injection-recovery tests in Appendices A and B, and the cycle claim is benchmarked against external sunspot data and previous solar literature. Appendix B injects only a single fixed 13.5-day activity signal and does not test a cycle-modulated residual, so the possibility that activity-dependent residual power biases the fitted tau_SG is a genuine model-misspecification and robustness risk, not a circularity: it cannot be exhibited as an equation in which the fitted quantity equals its input. Similarly, Section 5's Fisher-information survey uses the measured tau_SG and sigma_SG values as assumed inputs for an observing-strategy calculation; that is a planning/sensitivity exercise, not a prediction of the solar cycle from the same fit. No step in the paper reduces by definition or by self-citation to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities. The central claim rests on the GP kernel choice, the two activity-correction pipelines, the chunking and sampling assumptions, and the MCMC fitting of five hyperparameters per chunk. One arbitrary threshold, the 30% target precision, drives the campaign-planning conclusions.

free parameters (4)
  • granulation amplitude S0,G and frequency omega0,G = varies per chunk; typical sigma_G about 0.33 m/s, tau_G about 0.03 days
    Fitted by MCMC in the two-component GP model (Section 3); defines the granulation component that must be separated from supergranulation.
  • supergranulation amplitude S0,SG and frequency omega0,SG = varies per chunk; typical sigma_SG about 0.7-0.9 m/s, tau_SG about 0.6-1.6 days (Table 2)
    These fitted values are the paper's central measurements; the tau_SG anti-correlation with sunspot number is the main claim.
  • white noise standard deviation sigma_w = about 0.20-0.25 m/s
    Fitted per chunk (Section 3, Eq. 8); absorbs photon noise, instrumental systematics, and any residual unmodelled signals.
  • target fractional uncertainty threshold of 0.3 on tau_SG = 0.3
    Chosen by hand in Section 5 as the precision needed to detect cycle variation; it sets the 23-night and 10-star conclusions of the survey design.
assumptions (5)
  • domain assumption The quiet-Sun RV PSD is the sum of two independent aperiodic SHO components (granulation and supergranulation) with Q=1/sqrt(2), plus white noise.
    Used in Section 3, Eq. 6-7; fixes what 'characteristic timescale' means. A different PSD slope or Q would shift tau_SG.
  • domain assumption The SDO/HMI active-region correction removes active-region RVs without removing supergranulation.
    Section 2.2.1; inherits thresholds from Haywood et al. (2016) and Milbourne et al. (2019). Regions below 20 micro-hemispheres remain in the quiet-Sun RVs.
  • domain assumption The YARARA linear decorrelation against the Ca II H&K S-index removes plage and faculae without attenuating supergranulation in an activity-dependent way.
    Section 2.2.2; the authors acknowledge supergranulation could be partially removed if correlated with S-index and argue agreement with the SDO correction makes this minimal.
  • domain assumption GP parameter estimates from 4-week chunks with about 5.3 hours of daily sampling are unbiased for the supergranulation timescale.
    Section 3 and Appendix A; Appendix A tests only one month of simulated data and sampling windows, not the full range of activity states and gap patterns; the 4-week scatter claim relies on injection-recovery in O'Sullivan & Aigrain (2024).
  • standard math Fisher information uncertainties are accurate for campaign planning under the assumption that the GP kernel is the true generative model.
    Section 5, Eq. 9-11; validated with a 5-day simulation, but the authors state the uncertainties are approximate.

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Cite this review

Pith. "Pith review of Measuring the Suns radial velocity variability due to supergranulation over a magnetic cycle." pith.science (2026). https://pith.science/paper/DZSUAIVE

@misc{pith2026250623693,
  author       = {Pith},
  title        = {Pith review of: Measuring the Suns radial velocity variability due to supergranulation over a magnetic cycle},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DZSUAIVE}},
  note         = {Machine review of arXiv:2506.23693}
}
read the original abstract

In recent years supergranulation has emerged as one of the biggest challenges for the detection of Earth-twins in radial velocity planet searches. We used eight years of Sun-as-a-star radial velocity observations from HARPS-N to measure the quiet-Sun's granulation and supergranulation properties of most of its 11-year activity cycle, after correcting for the effects of magnetically active regions using two independent methods. In both cases, we observe a clear, order of magnitude variation in the time-scale of the supergranulation component, which is largest at activity minimum and is strongly anti-correlated with the relative Sunspot number. We also explored a range of observational strategies which could be employed to characterise supergranulation in stars other than the Sun, showing that a comparatively long observing campaign of at least 23 nights is required, but that up to 10 stars can be monitored simultaneously in the process. We conclude by discussing plausible explanations for the "supergranulation" cycle.

Figures

Figures reproduced from arXiv: 2506.23693 by the authors.

Figure 1
Figure 1. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. HARPS-N solar RVs (light blue, top), SDO quiet-Sun RVs (green, middle), and YARARA quiet-Sun RVs (pink, bottom), with arbitrary offset for graphical consideration. The vertical lines delimitate the end of cycle 24, the solar minimum, and the start of cycle 25 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Lomb-Scargle Periodogram of the HARPS-N Solar RVs (light blue), SDO quiet-Sun RVs (green), and YARARA quiet-Sun RVs (pink). The vertical lines indicate the solar rotation period and the first two harmonics (dashed). 2.2.2 YARARA activity correction Our second method uses YARARA (Cretignier et al. 2021), a post￾processing methodology designed primarily to deliver improved RV precision compared to the DRS data product… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Parameters of the GP fits to the SDO and YARARA quiet-Sun RVs obtained in 4-week chunks over the solar cycle. The parameters of the granulation component, logSG and logωG, are shown in the left hand column, while the supergranulation parameters logSSG and logωSG are sh…
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Supergranulation parameters obtained from SDO and YARARA quiet-Sun RVs when fitting longer chunks of 12 weeks (stars) and 1 year (circles). The colour scheme is the same as for Figures 4 and 5, and the horizontal line and shaded area once again shows the literature val…
Figure 7
Figure 7. Figure 7: Correlation between the supergranulation parameters obtained from the 12-week (3-month) chunks and the Sun-spot numbers, for the SDO-corrected RVs (left, green) and the YARARA-corrected RVs (right, pink). In each panel we also report the p-values derived from a Spearma…
Figure 8
Figure 8. Figure 8: Expected σ and τ fractional uncertainty as a function of number of nights of observation for continuous observations of a single star. The fractional uncertainty is calculated for various σ and τ values corresponding to different phases of the solar cycle. The hyperpar…
Figure 9
Figure 9. Figure 9: Number of nights needed to reach a fractional uncertainty of 0.3 in the supergranulation timescale τ as a function of the number of stars observed each night. Different colours correspond to different observational strategies, as described in the text. the supergranula…
Figure 10
Figure 10. Figure 10: Structure functions corresponding to the YARARA (middle) and SDO (right) hyperparameters calculated using year long chunks. The lines are coloured by the average sun spot number that year. The original results from Lakeland et al. (2024) are shown on the left. ity, as…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.