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REVIEW 4 major objections 6 minor 67 references

Gaussian process regression of temperature-dependent radial velocities

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Solar radial velocities measured from spectral lines formed at 4000–4750 K show the least activity-driven scatter, in both high- and low-activity phases.

desk verdict A careful, reproducible solar RV study whose headline 'sweet spot' finding needs error bars before it should be cited as robust; the GP hyperparameter mapping and SDO comparison are the more solid contributions. read the letter →

arxiv 2501.02959 v1 pith:2DYACVJE submitted 2025-01-06 astro-ph.SR

Federica Rescigno , Khaled Al Moulla This is my paper · ORCID
classification astro-ph.SR
keywords Gaussianprocessregressionstellaractivitytemperature-dependentradialvelocitiessolarphotosphereHARPS-NDopplergramsquasi-periodickernelexoplanetdetection
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 tries to establish that stellar activity imprints on radial-velocity (RV) measurements in a way that depends on the temperature of the spectral lines used, and that a specific intermediate-cool range (4000–4750 K) is the least affected by activity, regardless of whether the Sun is at high or low activity. The authors apply Gaussian-process regression with a quasi-periodic covariance kernel to 11 temperature-dependent RV time series from three years of HARPS-N Sun-as-a-star spectra, using two 140-day intervals at high and low activity. They find that the 4000–4750 K range yields the smallest RV scatter both before and after subtracting the GP model, and that the GP hyperparameters behave differently across activity phases and temperature ranges. This matters because activity noise is the principal obstacle to detecting Earth-like exoplanets, so finding spectral segments that are intrinsically quieter, or whose activity is easier to model, could improve planet detection and characterisation. The paper also connects the temperature-dependent RVs to disk-resolved SDO Dopplergram components, identifying the inhibition of convective blueshift as the dominant source in hotter-line RVs.

What carries the argument

The object carrying the argument is the quasi-periodic covariance kernel $k(t_i,t_j) = A^2 \exp\!\left(-\frac{|t_i-t_j|^2}{\tau^2} - \frac{\sin^2(\pi|t_i-t_j|/P_{\rm rot})}{\mu^2}\right) + \delta_{ij}\beta^2$, with amplitude $A$, evolution timescale $\tau$, rotation period $P_{\rm rot}$, inverse harmonic complexity $\mu$, and jitter $\beta$. The RVs are extracted with the ARVE pipeline from spectral segments binned by their average formation temperature $T_{1/2}$, defined as the photospheric temperature where the cumulative flux contribution reaches 50% of its maximum, using a formation-temperature map computed from PySME spectral synthesis with MARCS atmospheres and VALD line lists. GP hyperparameters are fit via MCMC with MAGPy_RV, and the temperature-dependent RVs are additionally correlated with convective and photometric RV components from SDO Dopplergrams extracted with SolAster.

What would settle it

Recomputing the same HARPS-N RVs with a different spectral synthesis code or a shifted temperature scale would either preserve the 4000–4750 K minimum or move it; if the minimum disappears or shifts substantially, the result is an artifact of the adopted model, not a property of the Sun.

Watch

Extended reading notes

Core claim

The central claim is that the formation-temperature range giving the smallest RV dispersion is not the full spectral range (4000–5500 K) but an intermediately cool range (4000–4750 K). This holds for both the observed RVs and the residuals after subtracting the best-fit quasi-periodic GP model, at both high and low solar activity. The paper further claims that the GP evolution timescale τ is invariant to activity level and temperature range, that the rotation period is better constrained at high activity, that the inverse harmonic complexity tends to be smaller at high activity, and that the jitter term is bimodal in several cases, reflecting a degeneracy with the other hyperparameters. Finally, comparing the temperature-dependent RVs with convective and photometric RV components extracted from SDO Dopplergrams, the paper finds a consistently strong correlation between hotter-temperature RVs and the convective component due to inhibition of convective blueshift, transitioning to an anti-correlation at the coolest range.

Load-bearing premise

The formation-temperature map from spectral synthesis with the adopted solar parameters (Teff=5770 K, log g=4.40, [Fe/H]=0.00) correctly assigns each spectral segment's photospheric temperature, so the ordering of 'hot' and 'cool' ranges is physically meaningful.

Editorial extensions

If this is right

  • RVs extracted from the 4000–4750 K range are intrinsically less scattered and better described by a quasi-periodic GP, so using this line-formation range could reduce the need for aggressive detrending in exoplanet surveys.
  • The invariance of the evolution timescale $\tau$ across activity levels and temperature ranges allows a multi-season GP model with a single shared $\tau$, reducing the free parameters from $5N_k$ to $4N_k+1$ when modelling $N_k$ independent intervals.
  • The common residual floor near 50 cm s$^{-1}$ across all temperature ranges and activity states indicates unmodelled granulation or supergranulation, motivating more complex covariance kernels or additional high-cadence indicators to reach the EPRV regime.
  • The dominance of the convective component in hotter-line RVs, confirmed by the SDO correlation, implies that activity mitigation in those lines must target convection inhibition rather than photometric contrast.
  • The periodogram transition from $P_{\rm rot}$ at hotter ranges to $P_{\rm rot}/2$ at cooler ranges is consistent with a changing balance between convective and photometric contributions, providing a diagnostic for the dominant activity process from a single spectrum.

Reading between the lines

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

  • If the 4000–4750 K advantage is not a solar coincidence, pipeline builders could weigh spectral segments by formation temperature to produce a 'quiet RV' channel for Sun-like stars, a testable prediction for existing HARPS and ESPRESSO data.
  • The shared 8–10 day residual peak could be a genuine solar oscillation signal (e.g., r-modes or a rotational harmonic); a longer-baseline analysis or a search for mode lifetimes would distinguish it from a systematic.
  • The ratio of RVs from hot-line and cool-line segments may serve as a new activity diagnostic that separates convective inhibition from photometric imbalances, independent of traditional indicators like the $S$-index.
  • The temperature dependence of the correlation with the convective component suggests that a map of correlation versus $T_{1/2}$ could be used to empirically calibrate or validate spectral synthesis temperature scales across different stellar parameters.
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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

4 major / 6 minor

Summary. This paper applies quasi-periodic Gaussian process regression to solar RV time series extracted from spectral segments formed at different photospheric temperatures, using HARPS-N solar data over two 140-day intervals at high and low activity. The authors fit GP hyperparameters for 11 overlapping temperature ranges, examine the posterior distributions, compute RV RMS before and after GP subtraction, and correlate the temperature-dependent RVs with SDO/HMI Dopplergram-derived convective and photometric components. The main claimed result is that the 4000–4750 K range yields the smallest RV dispersion for both observed and GP-subtracted RVs, and that hotter temperature ranges correlate strongly with the convective component.

Significance. If the central claim were robustly established, the paper would be a valuable contribution: it would identify a spectral window that is intrinsically less affected by stellar activity, inform GP kernel choices for activity mitigation, and connect disk-integrated RVs to physical surface components. The study has clear strengths: it uses public solar data, open-source pipelines (ARVE and MAGPy_RV), a well-documented MCMC setup with 100 chains, 50,000 iterations, burn-in, and Gelman-Rubin convergence checks, consistent priors across all time series, and an independent SDO comparison. These features make the analysis reproducible and the physical interpretation testable. However, the headline RMS ordering currently lacks uncertainty quantification, so the central empirical result is not yet demonstrated at the claimed level of certainty.

major comments (4)
  1. [§4.3, Figs. 3–4] The central claim that the 4000–4750 K range yields the smallest RV dispersion is not supported by any uncertainty quantification. The RMS values are reported as point estimates without error bars. With roughly 100 daily-binned points per series (Sect. 2), the sampling uncertainty on a sample RMS is approximately RMS/√(2(N−1)) ≈ 0.07 m/s for RMS ≈ 1 m/s and N = 100. The text itself states the advantage is "if only by a small margin" (§4.3). The differences between adjacent ranges (e.g., 4000–4750 K versus 4000–4500 K or 4000–5000 K) appear to be at this level. Please provide bootstrap or analytic error bars on every RMS value and a significance test for the ordering, rather than only point estimates.
  2. [§4.1] The 11 temperature ranges are constructed with overlapping boundaries: five ranges share the 4000 K lower bound with decreasing upper bounds, and five share the 5500 K upper bound with increasing lower bounds. The RMS values from these ranges are therefore not independent, because they are computed from largely the same spectral segments. A comparison that treats each range as an independent sample will overstate the significance of the differences. Use a paired or nested bootstrap that resamples days and recomputes all temperature-dependent RVs and their RMS values, or otherwise account for the correlated data structure.
  3. [§4.3] The GP-subtracted residuals are computed using only the 50th percentile hyperparameter values, as stated in the text, and the residual RMS values do not propagate the posterior uncertainty of the hyperparameters into the residuals. The conclusion that the QP kernel "particularly well describes" the 4000–4750 K series is therefore based on point-estimate fits. Please show that the residual RMS ordering is stable across the posterior distribution, or report a posterior predictive RMS distribution with uncertainties. This also affects the GP model plots in Figs. 3–4, which show only single best-fit curves.
  4. [§4.4, Fig. 5] The Pearson correlation coefficients between temperature-dependent RVs and the SDO convective and photometric components are reported without error bars or significance levels. Because the RV time series are strongly autocorrelated, the effective number of independent points is far smaller than the number of days, so the nominal p-values (if any) would be invalid. Please provide bootstrap or permutation-based confidence intervals for the correlations, especially for the claim of a "consistently strong correlation" with the convective component, which is used to support the physical interpretation.
minor comments (6)
  1. [§4.2] In the paragraph on the inverse harmonic complexity, the sentence "The distributions of the inverse harmonic complexity, μ, tend to be biased toward lower values during high activity and and higher values during low activity" contains a duplicated "and" and a grammatical issue.
  2. [Figs. 3–4] The RMS panels use a logarithmic x-axis, which visually compresses the differences between the key temperature ranges. Consider adding a table that lists the RMS values and their uncertainties for all 11 ranges and both activity intervals.
  3. [§3.2, Table 1] The prior on the evolution timescale τ is U[0, 140] days, which is exactly the baseline of the time series. Please state whether any posterior distribution hits or piles up against the upper boundary, since that would indicate that the prior is limiting the inference.
  4. [Fig. 2] The full range (4000–5500 K) appears twice, at the rightmost panel of the left group and the leftmost panel of the right group. The caption notes that the full range was analysed twice, but labelling the two runs explicitly (e.g., "full range, run 1" and "full range, run 2") would avoid confusion.
  5. [§4.3] The statement that the ~8–10 day peak in the residual periodograms is "unlikely to be a product of improper GP fitting" because it is consistent between datasets is an assertion rather than a demonstration. Showing that the peak persists under a more flexible kernel or in out-of-sample predictions would strengthen this point.
  6. [Abstract and §5] The abstract and conclusions state the 4000–4750 K result without hedging. Given the lack of uncertainty quantification identified in the major comments, the wording should be softened or qualified until the statistical support is added.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the minimal-dispersion finding is a descriptive comparison of in-sample fits, and the independent SDO Dopplergram comparison provides external grounding.

full rationale

I inspected the derivation chain from the formation-temperature map (PySME/MARCS/VALD, with stated solar parameters) through ARVE-based RV extraction, GP regression with MAGPy_RV, residual RMS ranking, and SDO Dopplergram correlation. The headline claim that the 4000–4750 K range has the smallest RV dispersion is a descriptive comparison of computed in-sample RMS values, not a prediction derived from a fitted parameter; no equation defines the claimed output in terms of an input in a way that would make the result true by construction. The formation-temperature map is adopted from Al Moulla et al. (2022) with stated assumptions that do not include the target result, so this self-citation is independent support rather than a circular premise. The SDO comparison uses an independent code (SolAster) and independent disk-resolved data, providing external grounding for the physical interpretation. The paper does report some marginal claims, such as the 4000–4750 K advantage being small, and it does not quote uncertainties on the RMS values; however, that is a robustness or correctness concern, not a circularity. The self-citations to ARVE, MAGPy_RV, and Al Moulla et al. (2022) are method and software attributions, not load-bearing justifications that reduce the conclusions to those citations. Therefore no significant circularity is present; the score reflects only the minor presence of non-load-bearing self-citations.

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

The core findings depend on five fitted GP hyperparameters per time series and on model assumptions: the QP kernel form, the accuracy of the spectral synthesis temperature map, and the representativeness of the two activity windows. No new physical entities are introduced.

free parameters (5)
  • GP amplitude A = posterior median varies with temperature range and activity (Fig. 2)
    Amplitude of the quasi-periodic kernel, fitted to each of the 22 RV time series with a uniform prior U[0,20] m/s.
  • GP evolution timescale tau = posterior median between 30 and 40 days (Fig. 2)
    Exponential decay timescale in the QP kernel, fitted with a uniform prior U[0,140] days.
  • GP rotation period P_rot = posterior median near 27 to 30 days, activity dependent (Fig. 2)
    Period of the quasi-periodic variation, fitted with a Gaussian prior N[27,10] days.
  • GP inverse harmonic complexity mu = posterior medians biased lower at high activity and higher at low activity (Fig. 2)
    Smoothness parameter of the QP kernel, fitted with a uniform prior U[0,1].
  • GP jitter beta = posterior median roughly 0.3 to 0.8 m/s, bimodal in some temperature ranges (Fig. 2)
    White-noise jitter term, fitted with a Gaussian prior centered on the mean RV uncertainty for each temperature range.
assumptions (5)
  • standard math GP regression and MCMC convergence (Gelman-Rubin) provide valid inference.
    Used throughout Sect. 3.2 to derive hyperparameter posteriors.
  • domain assumption The quasi-periodic kernel of Eq. 1 adequately describes the covariance of the solar activity signal in all temperature ranges.
    Sect. 3.2; this is the central modeling assumption.
  • domain assumption The spectral synthesis model (PySME, MARCS, VALD) with adopted solar parameters yields accurate line-formation temperatures.
    Sect. 3.1; all results depend on the assigned T1/2 values.
  • ad hoc to paper The two selected 140-day intervals are representative of high and low solar activity.
    Sect. 2; the high-activity interval deliberately excludes the solar maximum to maximize data completeness.
  • ad hoc to paper The prior distributions do not substantially bias the posterior hyperparameters.
    Table 1; the Gaussian prior on P_rot centered at 27 days could influence the retrieved period, and the jitter prior center is data-dependent.

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Cite this review

Pith. "Pith review of Gaussian process regression of temperature-dependent radial velocities." pith.science (2026). https://pith.science/paper/2DYACVJE

@misc{pith2026250102959,
  author       = {Pith},
  title        = {Pith review of: Gaussian process regression of temperature-dependent radial velocities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2DYACVJE}},
  note         = {Machine review of arXiv:2501.02959}
}
read the original abstract

Gaussian processes (GPs) described by quasi-periodic covariance functions have in recent years become a widely used tool to model the impact of stellar activity on radial velocity (RV) measurements. We perform a GP regression analysis on solar RV time series measured from spectral segments formed at different temperatures within the photosphere in order to evaluate the relation between the best-fit GP kernel hyperparameters and the observed activity signal as a function of temperature. The posterior distributions of the hyperparameters show subtle differences between high- and low-activity phases and as a function of the spectral formation temperature range, which could have implications on the characteristics of the activity signal and its optimal modelling. For the temperature-dependent RVs, we find that at high and low activity alike, the minimal RV dispersion is obtained at intermediately cool temperature ranges (4000-4750 K), for both the observed and GP model-subtracted RVs. Finally, we compare and correlate our temperature-dependent RVs with RV components derived from disk-resolved Dopplergrams of the Sun, for which we find a consistently strong correlation between RVs related to hotter temperature ranges and the dominant RV component due to the inhibition of convection.

Figures

Figures reproduced from arXiv: 2501.02959 by the authors.

Figure 1
Figure 1. Temperature-dependent solar RVs as a function of BJD. The RV time series are computed using spectral segments formed at different average formation temperatures, 𝑇1/2 . The black points represent the RVs computed using roughly the entire formation temperature range (4000−5500 K), the blue points represent RVs computed at sequentially cooler temperature regimes by decreasing the upper bound, and the red points repres… view at source ↗
Figure 2
Figure 2. Violin plots of the posterior distributions of the kernel hyperparameters from Eq. 1 after GP regression. Left panels: GP hyperparameters for the sequentially cooler temperature ranges, for both the high-activity (orange) and low-activity (green) time intervals indicated in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. GP regression of the high-activity time interval. Top left panel: RV time series at different formation temperature ranges. The curve colours represent the same average formation temperatures as in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Pearson correlations coefficients between the observed HARPS-N RVs, RVobs, and RVs extracted from SDO Dopplergrams, RVSDO. The up￾ward and downward triangles show the correlations for the RV variations from the inhibition of convective blueshift, RVSDO,conv, and from t…

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Works this paper leans on

67 extracted references · 8 canonical work pages

  1. [1]

    A., 2022, @doi [ ] 10.1051/0004-6361/202243276 , https://ui.adsabs.harvard.edu/abs/2022A&A...664A..34A 664, A34

    Al Moulla K., Dumusque X., Cretignier M., Zhao Y., Valenti J. A., 2022, @doi [ ] 10.1051/0004-6361/202243276 , https://ui.adsabs.harvard.edu/abs/2022A&A...664A..34A 664, A34

    doi:10.1051/0004-6361/202243276 2022

  2. [2]

    C., Wildi F., 2023, @doi [ ] 10.1051/0004-6361/202244663 , https://ui.adsabs.harvard.edu/abs/2023A&A...669A..39A 669, A39

    Al Moulla K., Dumusque X., Figueira P., Lo Curto G., Santos N. C., Wildi F., 2023, @doi [ ] 10.1051/0004-6361/202244663 , https://ui.adsabs.harvard.edu/abs/2023A&A...669A..39A 669, A39

    doi:10.1051/0004-6361/202244663 2023

  3. [3]

    Al Moulla K., Dumusque X., Cretignier M., 2024, @doi [ ] 10.1051/0004-6361/202348150 , https://ui.adsabs.harvard.edu/abs/2024A&A...683A.106A 683, A106

    doi:10.1051/0004-6361/202348150 2024

  4. [4]

    P., 2012, @doi [ ] 10.1088/0067-0049/200/2/15 , https://ui.adsabs.harvard.edu/abs/2012ApJS..200...15A 200, 15

    Anglada-Escud \'e G., Butler R. P., 2012, @doi [ ] 10.1088/0067-0049/200/2/15 , https://ui.adsabs.harvard.edu/abs/2012ApJS..200...15A 200, 15

    doi:10.1088/0067-0049/200/2/15 2012

  5. [5]

    Artigau \'E ., et al., 2022, @doi [ ] 10.3847/1538-3881/ac7ce6 , https://ui.adsabs.harvard.edu/abs/2022AJ....164...84A 164, 84

    doi:10.3847/1538-3881/ac7ce6 2022

  6. [6]

    J., Scott P., 2009, @doi [ ] 10.1146/annurev.astro.46.060407.145222 , https://ui.adsabs.harvard.edu/abs/2009ARA&A..47..481A 47, 481

    Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, @doi [ ] 10.1146/annurev.astro.46.060407.145222 , https://ui.adsabs.harvard.edu/abs/2009ARA&A..47..481A 47, 481

    arXiv 2009

  7. [7]

    Baranne A., et al., 1996, , https://ui.adsabs.harvard.edu/abs/1996A&AS..119..373B 119, 373

    work page 1996

  8. [8]

    Barros S. C. C., Demangeon O., D \' az R. F., Cabrera J., Santos N. C., Faria J. P., Pereira F., 2020, @doi [ ] 10.1051/0004-6361/201936086 , https://ui.adsabs.harvard.edu/abs/2020A&A...634A..75B 634, A75

    doi:10.1051/0004-6361/201936086 2020

Show all 67 references
  1. [9]

    D., Faria J

    Camacho J. D., Faria J. P., Viana P. T. P., 2022, arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2022arXiv220506627C p. arXiv:2205.06627

    2022 arXiv

  2. [10]

    Collier Cameron A., et al., 2019, @doi [ ] 10.1093/mnras/stz1215 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.1082C 487, 1082

    2019 doi

  3. [11]

    S., Ramsay S

    Cosentino R., et al., 2012, in McLean I. S., Ramsay S. K., Takami H., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 8446, Ground-based and Airborne Instrumentation for Astronomy IV. p. 84461V, @doi 10.1117/12.925738

    2012 doi

  4. [12]

    K., McLean I

    Cosentino R., et al., 2014, in Ramsay S. K., McLean I. S., Takami H., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 9147, Ground-based and Airborne Instrumentation for Astronomy V. p. 91478C, @doi 10.1117/12.2055813

    2014 doi

  5. [13]

    C., et al., 2021, @doi [ ] 10.1093/mnras/stab1183 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505..830C 505, 830

    Costes J. C., et al., 2021, @doi [ ] 10.1093/mnras/stab1183 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505..830C 505, 830

    2021 doi

  6. [14]

    arXiv:2107.14291

    Crass J., et al., 2021, @doi [arXiv e-prints] 10.48550/arXiv.2107.14291 , https://ui.adsabs.harvard.edu/abs/2021arXiv210714291C p. arXiv:2107.14291

    2021 doi arXiv

  7. [15]

    C., Pepe F., 2021, @doi [ ] 10.1051/0004-6361/202140986 , https://ui.adsabs.harvard.edu/abs/2021A&A...653A..43C 653, A43

    Cretignier M., Dumusque X., Hara N. C., Pepe F., 2021, @doi [ ] 10.1051/0004-6361/202140986 , https://ui.adsabs.harvard.edu/abs/2021A&A...653A..43C 653, A43

    2021 doi

  8. [16]

    Cretignier M., Dumusque X., Aigrain S., Pepe F., 2023, @doi [ ] 10.1051/0004-6361/202347232 , https://ui.adsabs.harvard.edu/abs/2023A&A...678A...2C 678, A2

    2023 doi

  9. [17]

    Cretignier M., Pietrow A. G. M., Aigrain S., 2024, @doi [ ] 10.1093/mnras/stad3292 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.2940C 527, 2940

    2024 doi

  10. [18]

    Dalal S., et al., 2024, @doi [ ] 10.1093/mnras/stae1367 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.531.4464D 531, 4464

    2024 doi

  11. [19]

    M., Galland F., Udry S., Mayor M., 2007, @doi [ ] 10.1051/0004-6361:20078144 , https://ui.adsabs.harvard.edu/abs/2007A&A...473..983D 473, 983

    Desort M., Lagrange A. M., Galland F., Udry S., Mayor M., 2007, @doi [ ] 10.1051/0004-6361:20078144 , https://ui.adsabs.harvard.edu/abs/2007A&A...473..983D 473, 983

    2007 doi

  12. [20]

    Dumusque X., 2018, @doi [ ] 10.1051/0004-6361/201833795 , https://ui.adsabs.harvard.edu/abs/2018A&A...620A..47D 620, A47

    2018 doi

  13. [21]

    C., Monteiro M

    Dumusque X., Udry S., Lovis C., Santos N. C., Monteiro M. J. P. F. G., 2011, @doi [ ] 10.1051/0004-6361/201014097 , https://ui.adsabs.harvard.edu/abs/2011A&A...525A.140D 525, A140

    2011 doi

  14. [22]

    Dumusque X., et al., 2015, @doi [ ] 10.1088/2041-8205/814/2/L21 , https://ui.adsabs.harvard.edu/abs/2015ApJ...814L..21D 814, L21

    2015 doi

  15. [23]

    Dumusque X., et al., 2021, @doi [ ] 10.1051/0004-6361/202039350 , https://ui.adsabs.harvard.edu/abs/2021A&A...648A.103D 648, A103

    2021 doi

  16. [24]

    Ervin T., et al., 2022, @doi [ ] 10.3847/1538-3881/ac67e6 , https://ui.adsabs.harvard.edu/abs/2022AJ....163..272E 163, 272

    2022 doi

  17. [25]

    A., et al., 2016, @doi [PASP] 10.1088/1538-3873/128/964/066001 , https://ui.adsabs.harvard.edu/abs/2016PASP..128f6001F 128, 066001

    Fischer D. A., et al., 2016, @doi [PASP] 10.1088/1538-3873/128/964/066001 , https://ui.adsabs.harvard.edu/abs/2016PASP..128f6001F 128, 066001

    2016 doi

  18. [26]

    Foreman-Mackey D., Agol E., Ambikasaran S., Angus R., 2017, @doi [ ] 10.3847/1538-3881/aa9332 , https://ui.adsabs.harvard.edu/abs/2017AJ....154..220F 154, 220

    2017 doi

  19. [27]

    F., 2008, The Observation and Analysis of Stellar Photospheres , 3 edn

    Gray D. F., 2008, The Observation and Analysis of Stellar Photospheres , 3 edn. Cambridge University Press

    2008

  20. [28]

    G., Nordlund A ., Plez B., 2008, @doi [ ] 10.1051/0004-6361:200809724 , https://ui.adsabs.harvard.edu/abs/2008A&A...486..951G 486, 951

    Gustafsson B., Edvardsson B., Eriksson K., J rgensen U. G., Nordlund A ., Plez B., 2008, @doi [ ] 10.1051/0004-6361:200809724 , https://ui.adsabs.harvard.edu/abs/2008A&A...486..951G 486, 951

    2008 doi

  21. [29]

    D., et al., 2014, @doi [ ] 10.1093/mnras/stu1320 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.443.2517H 443, 2517

    Haywood R. D., et al., 2014, @doi [ ] 10.1093/mnras/stu1320 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.443.2517H 443, 2517

    2014 doi

  22. [30]

    D., et al., 2016, @doi [ ] 10.1093/mnras/stw187 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.457.3637H 457, 3637

    Haywood R. D., et al., 2016, @doi [ ] 10.1093/mnras/stw187 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.457.3637H 457, 3637

    2016 doi

  23. [31]

    D., et al., 2022, @doi [ ] 10.3847/1538-4357/ac7c12 , https://ui.adsabs.harvard.edu/abs/2022ApJ...935....6H 935, 6

    Haywood R. D., et al., 2022, @doi [ ] 10.3847/1538-4357/ac7c12 , https://ui.adsabs.harvard.edu/abs/2022ApJ...935....6H 935, 6

    2022 doi

  24. [32]

    Janssen K., Cauzzi G., 2006, @doi [ ] 10.1051/0004-6361:20054310 , https://ui.adsabs.harvard.edu/abs/2006A&A...450..365J 450, 365

    2006 doi

  25. [33]

    A., Collier Cameron A., Wilson T

    John A. A., Collier Cameron A., Wilson T. G., 2022, @doi [ ] 10.1093/mnras/stac1814 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.515.3975J 515, 3975

    2022 doi

  26. [34]

    Klein B., et al., 2024, @doi [ ] 10.1093/mnras/stae1313 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.531.4238K 531, 4238

    2024 doi

  27. [35]

    G., Ryabchikova T

    Kupka F. G., Ryabchikova T. A., Piskunov N. E., Stempels H. C., Weiss W. W., 2000, @doi [Baltic Astronomy] 10.1515/astro-2000-0420 , https://ui.adsabs.harvard.edu/abs/2000BaltA...9..590K 9, 590

    2000 doi

  28. [36]

    S., et al., 2024, @doi [ ] 10.1093/mnras/stad3723 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.7681L 527, 7681

    Lakeland B. S., et al., 2024, @doi [ ] 10.1093/mnras/stad3723 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.7681L 527, 7681

    2024 doi

  29. [37]

    F., Gizon L., Zaqarashvili T

    Lanza A. F., Gizon L., Zaqarashvili T. V., Liang Z. C., Rodenbeck K., 2019, @doi [ ] 10.1051/0004-6361/201834712 , https://ui.adsabs.harvard.edu/abs/2019A&A...623A..50L 623, A50

    2019 doi

  30. [38]

    R., 1976, @doi [ ] 10.1007/BF00648343 , https://ui.adsabs.harvard.edu/abs/1976Ap&SS..39..447L 39, 447

    Lomb N. R., 1976, @doi [ ] 10.1007/BF00648343 , https://ui.adsabs.harvard.edu/abs/1976Ap&SS..39..447L 39, 447

    1976 doi

  31. [39]

    arXiv:2104.06072

    Meunier N., 2021, @doi [arXiv e-prints] 10.48550/arXiv.2104.06072 , https://ui.adsabs.harvard.edu/abs/2021arXiv210406072M p. arXiv:2104.06072

    2021 doi arXiv

  32. [40]

    M., 2010, @doi [ ] 10.1051/0004-6361/200913551 , https://ui.adsabs.harvard.edu/abs/2010A&A...512A..39M 512, A39

    Meunier N., Desort M., Lagrange A. M., 2010, @doi [ ] 10.1051/0004-6361/200913551 , https://ui.adsabs.harvard.edu/abs/2010A&A...512A..39M 512, A39

    2010 doi

  33. [41]

    M., Borgniet S., Rieutord M., 2015, @doi [ ] 10.1051/0004-6361/201525721 , https://ui.adsabs.harvard.edu/abs/2015A&A...583A.118M 583, A118

    Meunier N., Lagrange A. M., Borgniet S., Rieutord M., 2015, @doi [ ] 10.1051/0004-6361/201525721 , https://ui.adsabs.harvard.edu/abs/2015A&A...583A.118M 583, A118

    2015 doi

  34. [42]

    W., et al., 2019, @doi [ ] 10.3847/1538-4357/ab064a , https://ui.adsabs.harvard.edu/abs/2019ApJ...874..107M 874, 107

    Milbourne T. W., et al., 2019, @doi [ ] 10.3847/1538-4357/ab064a , https://ui.adsabs.harvard.edu/abs/2019ApJ...874..107M 874, 107

    2019 doi

  35. [43]

    Nava C., et al., 2022, @doi [ ] 10.3847/1538-3881/ac3141 , https://ui.adsabs.harvard.edu/abs/2022AJ....163...41N 163, 41

    2022 doi

  36. [44]

    A., Aigrain S., 2022, @doi [ ] 10.1093/mnras/stac2097 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.515.5251N 515, 5251

    Nicholson B. A., Aigrain S., 2022, @doi [ ] 10.1093/mnras/stac2097 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.515.5251N 515, 5251

    2022 doi

  37. [45]

    L., Ford E

    Palumbo M. L., Ford E. B., Gonzalez E. B., Wright J. T., Al Moulla K., Schlichenmaier R., 2024, @doi [ ] 10.3847/1538-3881/ad4c6d , https://ui.adsabs.harvard.edu/abs/2024AJ....168...46P 168, 46

    2024 doi

  38. [46]

    C., Udry S., Burnet M., 2002, @doi [ ] 10.1051/0004-6361:20020433 , https://ui.adsabs.harvard.edu/abs/2002A&A...388..632P 388, 632

    Pepe F., Mayor M., Galland F., Naef D., Queloz D., Santos N. C., Udry S., Burnet M., 2002, @doi [ ] 10.1051/0004-6361:20020433 , https://ui.adsabs.harvard.edu/abs/2002A&A...388..632P 388, 632

    2002 doi

  39. [47]

    D., Thompson B

    Pesnell W. D., Thompson B. J., Chamberlin P. C., 2012, @doi [SolPhys] 10.1007/s11207-011-9841-3 , https://ui.adsabs.harvard.edu/abs/2012SoPh..275....3P 275, 3

    2012 doi

  40. [48]

    F., et al., 2016, in Navarro R., Burge J

    Phillips D. F., et al., 2016, in Navarro R., Burge J. H., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 9912, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation II. p. 99126Z, @doi 10.1117/12.2232452

    2016 doi

  41. [49]

    A., 2017, @doi [ ] 10.1051/0004-6361/201629124 , https://ui.adsabs.harvard.edu/abs/2017A&A...597A..16P 597, A16

    Piskunov N., Valenti J. A., 2017, @doi [ ] 10.1051/0004-6361/201629124 , https://ui.adsabs.harvard.edu/abs/2017A&A...597A..16P 597, A16

    2017 doi

  42. [50]

    E., Kupka F., Ryabchikova T

    Piskunov N. E., Kupka F., Ryabchikova T. A., Weiss W. W., Jeffery C. S., 1995, , https://ui.adsabs.harvard.edu/abs/1995A&AS..112..525P 112, 525

    1995

  43. [51]

    Queloz D., et al., 2001, @doi [ ] 10.1051/0004-6361:20011308 , https://ui.adsabs.harvard.edu/abs/2001A&A...379..279Q 379, 279

    2001 doi

  44. [52]

    Queloz D., et al., 2009, @doi [ ] 10.1051/0004-6361/200913096 , https://ui.adsabs.harvard.edu/abs/2009A&A...506..303Q 506, 303

    2009 doi

  45. [53]

    A., Reece S., Roberts S., 2015, @doi [ ] 10.1093/mnras/stv1428 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.452.2269R 452, 2269

    Rajpaul V., Aigrain S., Osborne M. A., Reece S., Roberts S., 2015, @doi [ ] 10.1093/mnras/stv1428 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.452.2269R 452, 2269

    2015 doi

  46. [54]

    Rajpaul V., Aigrain S., Roberts S., 2016, @doi [ ] 10.1093/mnrasl/slv164 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.456L...6R 456, L6

    2016 doi

  47. [55]

    D., 2023, MAGPy-RV: Gaussian Process regression pipeline with MCMC parameter searching , Astrophysics Source Code Library, record ascl:2310.006 ( @eprint ascl 2310.006 )

    Rescigno F., Dixon B., Haywood R. D., 2023, MAGPy-RV: Gaussian Process regression pipeline with MCMC parameter searching , Astrophysics Source Code Library, record ascl:2310.006 ( @eprint ascl 2310.006 )

    2023

  48. [56]

    Rescigno F., et al., 2024a, @doi [ ] 10.1093/mnras/stad3255 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.5385R 527, 5385

    doi

  49. [57]

    Rescigno F., et al., 2024b, @doi [ ] 10.1093/mnras/stae1634 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.532.2741R 532, 2741

    doi

  50. [58]

    L., Stempels H

    Ryabchikova T., Piskunov N., Kurucz R. L., Stempels H. C., Heiter U., Pakhomov Y., Barklem P. S., 2015, @doi [ ] 10.1088/0031-8949/90/5/054005 , https://ui.adsabs.harvard.edu/abs/2015PhyS...90e4005R 90, 054005

    2015 doi

  51. [59]

    D., 1982, @doi [ ] 10.1086/160554 , https://ui.adsabs.harvard.edu/abs/1982ApJ...263..835S 263, 835

    Scargle J. D., 1982, @doi [ ] 10.1086/160554 , https://ui.adsabs.harvard.edu/abs/1982ApJ...263..835S 263, 835

    1982 doi

  52. [60]

    H., et al., 2012, @doi [Solar Physics] 10.1007/s11207-011-9834-2 , https://ui.adsabs.harvard.edu/abs/2012SoPh..275..207S 275, 207

    Scherrer P. H., et al., 2012, @doi [Solar Physics] 10.1007/s11207-011-9834-2 , https://ui.adsabs.harvard.edu/abs/2012SoPh..275..207S 275, 207

    2012 doi

  53. [61]

    Schou J., et al., 2012, @doi [Solar Physics] 10.1007/s11207-011-9842-2 , https://ui.adsabs.harvard.edu/abs/2012SoPh..275..229S 275, 229

    2012 doi

  54. [62]

    M., Barros S

    Serrano L. M., Barros S. C. C., Oshagh M., Santos N. C., Faria J. P., Demangeon O., Sousa S. G., Lendl M., 2018, @doi [ ] 10.1051/0004-6361/201731206 , https://ui.adsabs.harvard.edu/abs/2018A&A...611A...8S 611, A8

    2018 doi

  55. [63]

    A., Fischer D

    Valenti J. A., Fischer D. A., 2005, @doi [ ] 10.1086/430500 , https://ui.adsabs.harvard.edu/abs/2005ApJS..159..141V 159, 141

    2005 doi

  56. [64]

    A., Piskunov N., 1996, , https://ui.adsabs.harvard.edu/abs/1996A&AS..118..595V 118, 595

    Valenti J. A., Piskunov N., 1996, , https://ui.adsabs.harvard.edu/abs/1996A&AS..118..595V 118, 595

    1996

  57. [65]

    Wehrhahn A., Piskunov N., Ryabchikova T., 2023, @doi [ ] 10.1051/0004-6361/202244482 , https://ui.adsabs.harvard.edu/abs/2023A&A...671A.171W 671, A171

    2023 doi

  58. [66]

    C., 1968, @doi [ ] 10.1086/149652 , https://ui.adsabs.harvard.edu/abs/1968ApJ...153..221W 153, 221

    Wilson O. C., 1968, @doi [ ] 10.1086/149652 , https://ui.adsabs.harvard.edu/abs/1968ApJ...153..221W 153, 221

    1968 doi

  59. [67]

    Zechmeister M., K \"u rster M., 2009, @doi [ ] 10.1051/0004-6361:200811296 , https://ui.adsabs.harvard.edu/abs/2009A&A...496..577Z 496, 577

    2009 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.