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REVIEW 4 major objections 6 minor 59 references

The Influence of Stellar Chromospheres and Coronae on Exoplanet Transmission Spectroscopy

T0 review · 4 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Stellar chromospheres and coronae bias exoplanet transmission spectra, and including them raises HAT-P-18 b's retrieved temperature from 536 K to about 736 K.

desk verdict New transit model (TACHELES) worth knowing, but the headline temperature claim is about 0.7 sigma and the abstract overstates it. read the letter →

arxiv 2502.00553 v1 pith:6R4V7EJE submitted 2025-02-01 astro-ph.EP astro-ph.SR

Volker Perdelwitz , Adam Chaikin-Lifshitz , Aviv Ofir , Oded Aharonson This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords exoplanetatmospherestransmissionspectroscopystellarchromospherecoronaHAT-P-18bJWSTNIRISS/SOSStransitlightcurvemodelingactivity
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

Transmission spectroscopy measures the starlight filtered through a planet's atmosphere during transit, and standard models assume the star's light comes from a sharp photospheric disk. This paper argues that main-sequence stars also possess optically thin chromospheres and coronae that emit at near-infrared wavelengths, and that these layers make transits shallower and wider in a wavelength-dependent way. Using JWST observations of the hot Jupiter HAT-P-18 b, the authors show that adding such a layer to the transit model changes the derived transmission spectrum enough to raise the best-fit atmospheric temperature from 536 K to about 736 K, close to the predicted equilibrium temperature of 852 K, and to lower the CO2 abundance by nearly an order of magnitude. A sympathetic reader would care because most JWST transmission-spectroscopy targets orbit stars at least as active as HAT-P-18, so this neglected effect may be biasing many published atmospheric retrievals.

What carries the argument

The carrying object is TACHELES, a transit model that adds an optically thin, spherically symmetric, exponentially decaying emitting shell with brightness profile $I_0 e^{-r/H}$ around a standard photospheric Mandel-Agol limb-darkened disk. The shell brightness is integrated along the line of sight (Eq. 2) to give an on-sky radial profile, and the planet occults both photosphere and shell. Two new free parameters, the brightness ratio $\mathrm{Br}$ and scale height $H$, capture the wavelength-dependent line emission of the chromosphere and corona; at near-IR wavelengths this emission is strong enough in some bins to alter the transit shape and depth. The model is validated against solar EUV images showing an exponential line-of-sight integrated profile, and its detection limits are characterized with simulated light curves.

What would settle it

Take a JWST transmission-spectroscopy target whose coronal and chromospheric emission is independently measured in X-ray and ultraviolet at the same epoch; if TACHELES-fitted brightness ratios and scale heights do not track the independently measured emission strengths and their wavelength pattern, the exponential-shell interpretation is wrong. A cheaper check is to measure the Sun's off-limb brightness at 0.85 to 2.8 microns to test whether the exponential line-of-sight model holds at the near-infrared wavelengths where the paper applies it.

Watch

Extended reading notes

Core claim

The paper's central claim is that the chromosphere and corona of the host star, not just its photosphere, must be included in transit models before the planetary transmission spectrum is interpreted. For HAT-P-18 b, the authors find that 24 wavelength bins show substantial and 6 show strong statistical evidence for the extended-layer model over a purely photospheric one, with fitted brightness ratios of 0.04 to 0.25 and scale heights of 0.07 to 0.31 stellar radii. Once these layers are accounted for, the best-fit atmospheric temperature rises from 536 K to about 721 to 736 K, much closer to the 852 K equilibrium temperature, and the CO2 mixing ratio drops by almost an order of magnitude. The retrieved chromospheric and coronal spectrum contains nine lines above 5 sigma, all matched to CHIANTI plasma-model lines, including coronal Fe X emission. If this is right, the usual assumption of a purely photospheric transit source is a systematic error source for active host stars.

Load-bearing premise

The argument rests on the assumption that the chromosphere and corona of HAT-P-18 can be described as a single optically thin exponential shell whose brightness falls off as $e^{-r/H}$ at near-infrared wavelengths, an assumption validated only by solar EUV images at 17.1 nm and not by any near-infrared measurement of the target star.

Editorial extensions

If this is right

  • Atmospheric temperatures retrieved from transmission spectra of active-host exoplanets are biased low when chromospheric and coronal emission is ignored; the effect can be hundreds of kelvin.
  • For HAT-P-18 b, including the outer stellar layers raises the best-fit temperature to near the equilibrium temperature and reduces the CO2 abundance by almost an order of magnitude.
  • Wavelength-dependent residuals attributed to spots or third-light dilution may partly be chromospheric and coronal line emission, so published spectra of active stars may need reanalysis.
  • TACHELES turns transmission spectroscopy into a probe of stellar chromospheres and coronae, with detected lines such as Fe X, Mg II, and He I in a K dwarf other than the Sun.
  • Since most current and scheduled JWST targets orbit stars more active than HAT-P-18, the bias should be larger, not smaller, for the wider sample.

Reading between the lines

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

  • A natural extension, not tested here, is to fold chromospheric and coronal emission into retrieval codes as a standard stellar nuisance parameter alongside spots and faculae; this would let archival JWST datasets be re-fit without new observations.
  • The paper's line detections suggest that high-SNR transmission spectroscopy could be used to build differential emission measure models of other stars, effectively extending solar coronal physics to exoplanet hosts.
  • If the exponential shell is confirmed at near-infrared wavelengths on the Sun, the same model could be applied to smaller planets or grazing transits, where the finite planet size does not smear out the chromospheric geometry, to map the layer structure.
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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. The paper introduces TACHELES, a transit model that adds an exponentially decaying, optically thin emitting shell to a standard Mandel-Agol photospheric light curve, parameterized by a brightness ratio Br and a scale height H. The model is fit to JWST NIRISS/SOSS observations of HAT-P-18 b; wavelength bins with Bayes factors favoring TACHELES are used to construct a 'chromospheric/coronal spectrum' and to identify emission lines using CHIANTI. The corrected transmission spectrum is then passed to POSEIDON atmospheric retrievals. The authors report that including the stellar outer layers raises the retrieved temperature from 536 K to about 721-736 K, closer to the equilibrium temperature, decreases the retrieved H2O and CO2 abundances, and opens a new window on stellar outer layers.

Significance. If the claims were robust, TACHELES would address an important systematic in transmission spectroscopy: stellar chromospheres and coronae are usually neglected, and for active stars they could bias retrieved temperatures and abundances. The model derivation is transparent, the code and derived data are publicly available, and the synthetic retrieval tests in Appendix B and the solar validation in Appendix A are useful contributions. However, the headline quantitative claim is not supported by the reported uncertainties, and the NIR detection lacks independent validation. The concept is promising and worth publishing after major revision that tempers the claims and adds supporting tests.

major comments (4)
  1. [§4, Table 3; Abstract] The central claim that accounting for the chromosphere/corona increases the retrieved temperature from 536 K to about 736 K is not statistically supported. Table 3 reports Tref = 536.0+188.9-100.8 K for the photospheric one-heterogeneity model and Tref = 720.8+376.4-188.0 K for the TACHELES one-heterogeneity model. The 1-sigma intervals overlap; the point-estimate shift of 184.8 K is smaller than the lower 1-sigma error on the TACHELES value and comparable to the upper error on the photospheric value, corresponding to roughly 0.7 sigma if the asymmetric errors are combined in quadrature. The abstract's value of 736 K also does not match the body's 720.8 K. The conclusion that ignoring the stellar outer layers biases retrieved atmospheric temperatures is therefore not established by this dataset and should be reframed as tentative or suggestive.
  2. [§2, Eq. (2); Appendix A] The exponential, optically thin emission law I0 e^{-r/H} integrated along the line of sight (Eq. 2) is the foundation of the TACHELES detection, but its applicability at 0.85-2.8 um is not independently validated. Appendix A validates the exponential form only with SDO EUV images at 17.1 nm, a very different spectral regime, and the fitted Br and H values are not checked against alternative explanations such as unocculted spots, faculae, or wavelength-dependent systematics. Because the derived chromospheric/coronal spectrum and the line identifications are constructed from these same fitted parameters, the CHIANTI matching in §5 is a consistency check of the fit rather than an independent confirmation. The manuscript needs an explicit test (e.g., injection-recovery with spot/faculae models, or a comparison of the NIR line ratios with a solar NIR spectrum) before claiming a detection.
  3. [§3, §5] The statistical evidence for TACHELES is evaluated bin-by-bin without addressing the multiplicity of wavelength bins: the paper reports 24 bins with Bayes factor >=3 and 6 with Bayes factor >=10, but it never states the total number of bins, so the false-positive rate cannot be assessed. The same issue affects the line identifications: 9 emission peaks at >=5 sigma are matched to CHIANTI lines, but no estimate is given for the expected number of chance matches given the line density in the CHIANTI list and the NIRISS spectral resolution. A binomial or false-discovery-rate calculation, or a null test on the photospheric residuals, is needed to support the per-bin detections and the line identifications.
  4. [Abstract; §4] The abstract states that the analysis 'decreases the best-fit abundance of CO2 by almost an order of magnitude,' but §4 describes the CO2 decrease as tentative and based on a singular feature at the edge of the spectrum, and it notes that CO2 is hard to constrain with NIRISS/SOSS data. Similarly, the H2O decrease is only about 2 sigma. The abstract and conclusions should carry the same caveats as the body, otherwise readers will take an unsecured abundance shift as a principal result.
minor comments (6)
  1. [Abstract; §6; Table 3] The temperature value in the abstract (736 K) differs from the value quoted in §6 (721 K) and in Table 3 (720.8 K); please harmonize these numbers.
  2. [§3] 'Jeffrey's scale' should be 'Jeffreys scale'.
  3. [Table 4] The column header 'of f' appears to be a typo for the baseline offset parameter.
  4. [Fig. 6] The black and red line identifications in the figure are hard to distinguish; a legend or distinct marker styles would improve clarity.
  5. [§5] The statement that the H-alpha peak is 34 A blueward of line center deserves a quantitative discussion, since such a large offset may undermine the line-identification procedure.
  6. [Appendix A] The azimuthally averaged SDO brightness profile is shown only over a limited radial range (roughly 1-1.2 R*), whereas the fitted scale heights in §3 range from 0.07 to 0.31 R*; please comment on the extrapolation of the solar validation to the fitted regime.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the per-wavelength TACHELES fits do not use the CHIANTI line list, and the claimed temperature shift is a fitted retrieval rather than a prediction from the model inputs.

full rationale

The paper's central derivation, the TACHELES forward model in Eq. (1)-(2), is built from an assumed exponential emission law that is independently motivated by SDO observations in Appendix A. The per-wavelength brightness ratios and scale heights are fit to the JWST light curves with uniform priors (Table 1) and without any line-list priors, so the resulting transmission spectrum is an independent fit output rather than a restatement of an input. The CHIANTI comparison in Section 5 is explicitly described as a 'sanity check' performed after the fits; matching fitted peaks to known atomic lines is a post-hoc consistency test, and the paper even reports mismatches, such as the H-alpha peak offset by 34 Angstroms, which shows the matching is not forced. The POSEIDON retrieval temperature increase (from 536.0 K to 720.8 K in Table 3) is a posterior estimate obtained from the corrected spectrum, not a quantity used to construct the TACHELES model. The citation to Perdelwitz et al. (2024) supplies archival activity data for broader context and is not load-bearing for the derivation. Therefore no step reduces by construction to its own inputs; concerns about the statistical significance of the temperature shift are a validity issue, not a circularity issue.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a geometric shell model with two fitted parameters per wavelength bin and on several astrophysical assumptions inherited from the Solar and retrieval literature. The exponential shell is validated against the Sun only at 17.1 nm, so its NIR validity is assumed. The retrieval setup and spot treatment are taken from Fournier-Tondreau et al. (2024), and the plasma line list from Solar CHIANTI models.

free parameters (6)
  • Br = 0.04 to 0.25 for significant bins
    Brightness ratio of the chromosphere/corona to the photosphere, fitted per wavelength bin with a log-uniform prior over [-6, 1]; drives the transit depth corrections.
  • H = 0.07 to 0.31 R_star for significant bins
    Scale height of the exponential emission shell, fitted per wavelength bin with a log-uniform prior over [-3, 0]; controls the wavelength-dependent transit shape.
  • rp = varies per bin around 0.138 R_star
    Effective planetary radius, fitted per bin; the TACHELES minus photospheric radius difference is the reported 5.3% effect and the input to the retrieval.
  • u1 = Gaussian prior centered on exotik-ld PHOENIX prediction, width 0.2
    Quadratic limb darkening coefficient fitted per bin; standard, but it affects the transit shape and depth.
  • u2 = Gaussian prior centered on exotik-ld PHOENIX prediction, width 0.2
    Quadratic limb darkening coefficient fitted per bin; standard, but it affects the transit shape and depth.
  • alpha = uniform prior 0 to 10000
    Flux normalization fitted per light curve; standard nuisance parameter.
assumptions (6)
  • domain assumption Chromospheric and coronal line emission follows I0 e^{-r/H} with a single scale height H.
    Eq. 2 in Section 2; validated against SDO EUV images of the Sun in Appendix A, but assumed for NIR wavelengths and for HAT-P-18.
  • domain assumption The chromosphere/corona is optically thin and contributes only emission, not absorption, along the line of sight.
    Eq. 2 integrates a transparent shell; standard for these layers following Linsky 1980, but an assumption at these wavelengths.
  • standard math The photospheric light curve is exactly a Mandel and Agol (2002) model with quadratic limb darkening.
    Section 2, computed with batman; standard transit model used throughout the field.
  • domain assumption The POSEIDON retrieval setup, including the P-T parameterization, cloud model, composition set, and spot treatment, is inherited from Fournier-Tondreau et al. (2024).
    Section 4 and Table 2; the atmospheric results depend on these choices.
  • domain assumption The CHIANTI line list based on a Solar prominence differential emission measure and solar abundances is representative of HAT-P-18's outer atmosphere.
    Section 5; the paper states no UV/X-ray DEM for HAT-P-18 is available, so the Solar model is used as a proxy.
  • ad hoc to paper The spot crossing event is masked by removing all data within 0.011 d of 0.005 d after t0.
    Section 3; follows Fournier-Tondreau et al. (2024) and affects the fitted transit depths and hence the derived spectra.

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Cite this review

Pith. "Pith review of The Influence of Stellar Chromospheres and Coronae on Exoplanet Transmission Spectroscopy." pith.science (2026). https://pith.science/paper/6R4V7EJE

@misc{pith2026250200553,
  author       = {Pith},
  title        = {Pith review of: The Influence of Stellar Chromospheres and Coronae on Exoplanet Transmission Spectroscopy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6R4V7EJE}},
  note         = {Machine review of arXiv:2502.00553}
}
read the original abstract

A main source of bias in transmission spectroscopy of exoplanet atmospheres is magnetic activity of the host star in the form of stellar spots, faculae or flares. However, the fact that main-sequence stars have a chromosphere and a corona, and that these optically thin layers are dominated by line emission may alter the global interpretation of the planetary spectrum, has largely been neglected. Using a JWST NIRISS/SOSS data set of hot Jupiter HAT-P-18 b, we show that even at near-IR and IR wavelengths, the presence of these layers leads to significant changes in the transmission spectrum of the planetary atmosphere. Accounting for these stellar outer layers thus improves the atmospheric fit of HAT-P-18 b, and increases its best-fit atmospheric temperature from 536 K to 736 K, a value much closer to the predicted equilibrium temperature of 852 K. Our analysis also decreases the best-fit abundance of CO2 by almost an order of magnitude. The approach provides a new window to the properties of chromospheres/corona in stars other than our Sun.

Figures

Figures reproduced from arXiv: 2502.00553 by the authors.

Figure 1
Figure 1. Depiction of the effect of chromospheres/coronae on transit shapes. We computed three scenarios of a stellar disk with a photosphere and an optically thin outer layer, with increasing brightness ratio Br (i.e. the ratio between the brightness of the chromosphere/corona and that of the photosphere) from zero to 0.2 and unity. The lower panel shows the light curve of a planet transiting a star with the three brightnes… view at source ↗
Figure 2
Figure 2. The geometry of the observation. Left: In perspective view, the chromospheric/coronal intensity falls off exponentially with radial distance r from the surface of the star. We integrate this quantity along chords parallel to the line of sight (for example, inside and outside the photospheric limb as dashed blue lines). Right: In the x−y plane perpendicular to the observer’s line-of-sight, the chromosphere is discret… view at source ↗
Figure 3
Figure 3. Example of a wavelength bin exhibiting significant chromospheric/coronal emission (left column) and an adjacent nearly unaffected wavelength bin (right column). Top row:Illustration of the best-fit TACHELES models. Second row: The observed light curve along with the resulting model fits. Third row: Residuals from the traditional Mandel-Agol photospheric model fit, highlighting the difference between MA and TACHELES … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Relative difference in transit depth derived for the TACHELES model radius (rp,TACH) and the photospheric model radius (rp,phot) as a function of the TACHELES brightness ratio. The color coding denotes the Bayes fac￾tor. Parameter Priors Composition log Xi U{-12,-1} P-…
Figure 5
Figure 5. Figure 5: Transmission spectra of HAT-P-18 b and POSEIDON fits, binned to a resolution of 100. The POSEIDON models (one active region) are plotted as solid lines and 1σ errors are marked by the shaded regions. The lower panel shows the relative point-by-point difference between …
Figure 6
Figure 6. Figure 6: Chromospheric/coronal emission spectrum of HAT-P-18 derived by multiplication of the TACHELES model bright￾ness ratios with a PHOENIX photospheric spectrum. The solid blue line shows the spectrum smoothed to the instrumental resolution, along with the 1σ error region i…
Figure 7
Figure 7. Figure 7: Solar Dynamics Observatory (Pesnell et al. 2012) measurements of the Sun’s brightness distribution, azimuthally averaged. The data was acquired at 17.1 nm. As highlighted in the enlarged panel, exterior to the solar disk, an exponentially decaying emission law integrat…
Figure 8
Figure 8. Figure 8: Results of the retrieval tests. a Accuracy of the brightness ratio as a function of SNR. Points with error bars denote the retrieved values and uncertainties for different actual values shown in colors. For each value of Br and SNR, multiple scale heights were tested, …
Figure 9
Figure 9. Figure 9: Example corner plot of a light curve fit for a wavelength bin where H and Br are well-constrained (λ = 0.7516 µm). Alderson, L., Wakeford, H. R., Alam, M. K., et al. 2023, Nature, 614, 664, doi: 10.1038/s41586-022-05591-3 Astropy Collaboration, Robitaille, T. P., Tolle…

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Works this paper leans on

59 extracted references · 13 canonical work pages

  1. [1]

    B., Mansfield , M., et al

    Ahrer , E.-M., Stevenson , K. B., Mansfield , M., et al. 2023, , 614, 653, 10.1038/s41586-022-05590-4

    doi:10.1038/s41586-022-05590-4 2023

  2. [2]

    2023, , 135, 075001, 10.1088/1538-3873/acd7a3

    Albert et al., , L. 2023, , 135, 075001, 10.1088/1538-3873/acd7a3

    doi:10.1088/1538-3873/acd7a3 2023

  3. [3]

    R., Alam , M

    Alderson , L., Wakeford , H. R., Alam , M. K., et al. 2023, , 614, 664, 10.1038/s41586-022-05591-3

    doi:10.1038/s41586-022-05591-3 2023

  4. [4]

    P., Tollerud , E

    Astropy Collaboration , Robitaille , T. P., Tollerud , E. J., et al. 2013, , 558, A33, 10.1051/0004-6361/201322068

    doi:10.1051/0004-6361/201322068 2013

  5. [5]

    M., Sip o cz , B

    Astropy Collaboration , Price-Whelan , A. M., Sip o cz , B. M., et al. 2018, , 156, 123, 10.3847/1538-3881/aabc4f

    doi:10.3847/1538-3881/aabc4f 2018

  6. [6]

    2022, , 935, 167, 10.3847/1538-4357/ac7c74

    Astropy Collaboration et al., . 2022, , 935, 167, 10.3847/1538-4357/ac7c74

    doi:10.3847/1538-4357/ac7c74 2022

  7. [7]

    2021, The Journal of Open Source Software, 6, 3001, 10.21105/joss.03001

    Buchner , J. 2021, The Journal of Open Source Software, 6, 3001, 10.21105/joss.03001

    doi:10.21105/joss.03001 2021

  8. [8]

    J., et al

    Cadieux , C., Doyon , R., MacDonald , R. J., et al. 2024, , 970, L2, 10.3847/2041-8213/ad5afa

    doi:10.3847/2041-8213/ad5afa 2024

Show all 59 references
  1. [9]

    2024, Master's thesis, Weizmann Institute of Science, Rehovot, Israel

    Chaikin-Lifshitz, A. 2024, Master's thesis, Weizmann Institute of Science, Rehovot, Israel

    2024

  2. [10]

    2024, , 682, A136, 10.1051/0004-6361/202347079

    Claudi , R., Bruno , G., Fossati , L., et al. 2024, , 682, A136, 10.1051/0004-6361/202347079

    2024 doi

  3. [11]

    2023, , 943, L10, 10.3847/2041-8213/acaead

    Constantinou , S., Madhusudhan , N., & Gandhi , S. 2023, , 943, L10, 10.3847/2041-8213/acaead

    2023 doi

  4. [12]

    de Ferrer, J. J. 1809, Transactions of the American Philosophical Society, 6, 264. http://www.jstor.org/stable/1004801

  5. [13]

    2021, , 909, 38, 10.3847/1538-4357/abd8ce

    Del Zanna et al., , G. 2021, , 909, 38, 10.3847/1538-4357/abd8ce

    2021 doi

  6. [14]

    1997, , 125, 149, 10.1051/aas:1997368

    Dere , K. 1997, , 125, 149, 10.1051/aas:1997368

    1997 doi

  7. [15]

    2013, ChiantiPy: Python package for the CHIANTI atomic database, Astrophysics Source Code Library, record ascl:1308.017

    ---. 2013, ChiantiPy: Python package for the CHIANTI atomic database, Astrophysics Source Code Library, record ascl:1308.017

    2013

  8. [16]

    J., Hutchings , J

    Doyon , R., Willott , C. J., Hutchings , J. B., et al. 2023, , 135, 098001, 10.1088/1538-3873/acd41b

    2023 doi

  9. [17]

    2023, , 614, 670, 10.1038/s41586-022-05674-1

    Feinstein et al., , A. 2023, , 614, 670, 10.1038/s41586-022-05674-1

    2023 doi

  10. [18]

    2024, , 528, 3354, 10.1093/mnras/stad3813

    Fournier-Tondreau et al., , M. 2024, , 528, 3354, 10.1093/mnras/stad3813

    2024 doi

  11. [19]

    France , K., Loyd , R. O. P., Youngblood , A., et al. 2016, , 820, 89, 10.3847/0004-637X/820/2/89

    2016 doi

  12. [20]

    2022, , 940, L35, 10.3847/2041-8213/ac9977

    Fu et al., , G. 2022, , 940, L35, 10.3847/2041-8213/ac9977

    2022 doi

  13. [21]

    2009, The Solar Corona (Cambridge University Press)

    Golub , L. 2009, The Solar Corona (Cambridge University Press)

    2009

  14. [22]

    Grant, D., & Wakeford, H. R. 2022, Exo-TiC/ExoTiC-LD: ExoTiC-LD v3.0.0, v3.0.0, Zenodo, 10.5281/zenodo.7437681

    2022 doi

  15. [23]

    1939, Naturwissenschaften, 27, 214, 10.1007/BF01488890

    Grotrian , W. 1939, Naturwissenschaften, 27, 214, 10.1007/BF01488890

    1939 doi

  16. [24]

    D., Bakos , G

    Hartman , J. D., Bakos , G. \'A ., Sato , B., et al. 2011, , 726, 52, 10.1088/0004-637X/726/1/52

    2011 doi

  17. [25]

    2023, , 524, 377, 10.1093/mnras/stad1580

    Holmberg , M., & Madhusudhan , N. 2023, , 524, 377, 10.1093/mnras/stad1580

    2023 doi

  18. [26]

    2023, , 959, 64, 10.3847/1538-4357/acfe75

    Howard et al., , W. 2023, , 959, 64, 10.3847/1538-4357/acfe75

    2023 doi

  19. [27]

    2013, , 553, A6, 10.1051/0004-6361/201219058

    Husser , T.-O. 2013, , 553, A6, 10.1051/0004-6361/201219058

    2013 doi

  20. [28]

    1939, Theory of Probability (Oxford, England: Clarendon Press)

    Jeffreys, H. 1939, Theory of Probability (Oxford, England: Clarendon Press)

    1939

  21. [29]

    W., Corrales , L

    King , G. W., Corrales , L. R., Wheatley , P. J., Cilley , R. C., & Hollands , M. 2024, arXiv e-prints, arXiv:2410.01559, 10.48550/arXiv.2410.01559

    2024 doi arXiv

  22. [30]

    2015, , 127, 1161, 10.1086/683602

    Kreidberg , L. 2015, , 127, 1161, 10.1086/683602

    2015 doi

  23. [31]

    2023, , 955, L22, 10.3847/2041-8213/acf7c4

    Lim et al., , O. 2023, , 955, L22, 10.3847/2041-8213/acf7c4

    2023 doi

  24. [32]

    2019, Host Stars and their Effects on Exoplanet Atmospheres : An Introductory Overview, 1st edn., Lecture Notes in Physics, 955 (Cham: Springer International Publishing)

    Linsky, J. 2019, Host Stars and their Effects on Exoplanet Atmospheres : An Introductory Overview, 1st edn., Lecture Notes in Physics, 955 (Cham: Springer International Publishing)

    2019

  25. [33]

    Linsky , J. L. 1980, , 18, 439, 10.1146/annurev.aa.18.090180.002255

    1980

  26. [34]

    1868, Proceedings of the Royal Society of London Series I, 17, 91

    Lockyer , J. 1868, Proceedings of the Royal Society of London Series I, 17, 91

  27. [35]

    MacDonald, R. J. 2023, Journal of Open Source Software, 8, 4873, 10.21105/joss.04873

    2023 doi

  28. [36]

    J., & Madhusudhan , N

    MacDonald , R. J., & Madhusudhan , N. 2017, , 469, 1979, 10.1093/mnras/stx804

    2017 doi

  29. [37]

    MacDonald et al., , R. J. 2020, , 893, L43, 10.3847/2041-8213/ab8238

    2020 doi

  30. [38]

    2009, , 707, 24, 10.1088/0004-637X/707/1/24

    Madhusudhan , N., & Seager , S. 2009, , 707, 24, 10.1088/0004-637X/707/1/24

    2009 doi

  31. [39]

    2002, , 580, L171, 10.1086/345520

    Mandel , K., & Agol , E. 2002, , 580, L171, 10.1086/345520

    2002 doi

  32. [40]

    M., MacDonald , R

    May , E. M., MacDonald , R. J., Bennett , K. A., et al. 2023, , 959, L9, 10.3847/2041-8213/ad054f

    2023 doi

  33. [41]

    E., Stevenson , K

    Moran , S. E., Stevenson , K. B., Sing , D. K., et al. 2023, , 948, L11, 10.3847/2041-8213/accb9c

    2023 doi

  34. [42]

    2022, Research Notes of the American Astronomical Society, 6, 272, 10.3847/2515-5172/acabc7

    Nikolov et al., , N. 2022, Research Notes of the American Astronomical Society, 6, 272, 10.3847/2515-5172/acabc7

    2022 doi

  35. [43]

    A., et al

    Paragas , K., Vissapragada , S., Knutson , H. A., et al. 2021, , 909, L10, 10.3847/2041-8213/abe706

    2021 doi

  36. [44]

    A., & Espinoza, N

    Patel, J. A., & Espinoza, N. 2022, The Astronomical Journal, 163, 228, 10.3847/1538-3881/ac5f55

    2022 doi

  37. [45]

    2024, , 683, A125, 10.1051/0004-6361/202348263

    Perdelwitz et al., , V. 2024, , 683, A125, 10.1051/0004-6361/202348263

    2024 doi

  38. [46]

    D., Thompson , B

    Pesnell , W. D., Thompson , B. J., & Chamberlin , P. C. 2012, , 275, 3, 10.1007/s11207-011-9841-3

    2012 doi

  39. [47]

    Peter , H., & Dwivedi , B. N. 2014, Frontiers in Astronomy and Space Sciences, 1, 2, 10.3389/fspas.2014.00002

    2014

  40. [48]

    2024, , 626, 979, 10.1038/s41586-024-07040-9

    Powell et al., , D. 2024, , 626, 979, 10.1038/s41586-024-07040-9

    2024 doi

  41. [49]

    2018, , 853, 122, 10.3847/1538-4357/aaa08c

    Rackham , B. 2018, , 853, 122, 10.3847/1538-4357/aaa08c

    2018 doi

  42. [50]

    2024 a , , 962, L20, 10.3847/2041-8213/ad20e4

    Radica , M., Coulombe , L.-P., Taylor , J., et al. 2024 a , , 962, L20, 10.3847/2041-8213/ad20e4

    2024 doi

  43. [51]

    2024 b , arXiv e-prints, arXiv:2409.19333, 10.48550/arXiv.2409.19333

    Radica , M., Piaulet-Ghorayeb , C., Taylor , J., et al. 2024 b , arXiv e-prints, arXiv:2409.19333, 10.48550/arXiv.2409.19333

    2024 doi arXiv

  44. [52]

    Rustamkulov et al. , Z. 2023, , 614, 659, 10.1038/s41586-022-05677-y

    2023 doi

  45. [53]

    2024, arXiv e-prints, arXiv:2404.15505, 10.48550/arXiv.2404.15505

    Saba et al., , A. 2024, arXiv e-prints, arXiv:2404.15505, 10.48550/arXiv.2404.15505

    2024 doi arXiv

  46. [54]

    2023, , 524, 817, 10.1093/mnras/stad1547

    Taylor , J., Radica , M., Welbanks , L., et al. 2023, , 524, 817, 10.1093/mnras/stad1547

    2023 doi

  47. [55]

    2000, Journal of Mathematical Psychology, 44, 92, https://doi.org/10.1006/jmps.1999.1278

    Wasserman, L. 2000, Journal of Mathematical Psychology, 44, 92, https://doi.org/10.1006/jmps.1999.1278

    2000

  48. [56]

    E., Schmieder , B., Kucera , T., et al

    Wiik , J. E., Schmieder , B., Kucera , T., et al. 1997, , 175, 411, 10.1023/A:1004925024794

    1997 doi

  49. [57]

    E., & Linsky , J

    Wood , B. E., & Linsky , J. L. 2006, , 643, 444, 10.1086/501521

    2006 doi

  50. [58]

    2024, , 963, L5, 10.3847/2041-8213/ad2682

    Xue et al., , Q. 2024, , 963, L5, 10.3847/2041-8213/ad2682

    2024 doi

  51. [59]

    write newline

    " write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTI...

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.