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REVIEW 4 major objections 5 minor 55 references

Hubble's Multi-Year Search for Exospheres in the TRAPPIST-1 System Reveals Frequent Microflares

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Pith's one-line read A five-year Hubble campaign finds no TRAPPIST-1 exospheres, and identifies the noise floor as frequent microflares.

desk verdict Solid non-detection and rotation period, but the microflare statistics and the abstract's escape-rate limit need tightening before the quantitative claims stand. read the letter →

arxiv 2506.12140 v1 pith:22UYJYUI submitted 2025-06-13 astro-ph.EP astro-ph.SR

classification astro-ph.EPastro-ph.SR
keywords TRAPPIST-1Lyman-alphatransitsexospheresstellarmicroflaresMdwarfactivityHST/STISatmosphericescaperotationperiod
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 TRAPPIST-1's own ultraviolet flickering, not photon noise, is what limits searches for exospheres around its seven planets. Across 104 Hubble orbits spanning five years, no planet shows a statistically significant Lyman-$\alpha$ transit; the campaign rules out transit depths above about 20 percent and translates that into an upper limit near 1064 Earth-ocean-equivalent hydrogen per gigayear for planet b, consistent with an airless planet b. The excess scatter in the light curves is traced to frequent microflares of about $10^{29}$ erg: STIS time-tagged data show sub-hour Lyman-$\alpha$ enhancements of 300-500 percent, and independent VLT g-band photometry shows one to two flares per hour. If correct, the finding changes how null exosphere searches around active M dwarfs should be read: the detection floor is the star, and thin atmospheres cannot yet be ruled out.

What carries the argument

The load-bearing tool is the TIME-TAG mode of STIS, which records each detected photon's arrival time; it lets the authors look inside the $\sim 45$-minute orbit and catch count-rate spikes that orbit-averaged photometry would smear out. They use the bright geocoronal airglow as a simultaneous reference to reject instrumental artifacts. The second mechanism is a waiting-time pairing rule taken from prior flare studies: flares of similar cadence are assumed to share an emission mechanism, so a Lyman-$\alpha$ event and a $g'$-band event of the same waiting time can be combined and fit by a one-component blackbody, yielding the flare temperature and filling factor. The third mechanism is a Lomb-Scargle periodogram applied to the multi-year, orbit-averaged Lyman-$\alpha$ fluxes, which recovers the stellar rotation period.

What would settle it

Simultaneous HST/STIS Lyman-$\alpha$ and VLT g'-band monitoring of TRAPPIST-1 would settle it: if the 300-500 percent Lyman-$\alpha$ bursts do not coincide with the few-percent g'-band brightenings predicted by an $11000$ K, $0.011\%$ filling-factor blackbody, the inferred microflare properties are wrong.

Watch

Extended reading notes

Core claim

On the paper's own terms, TRAPPIST-1's Lyman-$\alpha$ line is so intrinsically variable that the star sets the measurement floor. In 104 HST/STIS orbits (24 visits) covering three to five transits per planet, none of the seven planets shows a statistically significant transit; the data exclude depths $\gtrsim 20\%$ at $5\sigma$, place $2\sigma$ upper limits near $30\%$, and give an escape-rate upper limit of about $1064\ \mathrm{EO_H}/\mathrm{Gyr}$ for planet b under the adopted XUV cross-section. The out-of-transit scatter is three to five times the photon-noise expectation, and STIS TIME-TAG data resolve it into count-rate increases of 300-500 percent on sub-hour timescales, about three per high-signal visit. VLT/FORS2 $g'$-band photometry independently shows one to two flares per hour with amplitudes up to 50 percent. Pairing a $\sim 400\%$ Lyman-$\alpha$ enhancement with a $\sim 4\%$ $g'$-band enhancement of similar waiting time, the paper solves a one-component blackbody to obtain a flare temperature of $11000^{+4200}_{-3100}$ K and a filling factor of $0.011^{+0.03}_{-0.01}\%$ of the stellar disk. A periodogram of the multi-year baseline gives $P = 3.27 \pm 0.04$ days, matching the previously reported 3.295-day rotation period.

Load-bearing premise

The flare temperature and filling factor rest on the assumption that a Lyman-alpha flare and a g-band flare with similar waiting times are the same kind of event, so their amplitudes can be combined in a single blackbody model; if the two bands see different flare populations, the 11000 K and 0.011 percent values do not follow.

Editorial extensions

If this is right

  • For TRAPPIST-1, HST/STIS Lyman-alpha transit spectroscopy is now sensitivity-limited: exospheres producing transits shallower than roughly 20 percent cannot be detected, so null results do not prove the planets lack atmospheres.
  • The escape-rate upper limit near $1064\ \mathrm{EO_H}/\mathrm{Gyr}$ for planet b supports the emerging picture that planet b is airless or has already lost its hydrogen reservoir.
  • TRAPPIST-1 flares extend down to about $10^{29}$ erg with sub-hour cadence, a decade below the $\sim 10^{30}$-erg flares seen every $\sim 6$ hours by JWST, so microflares are a persistent part of this star's ultraviolet environment.
  • The inferred flare temperature near $11000$ K and filling factor of about $0.011\%$ place the microflares inside the usual range for solar and stellar flares.
  • The $3.27 \pm 0.04$ day periodicity in Lyman-alpha flux independently confirms the 3.295-day rotation period, implying that ultraviolet activity is rotationally modulated.

Reading between the lines

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

  • If microflares are as frequent as reported, the time-averaged XUV irradiation of the TRAPPIST-1 planets may exceed the quiescent value used in the escape model, making the derived water-loss upper limits conservative in the sense that true losses could be higher.
  • The same TIME-TAG analysis could be applied to archival STIS observations of other M dwarfs; the paper's method implies that the noise floor for exosphere searches is set by stellar microvariability rather than detector performance.
  • A direct test of the 11000 K inference would be simultaneous far-ultraviolet and g-band monitoring; if the strong Lyman-alpha bursts do not coincide with weak g-band brightenings at the expected amplitude ratio, the waiting-time pairing assumption would need revision.
  • If flare triggering is tied to the 3.27-day rotation, the microflare rate should vary with rotational phase, a prediction that could be checked by folding the TIME-TAG flare candidates on the recovered period.
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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 / 5 minor

Summary. This paper presents 104 orbits of HST/STIS G140M Ly-α monitoring of TRAPPIST-1 from 2017 to 2022, with 3–6 transits per planet. Using PSF fitting, the authors derive Ly-α light curves, rule out transit depths ≳20% at 5σ, and convert the non-detections into escape-rate upper limits, reporting 1064 Earth-ocean-equivalent hydrogen per Gyr for planet b under an assumed XUV cross-section. The paper further attributes the excess baseline scatter to frequent microflares, reporting sub-hour Ly-α count-rate enhancements in STIS TIME-TAG data and 1–2 flares/hour in VLT/FORS2 g-band photometry. From paired Ly-α and optical amplitudes it derives a flare temperature of 11000 K and a filling factor of 0.011%, and it reports a 3.27 ± 0.04 day rotation period consistent with the known 3.295-day period.

Significance. If the microflare interpretation holds, this is an important result for UV exosphere searches: stellar microvariability, not photon noise, sets the practical detection limit for Ly-α transits around active M dwarfs. The underlying dataset is substantial and publicly available, and the transit non-detections and rotation-period recovery are valuable independent constraints: the rotation period is checked against the external K2 value and passes an injection–recovery test, and the 20% transit-depth limits are directly supported by the light curves. The flare temperature and filling factor, however, rest on a chain of assumptions that the manuscript does not yet quantitatively justify, so the significance of the microflare characterization is currently conditional.

major comments (4)
  1. [Section 3.2] The TIME-TAG flare detection criterion is never specified. The text states that candidates are epochs where the count rate 'significantly exceeded the baseline trend,' but no threshold, signal-to-noise requirement, false-alarm rate, or candidate table is provided. The only systematic check is the absence of a concurrent airglow spike and an orbit-integrated correlation coefficient <0.5 with background/airglow; that check does not address time-resolved PSF drift, wavelength-solution jumps, or detector artifacts on 5-minute timescales. As written, the Section 5 claim that the excess scatter is 'a manifestation of intrinsic stellar variability, consistent with frequent, short-duration microflares' is not distinguished from a small number of unexplained count-rate excursions. Please define the detection threshold, compute the false-alarm rate from scrambled or airglow-referenced time series, and provide a table of candidates with their significances.
  2. [Section 3.3] The VLT/FORS2 corroboration is weaker than stated. Flare-like structures are 'identified by eye' in the Figure 4 caption, with no automated detection, no significance threshold, and no completeness estimate. The 1–2 flares/hour rate comes from only four nights, and the reported g'-band amplitudes range from 1% to 50%, yet the temperature inversion in Section 3.4 pairs a ~4% optical event with a ~400% Ly-α event. If the optical excursions are not robustly detected, or if the 4% event is not representative, the independent-corroboration argument loses its quantitative force. Please add a reproducible detection algorithm for the optical data, report per-event amplitudes and durations, and quantify how the spread in optical amplitudes affects the pairing used in Section 3.4.
  3. [Section 3.4] The flare temperature and filling factor depend on the assumption that Ly-α and optical flares with similar waiting times share the same emission mechanism, citing Loyd et al. (2018). This assumption is load-bearing because it justifies pairing a ~400% Ly-α enhancement with a ~4% g'-band enhancement to solve a one-component blackbody. If the paired events belong to different flare populations, or if the 4% optical amplitude is not representative given the observed 1–50% range, then Tfl = 11000 K and Xfl = 0.011% are not supported. The manuscript should either provide a sensitivity analysis showing how Tfl and Xfl vary when the pairings and the continuum-to-Ly-α ratio (0.03+0.14–0.02) are changed, or clearly present these numbers as an illustrative estimate rather than a measured flare property. The current abstract presents them as a headline result without this caveat.
  4. [Section 2.5 and Abstract] The abstract quotes 1064 EO_H/Gyr for planet b as the headline upper limit, but the text shows that this value corresponds to (R_XUV/R_star)^2 = 0.20, while the fiducial adopted value of 0.10 yields 533 EO_H/Gyr. The paper itself notes that (R_XUV/R_star)^2 = 0.10 is an upper limit and that smaller cross-sections would reduce the loss rate significantly. The abstract and conclusions should therefore state the range explicitly and distinguish the assumption-dependent escape-rate estimate from the measured transit-depth upper limit. As written, quoting only the doubled value overstates the robustness of the escape-rate constraint.
minor comments (5)
  1. [Section 2.4] The sentence 'We investigate its origin in Section 4' appears to be a cross-reference error: the variability origin is discussed in Section 3, not Section 4.
  2. [Table 1] Table 1 contains apparent anomalies: several visits appear twice (e.g., odhs33, odhs31, odhsd1) with different mean-flux values for the same visit, and some entries (e.g., '1.55-11', '1.50e-10') look like typos in the flux column. Please correct the table and ensure each visit appears exactly once with one consistent flux value.
  3. [Section 3.3] The filter is described as 'gHIGH (spectral range: 388–548 nm)' in Section 3.3, while the abstract, Section 3.4, and Figure 4 refer to g' or g-band observations. Please unify the filter nomenclature and specify whether the photometric band is the standard g' filter or the gHIGH filter.
  4. [Section 3.4] The text states that the filling factor 'aligned with values reported for TRAPPIST-2 flares' — this is likely a typo for TRAPPIST-1, since no TRAPPIST-2 system is otherwise referenced and the cited works concern TRAPPIST-1.
  5. [Figure 4] The Figure 4 caption says 'A flare of ~50% amplitude is visible (trimmed here)' but the plotted light curve shows six orange-shaded features. Please clarify which feature is the 50% flare and whether the flare shown was trimmed to preserve the transit window.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: main results are measured from the data and compared with external benchmarks; self-citations are not load-bearing.

full rationale

The paper's central claims are derived directly from calibrated observations and external benchmarks rather than from its own conclusions. The Ly-alpha transit upper limits are computed from the measured per-visit light curves and the quadrature-summed in-transit/out-of-transit scatter (Section 2.4, Table 2), so the limits are not restatements of an input. The rotation period is tested against the independent K2 rotation period of 3.295 days from Vida et al. (2017) and is checked with an injection-recovery test (Section 4), giving the comparison external content. The flare energies and occurrence rates come from photon-counting data: HST/STIS TIME-TAG events are identified as count-rate increases relative to a baseline (Section 3.2), and the VLT/FORS2 flares are independently measured differential photometry (Section 3.3). The microflare temperature and filling factor in Section 3.4 are obtained by combining the two measured amplitude ratios with the externally published Ly-alpha-to-continuum scaling of Loyd et al. (2018, Table 8) and Linsky et al. (2014); the equal-mechanism assumption for similar waiting times is explicitly stated as a standard approach, not hidden or derived from the target result. Self-citations such as Bourrier et al. (2017b) and Bolmont et al. (2017) are used as published parametric formulas and context, not as the proof of the new detections, and the paper itself flags the main assumption-sensitive inputs (the adopted XUV cross-section and the water-supply limitation) in Section 2.5. No equation or chain in the paper reduces to its own inputs by construction, so no circular step is identified.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on the stellar flare interpretation and the escape model. The derived microflare temperature relies on external scaling relations and a waiting-time equivalence assumption, while the escape-rate upper limit relies on an adopted XUV cross-section. No new particles, forces, or conserved quantities are introduced; 'microflares' is a label for known stellar flare phenomena at lower energy, not an invented entity.

free parameters (3)
  • (R_XUV/R_star)^2 = 0.10 (adopted), 0.20 (doubled upper limit)
    Chosen XUV absorption cross-section in the energy-limited escape model (Section 2.5). The 1064 EO_H/Gyr headline limit for planet b uses the doubled value 0.20, while the preferred 0.10 gives 533 EO_H/Gyr.
  • Continuum-to-Ly-alpha ratio for FUV flares = 0.03 (+0.14/-0.02)
    Taken from Loyd et al. (2018) to convert the Ly-alpha flare energy to a G140M continuum energy in the blackbody fit (Section 3.4). It is a prior empirical ratio, not measured here.
  • Airglow Voigt FWHM values = Gaussian 2.08911, Lorentzian 1.83458
    Fixed during fitting from preliminary global fits (Appendix B.1); may affect flux extraction but not the central claim.
assumptions (6)
  • domain assumption The energy-limited escape model with efficiency factor epsilon from Bolmont et al. (2017) describes hydrogen loss from TRAPPIST-1 planets.
    Used in Section 2.5 to convert Ly-alpha/XUV luminosity into mass-loss rates and EOH limits; the resulting 1064 EO_H/Gyr depends on this model and the chosen XUV cross-section.
  • domain assumption The Linsky et al. (2014) relation between Ly-alpha and XUV luminosity applies to TRAPPIST-1.
    Section 2.5 uses this relation to estimate XUV luminosity from the measured Ly-alpha luminosity; no simultaneous X-ray verification is shown.
  • ad hoc to paper Flares with similar waiting times share underlying emission mechanisms (Loyd et al. 2018 framework).
    Section 3.4 uses this to combine one Ly-alpha flare and one g' flare into a single blackbody temperature and filling factor; this is the key assumption behind Tfl=11000 K.
  • domain assumption The continuum-to-Ly-alpha ratio from Loyd et al. (2018) holds for TRAPPIST-1 microflares.
    Section 3.4 applies the ratio 0.03 (+0.14/-0.02) to derive EG140M; deviations by the allowed factor change Tfl and Xfl.
  • domain assumption Airglow and background signals are separable from the stellar Ly-alpha signal with the described PSF model, and the airglow position and shape can be treated as constant within a visit.
    Appendix B assumes a Voigt airglow with fixed FWHMs and a linear background; if the airglow model is wrong, extracted fluxes are biased.
  • domain assumption Candidate flares in TIME-TAG data are not artifacts of photon counting or airglow variability.
    Section 3.2 identifies flares as count-rate excesses above baseline with no concurrent airglow spike; no explicit false-positive rate is computed.

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Cite this review

Pith. "Pith review of Hubble's Multi-Year Search for Exospheres in the TRAPPIST-1 System Reveals Frequent Microflares." pith.science (2026). https://pith.science/paper/22UYJYUI

@misc{pith2026250612140,
  author       = {Pith},
  title        = {Pith review of: Hubble's Multi-Year Search for Exospheres in the TRAPPIST-1 System Reveals Frequent Microflares},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/22UYJYUI}},
  note         = {Machine review of arXiv:2506.12140}
}
abstract

Ly-$\alpha$ observations provide a powerful probe of stellar activity and atmospheric escape in exoplanetary systems. We present here an analysis of 104 HST/STIS orbits monitoring the TRAPPIST-1 system between 2017 and 2022, covering 3--5 transits for each of its seven planets. We rule out transit depths $\gtrsim20\%$, which translates into an upper limit on the escape rate of $1064~EO_H$/Gyr for planet b ($1~EO_H$ is the Earth-ocean-equivalent hydrogen content), in agreement with recent claims that planet b should be airless. These upper limits are $\sim$3 times larger than expected from the photon noise due to a large baseline scatter, which we ultimately link to TRAPPIST-1's intrinsic Ly-$\alpha$ variability from frequent ``microflares.'' While JWST observations of TRAPPIST-1 in the near infrared have shown that $\sim10^{30}$-erg flares occur every $\sim$6 hours, we report here $\sim10^{29}$-erg flares on sub-hour timescales in the HST/STIS and also Very Large Telescope (VLT) $g^{'}$ observations. The FUV and optical amplitudes ($\sim$400$\%$ vs $\sim$3$\%$, respectively) for flares with similar waiting-times indicate flare temperatures of 11000$^{+4200}_{-3100}$~K over 0.011$^{+0.03}_{-0.01}$\% of the stellar disk. Finally, our multi-year baseline reveals a variability with $P = 3.27 \pm 0.04$ days, providing further validation of the previously reported 3.295-day rotation period for TRAPPIST-1. These results highlight the importance of accounting for stellar microvariability when searching for exospheres around active M dwarfs.

Figures

Figures reproduced from arXiv: 2506.12140 by the authors.

Figure 1
Figure 1. Overview of the orbital positions of the TRAPPIST-1 planets during each of the 24 visits. Planets which transit during a visit are in bold, with the observer line of sight represented by the dashed black line. The bottom right corner highlights which planet each orbit corresponds to. The next frontier in the atmospheric exploration of the TRAPPIST-1 system involves searching for thin￾ner, secondary atmospheres. Such… view at source ↗
Figure 2
Figure 2. Analysis & Data Overview. (a) Top Left: Systematic-corrected signal image, for which a model fit is retrieved, which is shown in the central panel. Top Right: Spatially-flattened spectral profile of the image, indicating the strong airglow peak and blue-wing of TRAPPIST-1’s Ly-α emission, along with the best fit model in orange. Note that this is not the intrinsic Ly-α signal from TRAPPIST-1, but the signal after th… view at source ↗
Figure 3
Figure 3. [ ]Signs of frequent flares in TRAPPIST-1 HST/STIS TIME-TAG data. Count rates for individual sections on the detector based on photon TIME-TAG data for visit odhs33. Solid black lines denote time between orbits. The top row of orbit-integrated exposures shows a 50x50 pixel stamp centered on TRAPPIST-1, highlighting the variability of the Ly-α emission. The vertical line of emission to the right of the signal is the … view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: [ VlT g-band photometry]g-band light curve measured from the observations of TRAPPIST-1 by VLT on 30 Nov 2018. A flare of ∼50% amplitude is visible (trimmed here). The orange bands show flare-like structures identified by eye in the light curve. The green band marks th…
Figure 5
Figure 5. Figure 5: [ Microflare properties.]Properties and occurrence rate of TRAPPIST-1 microflares. Left: The observed ratio of G140M to g ′ flare continuum and uncertainty (gray) compared against that of a blackbody of Tfl (black) gives Tfl=11000+4200 −3100 K. Middle: Position of our …
Figure 6
Figure 6. Figure 6: [ TRAPPIST-1 Long Term Flux Trends]Complementary insights into TRAPPIST-1 from HST/STIS’s multi-year monitoring. Left: Absolute emission flux from TRAPPIST-1, folded to various periods. The blue data points are for each individual orbit, while the orange points are bin…
Figure 7
Figure 7. Figure 7: [ Ly-α emissions during transits of TRAPPIST-1 h]Ly-α time series normalized at the individual-visit level (mean visit flux reported in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: [ airglow var]Left: The central wavelength of the peak of the airglow signal (in pixels) as a function of time. Right: The variability of the airglow amplitude as a function of time. The orange curves in both figures represent best fit sin curves, which were found to h…

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Works this paper leans on

55 extracted references · 10 canonical work pages

  1. [1]

    L., et al

    Agol , E., Dorn , C., Grimm , S. L., et al. 2021, , 2, 1, 10.3847/PSJ/abd022

  2. [2]

    P., Tollerud , E

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

  3. [3]

    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

  4. [4]

    M., Lim , P

    Astropy Collaboration , Price-Whelan , A. M., Lim , P. L., et al. 2022, apj, 935, 167, 10.3847/1538-4357/ac7c74

  5. [5]

    I., Bertaux, J.-L., Quémerais, E., Izmodenov, V

    Baliukin, I. I., Bertaux, J.-L., Quémerais, E., Izmodenov, V. V., & Schmidt, W. 2019, Journal of Geophysical Research: Space Physics, 124, 861, https://doi.org/10.1029/2018JA026136

  6. [6]

    E., et al

    Bolmont , E., Selsis , F., Owen , J. E., et al. 2017, Monthly Notices of the Royal Astronomical Society, 464, 3728

  7. [7]

    2017 a , , 597, A26, 10.1051/0004-6361/201629253

    Bourrier , V., Ehrenreich , D., King , G., et al. 2017 a , , 597, A26, 10.1051/0004-6361/201629253

  8. [8]

    2017 b , , 154, 121

    Bourrier , V., de Wit , J., Bolmont , E., et al. 2017 b , , 154, 121

Show all 55 references
  1. [9]

    , Ehrenreich, D

    Bourrier, V. , Ehrenreich, D. , Wheatley, P. J. , et al. 2017, A&A, 599, L3, 10.1051/0004-6361/201630238

  2. [10]

    1995, , 378, 333, 10.1038/378333a0

    Burrows , A., & Lunine , J. 1995, , 378, 333, 10.1038/378333a0

  3. [11]

    2013, Science, 342, 1473, 10.1126/science.1245450

    de Wit , J., & Seager , S. 2013, Science, 342, 1473, 10.1126/science.1245450

  4. [12]

    R., Gillon , M., et al

    de Wit , J., Wakeford , H. R., Gillon , M., et al. 2016, , 537, 69, 10.1038/nature18641

  5. [13]

    2018, Nature Astronomy, 2, 10.1038/s41550-017-0374-z

    de Wit, J., Wakeford, H., Lewis, N., et al. 2018, Nature Astronomy, 2, 10.1038/s41550-017-0374-z

  6. [14]

    J., Moran, S

    Garcia , L. J., Moran, S. E. , Rackham, B. V. , et al. 2022, A&A, 665, A19, 10.1051/0004-6361/202142603

  7. [15]

    2007, Planetary and Space Science, 55, 1426, https://doi.org/10.1016/j.pss.2007.03.007

    García Muñoz , A. 2007, Planetary and Space Science, 55, 1426, https://doi.org/10.1016/j.pss.2007.03.007

  8. [16]

    Gillon, M., Triaud, A. H. M. J., Demory, B.-O., et al. 2017, Nature, 542, 456, 10.1038/nature21360

  9. [17]

    B., Lunine , J

    Guillot , T., Burrows , A., Hubbard , W. B., Lunine , J. I., & Saumon , D. 1996, , 459, L35, 10.1086/309935

  10. [18]

    G., Hudson , H

    Hannah , I. G., Hudson , H. S., Battaglia , M., et al. 2011, , 159, 263, 10.1007/s11214-010-9705-4

  11. [19]

    Hastings, W. K. 1970, Biometrika, 57, 97, 10.2307/2334940

  12. [20]

    S., Kowalski , A

    Howard , W. S., Kowalski , A. F., Flagg , L., et al. 2023, , 959, 64, 10.3847/1538-4357/acfe75

  13. [21]

    S., MacGregor , M

    Howard , W. S., MacGregor , M. A., Feinstein , A. D., et al. 2025, , 169, 27, 10.3847/1538-3881/ad93ce

  14. [22]

    Jackman , J. A. G., Shkolnik , E. L., Million , C., et al. 2023, , 519, 3564, 10.1093/mnras/stac3135

  15. [23]

    Kaltenegger , L., & Traub , W. A. 2009, , 698, 519, 10.1088/0004-637X/698/1/519

  16. [24]

    F., Hawley , S

    Kowalski , A. F., Hawley , S. L., Wisniewski , J. P., et al. 2013, , 207, 15, 10.1088/0067-0049/207/1/15

  17. [25]

    2003, The Astrophysical Journal, 598, L121, 10.1086/380815

    Lammer, H., Selsis, F., Ribas, I., et al. 2003, The Astrophysical Journal, 598, L121, 10.1086/380815

  18. [26]

    1993, , 408, 305, 10.1086/172589

    Landsman , W., & Simon , T. 1993, , 408, 305, 10.1086/172589

  19. [27]

    Lichtenberg, T., & Clement, M. S. 2022, The Astrophysical Journal Letters, 938, L3, 10.3847/2041-8213/ac9521

  20. [28]

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

    Lim , O., Benneke , B., Doyon , R., et al. 2023, , 955, L22, 10.3847/2041-8213/acf7c4

  21. [29]

    L., Fontenla , J., & France , K

    Linsky , J. L., Fontenla , J., & France , K. 2014, , 780, 61

  22. [30]

    Lomb , N. R. 1976, , 39, 447, 10.1007/BF00648343

  23. [31]

    Loyd , R. O. P., France , K., Youngblood , A., et al. 2018, , 867, 71, 10.3847/1538-4357/aae2bd

  24. [32]

    S., & Lincowski, A

    Lustig-Yaeger, J., Meadows, V. S., & Lincowski, A. P. 2019, The Astronomical Journal, 158, 27, 10.3847/1538-3881/ab21e0

  25. [33]

    J., Ilin , E., Oshagh , M., et al

    Maas , A. J., Ilin , E., Oshagh , M., et al. 2022, , 668, A111, 10.1051/0004-6361/202243869

  26. [34]

    1970, Planetary and Space Science, 18, 803, https://doi.org/10.1016/0032-0633(70)90080-2

    Meier, R., & Mange, P. 1970, Planetary and Space Science, 18, 803, https://doi.org/10.1016/0032-0633(70)90080-2

  27. [35]

    W., Rosenbluth, M

    Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. 1953, The Journal of Chemical Physics, 21, 1087–1092, 10.1063/1.1699114

  28. [36]

    V., Knutson , H., Line , M., et al

    Morley , C. V., Knutson , H., Line , M., et al. 2017, , 153, 86, 10.3847/1538-3881/153/2/86

  29. [37]

    A., Queloz , D., Gillon , M., et al

    Murray , C. A., Queloz , D., Gillon , M., et al. 2022, , 513, 2615, 10.1093/mnras/stac1078

  30. [38]

    A., Chiang , E

    Murray-Clay , R. A., Chiang , E. I., & Murray , N. 2009, , 693, 23, 10.1088/0004-637X/693/1/23

  31. [39]

    E., & Jackson , A

    Owen , J. E., & Jackson , A. P. 2012, , 425, 2931, 10.1111/j.1365-2966.2012.21481.x

  32. [40]

    2025, , 979, L5, 10.3847/2041-8213/ada381

    Radica , M., Piaulet-Ghorayeb , C., Taylor , J., et al. 2025, , 979, L5, 10.3847/2041-8213/ada381

  33. [41]

    2016, , 596, A111

    Ribas , I., Bolmont , E., Selsis , F., et al. 2016, , 596, A111

  34. [42]

    E., Newton, E

    Rockcliffe, K. E., Newton, E. R., Youngblood, A., et al. 2021, The Astronomical Journal, 162, 116, 10.3847/1538-3881/ac126f

  35. [43]

    Scargle , J. D. 1982, , 263, 835, 10.1086/160554

  36. [44]

    2007, , 191, 453

    Selsis , F., Chazelas , B., Bord \'e , P., et al. 2007, , 191, 453

  37. [45]

    Sim, S. A. 2001, Monthly Notices of the Royal Astronomical Society, 326, 821, 10.1046/j.1365-8711.2001.04632.x

  38. [46]

    J., Sing , D

    Spake , J. J., Sing , D. K., Evans , T. M., et al. 2018, Nature, 557, 67. 1805.01298

  39. [47]

    TJCI , T.-. J. C. I., de Wit , J., Doyon , R., et al. 2023, arXiv e-prints, arXiv:2310.15895, 10.48550/arXiv.2310.15895

  40. [48]

    2020, A&A, 638, A41, 10.1051/0004-6361/201937151

    Turbet , M., Bolmont, Emeline , Ehrenreich, David , et al. 2020, A&A, 638, A41, 10.1051/0004-6361/201937151

  41. [49]

    T., Desch , S

    Unterborn , C. T., Desch , S. J., Hinkel , N. R., & Lorenzo , A. 2018, Nature Astronomy, 2, 297, 10.1038/s41550-018-0411-6

  42. [50]

    2017, The Astrophysical Journal, 841, 124, 10.3847/1538-4357/aa6f05

    Vida, K., Kővári, Z., Pál, A., Oláh, K., & Kriskovics, L. 2017, The Astrophysical Journal, 841, 124, 10.3847/1538-4357/aa6f05

  43. [51]

    2004, , 604, L69, 10.1086/383347

    Vidal-Madjar , A., D \'e sert , J.-M., Lecavelier des Etangs , A., et al. 2004, , 604, L69, 10.1086/383347

  44. [52]

    R., Lewis , N

    Wakeford , H. R., Lewis , N. K., Fowler , J., et al. 2019, , 157, 11, 10.3847/1538-3881/aaf04d

  45. [53]

    E., Redfield, S., Linsky, J

    Wood, B. E., Redfield, S., Linsky, J. L., Müller, H.-R., & Zank, G. P. 2005, The Astrophysical Journal Supplement Series, 159, 118, 10.1086/430523

  46. [54]

    Yelle , R. V. 2004, , 170, 167, 10.1016/j.icarus.2004.02.008

  47. [55]

    A., Wang , L., et al

    Zhang , M., Knutson , H. A., Wang , L., et al. 2022, , 163, 68, 10.3847/1538-3881/ac3f3b

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.