Pith. sign in

REVIEW 2 major objections 5 minor 44 references

Can Moons Exist around the Habitable-zone Planet K2-18b?

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Tidal forces would push any moon around K2-18b past its stability limit within ~10 million years, far under the system's 3-billion-year age, so the habitable-zone planet is moonless today.

desk verdict A solid, well-documented simulation that shows K2-18b likely has no moons if it formed as a rapid rotator, but the abstract oversells the result by dropping that caveat. read the letter →

arxiv 2507.11594 v1 pith:2W4HB5PI submitted 2025-07-15 astro-ph.EP

Shaan D. Patel , Billy Quarles , Manfred Cuntz , Nevin N. Weinberg This is my paper · ORCID
classification astro-ph.EP
keywords exomoonsK2-18btidalevolutionhabitablezoneM-dwarfplanetsN-bodysimulationsreboundxastrobiology
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

K2-18b sits in its star's habitable zone and has shown tentative signs of biosignature gases in its atmosphere, making it a natural test case for whether a large moon could add habitable surface area. This paper asks whether a moon as massive as Earth's own Moon could actually remain in orbit there. Across 2,439 N-body simulations that include tidal spin evolution, the authors find that tides push any moon outward past the orbital stability limit within about 10 million years, roughly 300 times shorter than the system's 3-billion-year age. They conclude that K2-18b cannot host an observable moon today, and that moon-based habitability for short-period M-dwarf planets is doubtful because moons are removed before they can stabilize climate.

What carries the argument

The argument rides on two mechanisms working together. The first is the constant time-lag model of tides, implemented as the tides_spin module: the planet's tidal bulge lags the moon by a fixed time $\tau_p$, transferring angular momentum and steadily evolving the moon's semi-major axis and eccentricity. The second is the critical semi-major axis $a_{\rm crit} = 0.4031(1 - 1.123\,e_p)\,R_H$, with $R_H$ the planet's Hill radius, which defines the stability boundary beyond which a moon counts as lost; each simulation is scored by the moon's maximum lifetime $t_{\max}$, the time to cross $a_{\rm crit}$. The assumed rapid initial spin of the planet (5-hour period) sets the sign of the tidal torque so that the moon always migrates outward, and the relatively small Hill radius of this close-in planet makes the outward journey short.

What would settle it

Two concrete tests would decide the matter: a transit-timing or transit-duration search that detects a moon signal around K2-18b would directly contradict the null prediction, and a re-run of the same simulations with a slow or retrograde initial planetary spin that yields lifetimes above 3 Gyr would show the conclusion depends on the spin assumption rather than on the system itself.

Watch

Extended reading notes

Core claim

The paper's central claim is that exomoons are extremely unlikely to survive around K2-18b because planetary tides drive a moon's orbit outward on a timescale far shorter than the system age. In the full grid of simulations, the longest moon lifetime is about 9.1 Myr, achieved only with the most favorable parameters tested: a Neptune-like tidal response (Love number $k_2 = 0.120$), the smallest tidal time-lag $\tau_p = 10$ s, and the lowest observed planetary eccentricity $e_p = 0.12$. Faster dissipation (larger $\tau_p$) and higher eccentricities shorten lifetimes, and even the circular-orbit limit only extends the maximum to roughly 22–24 Myr. Since the K2-18 system is about 3 Gyr old, the authors conclude that no moon can be observed there now, and they extend the result to short-period M-dwarf planets generally: rapid tidal-driven migration removes moons before they can play any climate-stabilizing role, so moon-based habitability scenarios for such systems are doubtful.

Load-bearing premise

The whole conclusion assumes K2-18b began as a rapid rotator with a 5-hour spin period, so tides always push a moon outward; if the planet instead started with a slow or retrograde spin, the tides could pull a moon inward and let it survive much longer.

Editorial extensions

If this is right

  • No moon is observable around K2-18b today: the ~10 Myr migration timescale is shorter than the 3 Gyr system age by a factor of about 300.
  • Because even the circular-planet limit gives lifetimes of only ~22–24 Myr, the null prediction is robust across the observed eccentricity range.
  • The result acts as a predictive filter for exomoon surveys, flagging K2-18b as a false-positive-prone target and helping prioritize other systems.
  • Moon-based habitability scenarios for short-period M-dwarf planets are doubtful in general, since tides remove moons before they can stabilize planetary obliquity or host subsurface oceans.
  • Changing the moon's mass changes the lifetime by at most a factor of a few, so the conclusion does not hinge on the assumed Luna-mass satellite.

Reading between the lines

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

  • The assumed 5-hour initial spin is load-bearing: if K2-18b instead formed with a slow or retrograde spin, the tidal torque would reverse and could pull a moon inward, letting it survive far beyond 10 Myr. The paper states this assumption but does not vary it, so the result is a statement about rapidly rotating young planets.
  • The ~10 Myr removal timescale is so short that even a moon formed in situ after the planet's birth would have to appear within an extremely narrow window to be observable now; this strengthens the null prediction but also means the simulations assume the moon existed at all.
  • The same simulation machinery could be turned into a quick screening catalog for other habitable-zone M-dwarf planets: any planet with a short period and small Hill radius is a poor exomoon target, no matter how promising its atmosphere.
  • If future JWST-style observations confirm biosignature gases while independent data rule out a moon, the habitability discussion for K2-18b would have to lean entirely on the planet itself rather than on moon-supported environments.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper investigates whether K2-18b could host a detectable exomoon by integrating star–planet–moon systems with rebound and reboundx's tides_spin module under the constant time-lag tidal model. The authors vary planetary mass (271 values), initial planetary eccentricity (three values), planetary tidal time-lag (three values), and two interior parameter sets (Earth-like and Neptune-like k2 and C). Each simulation places a Luna-mass moon at 3 R_Roche and defines instability as crossing the a_crit stability boundary of Eq. (3). Across 2,439 simulations, the maximum moon lifetime is found to be about 9.1 Myr, with an extrapolated circular-orbit limit of roughly 22–24 Myr, far shorter than the ~3 Gyr system age. The paper concludes that observable moons are unlikely around K2-18b and questions moon-based habitability scenarios for short-period M-dwarf planets in general.

Significance. If the result holds, it provides a concrete dynamical constraint on exomoon survivability in a high-profile habitable-zone M-dwarf system and offers a template for using N-body tidal simulations to filter exomoon survey targets. The main strengths are the broad parameter sweep (2,439 integrations, three eccentricities, three time-lags, two interior models), the use of a well-documented tidal evolution module that includes spin evolution, and the fact that the lifetimes are outputs of direct integration rather than assumed inputs. The principal weakness is that the fixed 5-hour initial spin period controls the sign of tidal migration and is not varied, so the headline conclusion is conditional on an unconstrained assumption. The absence of public code or data and the neglect of the known companion K2-18c further limit the strength of the broadest generalizations.

major comments (2)
  1. [Section 2, Table 1; Section 4] The fixed initial planetary spin period of 5 h (Table 1) places the planet in a super-synchronous state relative to the moon's initial orbit, which forces the tidal torque to push the moon outward. This single assumption controls the sign of the tidal migration that drives the headline result. If K2-18b instead began with a slower, near-synchronous, or retrograde spin, the tidal torque could draw the moon inward, keep it near a synchronous state, or otherwise allow substantially longer survival; the migration-reversal mechanism cited from Sasaki et al. (2012) is dismissed rather than simulated. Section 4 explicitly concedes that the conclusion assumes a rapid rotator, but the abstract and title present the result without this caveat. I request additional simulations with a range of initial spin periods (e.g., near the synchronous period, longer periods, and retrograde spin), or at least an analytic sign criterion for the tidal migration, and a revised abstract and title that state the conditional nature of the claim.
  2. [Abstract; Section 4] The generalization that the result "cast[s] doubt on moon-based habitability scenarios for short-period M-dwarf planets in general" goes beyond what the simulations establish. The study varies M_p, e_p, tau_p, k2, and C, but it holds the moon mass at a single lunar mass, fixes the initial moon semi-major axis at 3 R_Roche, fixes the initial planetary spin at 5 h, and omits the known companion K2-18c. Any of these choices could alter the tidal migration rate or the effective stability boundary. The broad statement should either be removed or supported by simulations that explore at least the moon-mass and initial-spin dimensions.
minor comments (5)
  1. [Table 1] The column header for a_m lists units of au, but the entry is "3 R_Roche"; please specify the corresponding au value or change the header so the units are consistent.
  2. [Section 3, Fig. 3, Table 2] The MCMC linear fits use only three eccentricity values per time-lag value, and the error bars are described as "not statistically significant." The slopes and y-intercepts in Table 2 should be presented as descriptive linear interpolations rather than robust statistical inferences, and the circular-orbit extrapolation should be labeled as such.
  3. [Section 2] The simulations treat the star and moon as point masses and the planet with a constant radius of 2.61 R_E. The tidal response of the star is not modeled; a brief justification or citation for neglecting stellar tides on the 10 Myr integration timescale would improve the completeness of the methods.
  4. [Data Availability] The statement that "the data underlying this article will be shared on reasonable request" is insufficient for a study with 2,439 simulations; please deposit the rebound/reboundx scripts, initial-condition files, and summary outputs in a public repository to enable reproducibility.
  5. [Section 1] K2-18c is mentioned as a companion but is not included in the N-body model. A sentence quantifying the expected perturbation from K2-18c (for example, the ratio of its semi-major axis to K2-18b's Hill radius) would make the Payne et al. (2013) assumption of negligible planetary perturbations more transparent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: lifetimes are direct N-body outputs; disclosed spin assumption is a limitation, not a circular step.

full rationale

The claimed prediction—moon lifetimes of ~10^4–10^7 yr and instability within ~9.1 Myr—is the output of direct rebound/reboundx integrations under the constant time-lag tidal model, with planetary mass, eccentricity, and time-lag varied over the stated ranges. No equation in the paper injects the lifetime as an input; the simulations determine when the moon crosses the adopted stability boundary a_crit (Eq. 3). That boundary is cited from Rosario-Franco et al. (2020), a same-group publication, but it is a parameter-free stability criterion from prior simulations used only to stop the clock, and the tidal migration times to reach it are computed, not fitted. The MCMC lines in Fig. 3 and Table 2 merely interpolate/extrapolate the simulated median lifetimes to e_p=0 and are not the central claim. The 5 h initial spin is an unvaried assumption (Kokubo & Genda 2010; Takaoka et al. 2023) that sets the direction of migration; Section 4 explicitly discloses the conclusion is conditional on K2-18b beginning as a rapid rotator and notes the migration-reversal scenario is not possible under that assumption. This is a model limitation and a correctness risk for the general 'M-dwarf moons' claim, not a circular reduction of the result to its inputs. Accordingly, no circular step is identified.

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

The paper introduces no new physical entities and fits no constants to the target result. Its central claim depends on seven model inputs (scanned or hand-chosen) and five domain assumptions about tidal physics, stability limits, initial spin, and neglect of other planets. These are typical for numerical tidal studies, but they mean the result is conditional on the chosen tidal model and boundary condition rather than a parameter-free derivation.

free parameters (7)
  • Planetary mass M_p = 7.28 to 9.98 M_Earth (scan, step 0.01)
    Scanned over the observational 1-sigma range from Sarkis et al. (2018) and Benneke et al. (2019); the lifetime contours depend on it.
  • Initial planetary eccentricity e_p = 0.12, 0.20, 0.28
    Three values representing lower, median, and upper observational bounds; higher e_p shortens lifetimes through the a_crit stability limit.
  • Planetary tidal time-lag tau_p = 10, 100, 698 s
    Three values chosen to represent different assumed compositions; 698 s is the Earth-like value. Strongly controls the outward migration rate.
  • Love number k2 and moment of inertia C = k2=0.298/C=0.3308 (Earth-like); k2=0.120/C=0.2200 (Neptune-like)
    Two fixed composition cases; lower k2 slows the moon's orbital evolution and lengthens lifetimes.
  • Initial planetary spin period P_s = 5 hours
    Chosen as representative of protoplanet spin; it forces outward tidal migration. Not varied, despite being load-bearing.
  • Initial moon semi-major axis a_m = 3 R_Roche
    Moons are initialized at 3 times the fluid Roche limit; lifetimes would differ for other initial separations.
  • Moon mass M_m = 0.0123 M_Earth (Luna mass)
    A single Earth-Moon-like mass is used; authors state varying it changes lifetimes by no more than a factor of a few.
assumptions (5)
  • domain assumption Constant time-lag tidal model (Eggleton et al. 1998)
    Section 2 uses reboundx tides_spin; the entire migration timescale depends on this tidal model being an adequate description of spin-orbit coupling.
  • domain assumption Stability criterion a_crit (Eq. 3)
    The boundary for moon instability comes from Rosario-Franco et al. (2020); it is a semi-empirical calibration rather than a theorem, and it originates from the same group.
  • domain assumption Negligible perturbations from other planets
    The simulations include only star, planet, and moon; K2-18c and any other bodies are ignored, justified only by a general citation (Payne et al. 2013).
  • domain assumption Rapid initial spin P_s=5 h
    Section 2 sets the initial spin; Section 4 says the result assumes a rapid rotator. This assumption selects outward migration and is not varied.
  • domain assumption Constant planetary radius
    Planet radius is fixed at 2.61 R_Earth (Benneke et al. 2019) throughout the integration; radius evolution is neglected.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Can Moons Exist around the Habitable-zone Planet K2-18b?." pith.science (2026). https://pith.science/paper/2W4HB5PI

@misc{pith2026250711594,
  author       = {Pith},
  title        = {Pith review of: Can Moons Exist around the Habitable-zone Planet K2-18b?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2W4HB5PI}},
  note         = {Machine review of arXiv:2507.11594}
}
read the original abstract

K2-18b closely orbits a nearby M3 dwarf within its habitable zone, where this planet could be either a super-Earth or a mini-Neptune. Recent studies using transit spectroscopy suggest that it is Hycean in nature, but this classification is currently controversial. We use the N-body integrator rebound and its extension library reboundx to investigate the possibility of exomoons around K2-18b. Due to tidal interactions that induce outward migration, we find that any moons would be extremely unlikely. If formed, their lifetimes would be relatively short, not exceeding 10 Myr assuming Earth-like or Neptune-like tidal parameters for K2-18b. Recent studies estimate the stellar (and system) lifetime as 3 Gyr, which is significantly longer than the tidal migration timescale. We show that exomoons are unlikely to survive around K2-18b due to rapid tidal-driven migration, casting doubt on moon-based habitability scenarios for short-period M-dwarf planets in general.

Figures

Figures reproduced from arXiv: 2507.11594 by the authors.

Figure 1
Figure 1. Logarithm of exomoon lifetime (log10 (𝑡max ); color coded) from stability simulations that vary a host planet’s mass, tidal constant time-lag, 𝜏p, and initial eccentricity while using Earth-like parameters for the 𝑘2 Love number and moment of inertia constant, 𝐶. 7.5 8.0 8.5 9.0 9.5 Mp (M ) 10 100 p 698 0.12 0.20 0.28 0.12 0.20 0.28 e p 0.12 0.20 0.28 4.0 4.5 5.0 5.5 6.0 6.5 7.0 lo g 1 0 ( t m a x ) 0.12 0.20 0.28 0… view at source ↗
Figure 2
Figure 2. Same as [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Median log10 (𝑡max ) values with 1𝜎 error bars over the range of 𝑀p values (rows in Figs. 1 and 2) for the (a) Earth-like and (b) Neptune-like results. Orange lines represent samples using Markov Chain Monte Carlo (MCMC) methods from emcee. Black, red, and blue points represent 𝜏p values of 698, 100, and 10 s, respectively. Piro A. L., 2018, AJ, 156, 54 Quarles B., Musielak Z. E., Cuntz M., 2012, ApJ, 750, 14 Quarle… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 14 canonical work pages

  1. [1]

    Barnes R., 2017, @doi [Celest. Mech. Dyn. Astron.] 10.1007/s10569-017-9783-7 , https://ui.adsabs.harvard.edu/abs/2017CeMDA.129..509B 129, 509

    doi:10.1007/s10569-017-9783-7 2017

  2. [2]

    W., O’Brien D

    Barnes J. W., O’Brien D. P., 2002, @doi [ ] 10.1086/341477 , 575, 1087

    doi:10.1086/341477 2002

  3. [3]

    Benneke B., et al., 2019, @doi [ ] 10.3847/2041-8213/ab59dc , https://ui.adsabs.harvard.edu/abs/2019ApJ...887L..14B 887, L14

    doi:10.3847/2041-8213/ab59dc 2019

  4. [4]

    N., Leconte J., Hersant F., Correia A

    Bolmont E., Raymond S. N., Leconte J., Hersant F., Correia A. C. M., 2015, @doi [A&A] 10.1051/0004-6361/201525909 , 583, A116

    work page doi:10.1051/0004-6361/201525909 2015

  5. [5]

    Cloutier R., et al., 2019, @doi [ ] 10.1051/0004-6361/201833995 , https://ui.adsabs.harvard.edu/abs/2019A&A...621A..49C 621, A49

    doi:10.1051/0004-6361/201833995 2019

  6. [6]

    F., 2016, @doi [ ] 10.3847/0004-637X/827/1/79 , https://ui.adsabs.harvard.edu/abs/2016ApJ...827...79C 827, 79

    Cuntz M., Guinan E. F., 2016, @doi [ ] 10.3847/0004-637X/827/1/79 , https://ui.adsabs.harvard.edu/abs/2016ApJ...827...79C 827, 79

    doi:10.3847/0004-637x/827/1/79 2016

  7. [7]

    P., Kiseleva L

    Eggleton P. P., Kiseleva L. G., Hut P., 1998, @doi [ ] 10.1086/305670 , https://ui.adsabs.harvard.edu/abs/1998ApJ...499..853E 499, 853

    doi:10.1086/305670 1998

  8. [8]

    W., Lang D., Goodman J., 2013, @doi [ ] 10.1086/670067 , https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F 125, 306

    Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, @doi [ ] 10.1086/670067 , https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F 125, 306

    doi:10.1086/670067 2013

Show all 44 references
  1. [9]

    France K., et al., 2013, @doi [ ] 10.1088/0004-637X/763/2/149 , https://ui.adsabs.harvard.edu/abs/2013ApJ...763..149F 763, 149

    2013 doi

  2. [10]

    Gaia Collaboration et al., 2023, @doi [ ] 10.1051/0004-6361/202243940 , https://ui.adsabs.harvard.edu/abs/2023A&A...674A...1G 674, A1

    2023 doi

  3. [11]

    Goodman J., Weare J., 2010, @doi [Comm. App. Math. Com. Sc.] 10.2140/camcos.2010.5.65 , https://ui.adsabs.harvard.edu/abs/2010CAMCS...5...65G 5, 65

    2010 doi

  4. [12]

    Heller R., et al., 2014, @doi [Astrobiology] 10.1089/ast.2014.1147 , https://ui.adsabs.harvard.edu/abs/2014AsBio..14..798H 14, 798

    2014

  5. [13]

    Hut P., 1981, , https://ui.adsabs.harvard.edu/abs/1981A&A....99..126H 99, 126

    1981

  6. [14]

    Jagtap O., Quarles B., Cuntz M., 2021, @doi [ ] 10.1017/pasa.2021.52 , https://ui.adsabs.harvard.edu/abs/2021PASA...38...59J 38, e059

    2021 doi

  7. [15]

    Kaltenegger L., 2010, @doi [ ] 10.1088/2041-8205/712/2/L125 , https://ui.adsabs.harvard.edu/abs/2010ApJ...712L.125K 712, L125

    2010 doi

  8. [16]

    M., Nesvorn \'y D., Buchhave L

    Kipping D. M., Nesvorn \'y D., Buchhave L. A., Hartman J., Bakos G. \'A ., Schmitt A. R., 2014, @doi [ ] 10.1088/0004-637X/784/1/28 , https://ui.adsabs.harvard.edu/abs/2014ApJ...784...28K 784, 28

    2014 doi

  9. [17]

    Kokubo E., Genda H., 2010, @doi [ ] 10.1088/2041-8205/714/1/L21 , https://ui.adsabs.harvard.edu/abs/2010ApJ...714L..21K 714, L21

    2010 doi

  10. [18]

    J., Barnes J

    Lissauer J. J., Barnes J. W., Chambers J. E., 2012, @doi [ ] 10.1016/j.icarus.2011.10.013 , https://ui.adsabs.harvard.edu/abs/2012Icar..217...77L 217, 77

    2012 doi

  11. [19]

    C., Laughlin G., 2023, @doi [ ] 10.3847/1538-4357/acc06d , https://ui.adsabs.harvard.edu/abs/2023ApJ...948...41L 948, 41

    Lu T., Rein H., Tamayo D., Hadden S., Mardling R., Millholland S. C., Laughlin G., 2023, @doi [ ] 10.3847/1538-4357/acc06d , https://ui.adsabs.harvard.edu/abs/2023ApJ...948...41L 948, 41

    2023 doi

  12. [20]

    M., Rein H., 2024, @doi [ ] 10.1093/mnras/stae1982 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.533.3708L 533, 3708

    Lu T., Hernandez D. M., Rein H., 2024, @doi [ ] 10.1093/mnras/stae1982 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.533.3708L 533, 3708

    2024 doi

  13. [21]

    L., Samra D., Steinrueck M

    Luque R., Piaulet-Ghorayeb C., Radica M., Xue Q., Zhang M., Bean J. L., Samra D., Steinrueck M. E., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2505.13407 , https://ui.adsabs.harvard.edu/abs/2025arXiv250513407L p. arXiv:2505.13407

    2025 doi arXiv

  14. [22]

    Madhusudhan N., Sarkar S., Constantinou S., Holmberg M., Piette A. A. A., Moses J. I., 2023, @doi [ ] 10.3847/2041-8213/acf577 , https://ui.adsabs.harvard.edu/abs/2023ApJ...956L..13M 956, L13

    2023 doi

  15. [23]

    Madhusudhan N., Constantinou S., Holmberg M., Sarkar S., Piette A. A. A., Moses J. I., 2025, @doi [ ] 10.3847/2041-8213/adc1c8 , https://ui.adsabs.harvard.edu/abs/2025ApJ...983L..40M 983, L40

    2025 doi

  16. [24]

    T., et al., 2015, @doi [ ] 10.1088/0004-637X/809/1/25 , https://ui.adsabs.harvard.edu/abs/2015ApJ...809...25M 809, 25

    Montet B. T., et al., 2015, @doi [ ] 10.1088/0004-637X/809/1/25 , https://ui.adsabs.harvard.edu/abs/2015ApJ...809...25M 809, 25

    2015 doi

  17. [25]

    D., Dermott S

    Murray C. D., Dermott S. F., 1999, Solar System Dynamics , @doi 10.1017/CBO9781139174817

    1999 doi

  18. [26]

    Neron de Surgy O., Laskar J., 1997, , https://ui.adsabs.harvard.edu/abs/1997A&A...318..975N 318, 975

    1997

  19. [27]

    L., Charbonneau D., Cherubim C., Garcia-Mejia J., 2024, A Search for Exoplanet Satellites that are the Same Size as the Earth's Moon , JWST Proposal

    Pass E., Bean J. L., Charbonneau D., Cherubim C., Garcia-Mejia J., 2024, A Search for Exoplanet Satellites that are the Same Size as the Earth's Moon , JWST Proposal. Cycle 3, ID. \#6193

    2024

  20. [28]

    D., Quarles B., Cuntz M., 2025, @doi [ ] 10.1093/mnras/staf131 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.537.2291P 537, 2291

    Patel S. D., Quarles B., Cuntz M., 2025, @doi [ ] 10.1093/mnras/staf131 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.537.2291P 537, 2291

    2025 doi

  21. [29]

    J., Deck K

    Payne M. J., Deck K. M., Holman M. J., Perets H. B., 2013, @doi [ ] 10.1088/2041-8205/775/2/L44 , https://ui.adsabs.harvard.edu/abs/2013ApJ...775L..44P 775, L44

    2013 doi

  22. [30]

    L., 2018, @doi [ ] 10.3847/1538-3881/aaca38 , https://ui.adsabs.harvard.edu/abs/2018AJ....156...54P 156, 54

    Piro A. L., 2018, @doi [ ] 10.3847/1538-3881/aaca38 , https://ui.adsabs.harvard.edu/abs/2018AJ....156...54P 156, 54

    2018 doi

  23. [31]

    E., Cuntz M., 2012, @doi [ ] 10.1088/0004-637X/750/1/14 , https://ui.adsabs.harvard.edu/abs/2012ApJ...750...14Q 750, 14

    Quarles B., Musielak Z. E., Cuntz M., 2012, @doi [ ] 10.1088/0004-637X/750/1/14 , https://ui.adsabs.harvard.edu/abs/2012ApJ...750...14Q 750, 14

    2012 doi

  24. [32]

    J., 2019, @doi [ ] 10.3847/1538-4357/ab46b5 , https://ui.adsabs.harvard.edu/abs/2019ApJ...886...56Q 886, 56

    Quarles B., Li G., Lissauer J. J., 2019, @doi [ ] 10.3847/1538-4357/ab46b5 , https://ui.adsabs.harvard.edu/abs/2019ApJ...886...56Q 886, 56

    2019 doi

  25. [33]

    J., 2022, @doi [ ] 10.1093/mnras/stab3179 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.2736Q 509, 2736

    Quarles B., Li G., Lissauer J. J., 2022, @doi [ ] 10.1093/mnras/stab3179 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.2736Q 509, 2736

    2022 doi

  26. [34]

    F., 2012, @doi [ ] 10.1051/0004-6361/201118085 , https://ui.adsabs.harvard.edu/abs/2012A&A...537A.128R 537, A128

    Rein H., Liu S. F., 2012, @doi [ ] 10.1051/0004-6361/201118085 , https://ui.adsabs.harvard.edu/abs/2012A&A...537A.128R 537, A128

    2012 doi

  27. [35]

    S., 2015, @doi [ ] 10.1093/mnras/stu2164 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1424R 446, 1424

    Rein H., Spiegel D. S., 2015, @doi [ ] 10.1093/mnras/stu2164 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1424R 446, 1424

    2015 doi

  28. [36]

    E., Cuntz M., 2020, @doi [ ] 10.3847/1538-3881/ab89a7 , https://ui.adsabs.harvard.edu/abs/2020AJ....159..260R 159, 260

    Rosario-Franco M., Quarles B., Musielak Z. E., Cuntz M., 2020, @doi [ ] 10.3847/1538-3881/ab89a7 , https://ui.adsabs.harvard.edu/abs/2020AJ....159..260R 159, 260

    2020 doi

  29. [37]

    Sairam L., Madhusudhan N., 2025, @doi [MNRAS] 10.1093/mnras/staf528 , 539, 1299

    2025 doi

  30. [38]

    Sarkis P., et al., 2018, @doi [ ] 10.3847/1538-3881/aac108 , https://ui.adsabs.harvard.edu/abs/2018AJ....155..257S 155, 257

    2018 doi

  31. [39]

    W., O'Brien D

    Sasaki T., Barnes J. W., O'Brien D. P., 2012, @doi [ ] 10.1088/0004-637X/754/1/51 , https://ui.adsabs.harvard.edu/abs/2012ApJ...754...51S 754, 51

    2012 doi

  32. [40]

    Takaoka K., Kuwahara A., Ida S., Kurokawa H., 2023, @doi [ ] 10.1051/0004-6361/202345915 , https://ui.adsabs.harvard.edu/abs/2023A&A...674A.193T 674, A193

    2023 doi

  33. [41]

    M., 2020, @doi [ ] 10.1093/mnras/stz2870 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.2885T 491, 2885

    Tamayo D., Rein H., Shi P., Hernandez D. M., 2020, @doi [ ] 10.1093/mnras/stz2870 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.2885T 491, 2885

    2020 doi

  34. [42]

    arXiv:2504.21788

    Welbanks L., et al., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2504.21788 , https://ui.adsabs.harvard.edu/abs/2025arXiv250421788W p. arXiv:2504.21788

    2025 doi

  35. [43]

    Youngblood A., et al., 2017, @doi [ ] 10.3847/1538-4357/aa76dd , https://ui.adsabs.harvard.edu/abs/2017ApJ...843...31Y 843, 31

    2017 doi

  36. [44]

    write newline

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

Pith tools

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