Searching for Hot Water World Candidates with CHEOPS: Refining the radii and analysing the internal structures and atmospheric lifetimes of TOI-238 b and TOI-1685 b

A. Bonfanti; A. Brandeker; A.C.M. Correia; A. Collier Cameron; A. Deline; A. Derekas; A. Erikson; A.E. Simon; A. Fortier; A. Heitzmann

REVIEW 3 major objections 3 minor 173 references

Searching for Hot Water World Candidates with CHEOPS: Refining the radii and analysing the internal structures and atmospheric lifetimes of TOI-238 b and TOI-1685 b

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

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Pith's one-line read TOI-238 b lies inside the hot water world triangle of mass-radius space at the 1σ level, and its water-dominated atmosphere could have survived to the present age, whereas TOI-1685 b is consistent with a bare core.

desk verdict Solid CHEOPS follow-up and a useful new selection criterion, but the water-world claim for TOI-238 b rests on a heating efficiency that the paper's own models suggest is not constant. read the letter →

arxiv 2502.07887 v1 pith:LIQF3Q64 submitted 2025-02-11 astro-ph.EP

J. A. Egger , D. Kubyshkina , Y. Alibert , H.P. Osborn , A. Bonfanti , T.G. Wilson , A. Brandeker , M.N. Günther

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M. Lendl D. Kitzmann L. Fossati C. Mordasini S.G. Sousa V. Adibekyan M. Fridlund C. Pezzotti D. Gandolfi S. Ulmer-Moll R. Alonso T. Bárczy D. Barrado Navascues S.C. Barros W. Baumjohann W. Benz N. Billot L. Borsato C. Broeg A. Collier Cameron A.C.M. Correia Sz. Csizmadia P.E. Cubillos M.B. Davies M. Deleuil A. Deline O.D.S. Demangeon B.-O. Demory A. Derekas B. Edwards D. Ehrenreich A. Erikson A. Fortier K. Gazeas M. Gillon M. Güdel A. Heitzmann Ch. Helling K.G. Isaak L. Kiss J. Korth K.W.F. Lam J. Laskar A. Lecavelier des Etangs A. Luntzer R. Luque D. Magrin P.F.L. Maxted B. Merín M. Munari V. Nascimbeni G. Olofsson R. Ottensamer I. Pagano E. Pallé G. Peter D. Piazza G. Piotto D. Pollacco D. Queloz R. Ragazzoni N. Rando H. Rauer I. Ribas N.C. Santos G. Scandariato D. Ségransan A.E. Simon A.M.S. Smith R. Southworth M. Stalport S. Sulis M. Gy. Szabó S. Udry V. Van Grootel J. Venturini E. Villaver N.A. Walton S. Wolf D. Wolter

This is my paper · ORCID

classification astro-ph.EP

keywords hotwaterworldsexoplanetcompositionmass-radiusdegeneracyatmosphericescapeplanetaryinteriorsTOI-238bTOI-1685transitphotometry

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

For close-in exoplanets, a low-mass hydrogen/helium envelope is quickly eroded by the host star's high-energy radiation, so there are triangular regions of the mass-radius diagram where a planet can only exist if it carries heavier volatiles, most plausibly water. The paper refines the measured radii of two such candidates with high-precision space photometry and combines them with published radial-velocity masses to test whether either planet falls inside its 'Hot Water World triangle.' It finds that TOI-238 b, at $1.559\pm0.047\,R_\oplus$ and $3.37\pm0.49\,M_\oplus$, sits inside its triangle at the $1\sigma$ level: a pure H/He envelope would have evaporated within 0.4–1.3 Myr, while a water-dominated atmosphere could survive to the system's current age. For TOI-1685 b, the refined radius of $1.421\pm0.060\,R_\oplus$ places it below the pure-silicate mass-radius curve, so a bare rocky core cannot be ruled out. If these conclusions hold, TOI-238 b is a strong target for atmospheric follow-up, and the mass-radius degeneracy that usually hides an exoplanet's composition is partially broken by evaporation physics alone.

What carries the argument

The load-bearing object is the Hot Water World triangle: the region in the mass-radius plane between the most extended bare-core model (iron-free silicate) and the most compact planet that still fits a 1% hydrogen/helium envelope, evaluated at a fixed equilibrium temperature and intrinsic luminosity. Inside this region a pure H/He atmosphere is not a viable explanation, so the planet must hold heavier volatiles such as water. The argument is carried by three complementary tools: the mass-radius exclusion geometry; an analytical energy-limited escape formula with a heating efficiency parameter $\eta$ whose plausible range is 0.01–0.15 and whose value is calibrated to about 0.05 for water-rich atmospheres using hydrodynamic escape simulations; and a neural-network-accelerated interior-structure inversion that maps measured mass and radius onto posterior distributions for the mass fractions of an iron core, silicate mantle, and volatile envelope.

What would settle it

A high-precision near-infrared transmission spectrum of TOI-238 b would settle the matter: the paper's models predict water absorption bands exceeding 100 ppm in transit depth for water mass fractions of 0.1 and 0.5, while a nearly flat spectrum at the level of about 20 ppm would contradict a detectable water layer and leave the water-world claim unsupported.

Watch

Extended reading notes

Core claim

The paper's central discovery is that the mass-radius degeneracy for close-in planets can be partially lifted by evaporation physics, and that applying this criterion to two targets of the photometric follow-up programme separates them cleanly. The 'Hot Water World triangle' for a given equilibrium temperature is bounded below by the lowest-density bare core (an iron-free rocky composition) and above by the most compact planet that could still carry a 1% H/He envelope (a Mercury-like core); because H/He envelopes below roughly 1% mass fraction evaporate within a few million years under strong irradiation, no purely rocky or H/He-enveloped planet should occupy the triangle. TOI-238 b falls inside this exclusion zone, meaning its low mean density requires a volatile layer heavier than H/He; the evaporation modelling shows hydrogen would be lost in under 1.3 Myr while a steam atmosphere could persist to the present age, making it a hot water world candidate. TOI-1685 b, by contrast, lies below the iron-free bare-rock model, so its density is compatible with a bare, rocky core even though a water-rich envelope is also allowed by the interior and evaporation analysis.

Load-bearing premise

The conclusion that a water atmosphere survives on TOI-238 b rests on the assumed heating efficiency of X-ray and extreme-ultraviolet irradiation on steam atmospheres: if the time-averaged efficiency is below the calibrated value of about 0.05, or if the XUV absorption radius is more compact than assumed, a 50% water envelope would be completely lost and the planet could be a bare core.

Editorial extensions

If this is right

TOI-238 b becomes a priority transmission-spectroscopy target: if its envelope holds water at mass fractions of 0.1–0.5, the paper's forward spectra predict water absorption bands with transit-depth variations of roughly 100 ppm or more.
Any atmosphere detected on TOI-238 b must have a high mean molecular weight, because a solar-composition H/He envelope cannot survive longer than about a million years under the assumed stellar XUV history.
TOI-1685 b should not be counted as a securely established water world in demographic samples, since its radius below the pure-silicate model makes a bare rocky interior the conservative interpretation.
Only about ten well-characterised planets currently lie fully inside hot water world triangles at the $2\sigma$ level, so radius-refinement follow-up can substantially enlarge the set of planets that definitely require heavy volatiles.
If many close-in planets are confirmed inside these triangles, it would support formation models in which planets migrate inward from beyond the ice line, which predict exactly such water-rich close-in worlds.

Reading between the lines

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

The triangle criterion is a necessary-condition test rather than a water detector: a planet inside the triangle could also be explained by envelopes dominated by CO$_2$, CO, or CH$_4$, and the paper itself notes that only atmospheric follow-up can break that remaining degeneracy.
The literature disagreement on TOI-238 b's radius shows how sensitive triangle membership is: with the smaller published radius the planet would lie outside the triangle entirely, so other candidate water worlds with conflicting radius measurements should be re-examined before being classified.
If TOI-238 b does retain a steam atmosphere, it would provide a rare calibration point for energy-limited evaporation of water-rich envelopes, but the paper states that self-consistently coupling the hydrodynamic escape model into the evolution calculation is not currently possible, leaving the surviving-water conclusion tied to the assumed heating efficiency.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

You should know two things before reading this. First, it is a useful observational paper with a smart selection criterion: the "Hot Water World triangle" in mass-radius space, where close-in planets must contain heavier volatiles because thin H/He envelopes evaporate. Second, the splashy conclusion that TOI-238 b is a hot water world candidate is real, but it hinges on a single heating efficiency η=0.05 applied over the planet's whole history, and the paper's own hydro models show that η should vary with atmospheric water fraction. That soft spot is worth taking seriously, but it doesn't sink the paper.

What's genuinely new: CHEOPS photometry for two planets, careful joint fits with TESS using public tools, updated radii that resolve a literature discrepancy for TOI-238 b (their radius agrees with Mistry et al. 2024, not Suárez Mascareño et al. 2024), and a demographic census of known planets inside the triangles. The paper is transparent about model limitations: fixed intrinsic luminosity, the 1% envelope cutoff, and the constant-η assumption are all acknowledged in the text. The interior structure runs with plaNETic and the evaporation analysis are clearly described.

The soft spots are mostly in the evaporation physics. The stress-test note is right: the CHAIN simulations show mass-loss rates that are non-monotonic in water fraction—higher than pure H/He at Z=10–30% and only ~3× lower at Z=95%. The back-evolution treats the envelope as pure water throughout, so early H/He-rich phases that would be stripped faster aren't captured. Their own Figure 9 shows f_atm0 rising steeply with η. If early η was closer to 0.15 than to 0.05, the initial water fraction needed to survive could exceed their 50% cap, meaning the planet could be a bare core. They also don't propagate the systematic uncertainty in the triangle boundaries (intrinsic luminosity, envelope fraction) into the "1σ inside" claim. None of this is hidden; they state in Section 4.1 that self-consistent coupling is not currently possible, but the abstract's "likely" is stronger than the evidence supports.

Who's this for? Exoplanet observers and theorists interested in close-in small-planet compositions and JWST target prioritization. The photometric results will be useful regardless of the water-world interpretation.

Recommendation: send it to peer review. It deserves a serious referee. The main revision should be a sensitivity analysis that allows η to vary with time or water fraction, and a more cautious wording of the TOI-238 b conclusion.

Referee Report

3 major / 3 minor

Summary. The paper introduces 'Hot Water World triangles' in mass-radius space for close-in planets, where low-mass H/He envelopes are expected to be unstable and heavier volatiles are required, and it presents a demographic census of known planets in these regions. It then reports CHEOPS photometry of TOI-238 b and TOI-1685 b, jointly fitted with TESS photometry and published radial velocities. For TOI-238 b the derived radius is 1.559 +/- 0.047 R_Earth and mass 3.37 +/- 0.49 M_Earth, placing it inside its Hot Water World triangle at the 1 sigma level; the paper argues that a pure H/He atmosphere would be lost in 0.4-1.3 Myr, while a water-dominated atmosphere could survive to the current age, making TOI-238 b a hot water world candidate. For TOI-1685 b the derived radius is 1.421 +/- 0.060 R_Earth and mass 3.07 +/- 0.34 M_Earth, placing it below the pure-silicate bare-core model, so a bare core cannot be ruled out. The paper also presents interior structure modelling with plaNETic, atmospheric escape simulations with CHAIN, synthetic JWST spectra, and comparisons with the NGPPS formation population.

Significance. The photometric analysis is careful and addresses long-standing literature discrepancies, and the paper is explicit about many of its model limitations. If the water-world status of TOI-238 b is confirmed, the planet would be an important atmospheric follow-up target, and the Hot Water World triangle framework is a useful target-selection tool. Strengths include the use of public codes (chexoplanet, plaNETic, FastChem, BeAR), the provision of detrended light curves, a systematic treatment of interior-structure priors, and the direct statement that self-consistent coupling of the hydrodynamic escape model into the evolution calculation is not currently possible. However, the central claim that a water-dominated atmosphere survives depends on escape-model parameters that are not fully propagated, and one calibration input in the hydrodynamic simulations is inconsistent with the fitted orbit.

major comments (3)

[§3.1.6] The CHAIN hydrodynamic simulations that motivate the adopted heating efficiency eta=0.05 are run for a semi-major axis a=0.02556 AU, whereas the joint fit in Table 3 gives a=0.02120 +/- 0.00038 AU for TOI-238 b. Because the orbital distance sets the incident XUV flux, this means the calibration is not performed for the actual planet. The derived heating efficiency should be re-evaluated at the fitted semi-major axis, or the sensitivity of the water-survival conclusion to this inconsistency should be quantified.
[§3.1.5 and §3.1.6] The back-evolution that yields the required initial water fractions treats the envelope as pure H2O over the entire lifetime and keeps eta=0.05 constant. CHAIN's own Figure 10 shows that the escape rate is non-monotonic in water fraction: at Z=10-30% the atmosphere is lost faster than a pure H/He envelope, so an early H/He-rich phase would correspond to a substantially higher effective heating efficiency than eta=0.05. Since the paper states in Section 3.1.6 that self-consistent coupling is not currently possible, the conclusion that a water-dominated atmosphere 'would have survived' should be presented as conditional on this assumption, with a quantitative test (e.g., an early phase at eta=0.15 with a fast-rotator XUV history) rather than as the main result.
[§2.1 and §4.1] The statement that TOI-238 b lies inside its Hot Water World triangle at the 1 sigma level treats the triangle boundaries as fixed. Section 4.1 reports that the upper boundary depends on the assumed intrinsic luminosity L_int=10^21 erg/s and shifts by up to 13-17% for L_int between 10^20 and 10^22 erg/s. This model-induced boundary uncertainty is comparable to the 3% radius precision and is not propagated into the membership claim. The paper should either quantify the boundary shift at the mass and equilibrium temperature of TOI-238 b or soften the 1 sigma membership statement accordingly.

minor comments (3)

[Figure 8 caption] The caption states 'the luminosity of 10^21 erg/s/cm2'; the units should be erg/s, not erg/s/cm2.
[Table 3] The row 'Impact parameter, b' appears twice in the TOI-238 b column; one duplicate entry should be removed.
[§3.1.5, Eq. (1)] The tidal correction factor K is introduced but its numerical evaluation is never specified; please state explicitly how K is computed.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the CHEOPS radius measurements and the H/He evaporation lifetimes are derived from independent data and external evaporation models; the water-survival inference depends on a calibrated heating efficiency but does not reduce to its inputs by construction.

full rationale

The paper's central measurements (CHEOPS/TESS photometry, adopted RV semi-amplitudes, and stellar parameters) are independent of the models used for interpretation. The Hot Water World triangle boundaries are defined using BICEPS mass-radius models and the Owen & Wu (2017) evaporation criterion, both external to this work, and the claim that TOI-238 b lies in the triangle is a data-driven classification. The pure H/He lifetime calculation (0.4-1.3 Myr) uses the Kubyshkina et al. (2018) grid and MESA, not the triangle definition, so it is an independent check. The water-survival inference does use the energy-limited formula with η=0.05, which is calibrated to the authors' CHAIN hydrodynamic simulations of the present-day planet. However, this is a model calibration, not a circular reduction: the survival conclusion (required initial water fraction below 50%) is not equal to the calibrated present-day mass-loss rate, and the paper explicitly explores the full η=0.01-0.15 range and fast/slow rotator cases, showing the conclusion is conditional. The paper also states that self-consistent coupling of hydrodynamics into the evolution is not currently possible, an honest limitation. Self-citations to BICEPS, plaNETic, CHAIN, Mors, and NGPPS are numerous, but they support model inputs rather than substitute for the measurement, and no uniqueness theorem or definitional identity forces the central claim.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The central claim rests on several model choices: an assumed H/He loss threshold of 1%, fixed intrinsic luminosity for triangle generation, an energy-limited escape formula with a free heating efficiency calibrated to the authors' own hydrodynamic runs, and layered interior structure models with formation-scenario priors. None of these are new physical entities; they are standard tools used with stated assumptions. The number of free parameters is moderate and the paper runs sensitivity tests over most of them.

free parameters (7)

Heating efficiency eta for energy-limited water escape = 0.01 to 0.15; preferred 0.05
Used in Eq. (1) for water atmospheric mass loss. The paper states eta is meant to fit the energy-limited rates to more sophisticated models and that its own CHAIN hydrodynamic simulations favor 0.05. The water survival conclusion depends on this choice.
Intrinsic luminosity L_int for HWW triangle BICEPS models = 1e21 erg/s (tests over 1e20 to 1e22 erg/s)
Mass-radius envelope models used to draw triangle boundaries assume a fixed intrinsic luminosity of 2.5 Lsun. Section 4.1 shows the upper boundary shifts by up to 13-17% under alternative luminosities.
H/He envelope mass fraction cutoff for triangle upper boundary = 1%
The triangle is bounded by a core plus 1% H/He envelope model, based on Owen & Wu (2017) that lower fractions are lost quickly. The exact threshold is planet-specific; the paper runs detailed evaporation for the two targets.
Photospheric pressure P_photo for XUV absorption radius = 100 mbar
Used in Eq. (2) to compute Reff for water escape. The paper says the value has negligible influence, but it is a chosen input.
Mean molecular weight mu for Reff in water escape = 1.3 mH
For calculating Reff the paper adopts mu=1.3 mH instead of 18 mH, justified by CHAIN hydrodynamic simulations showing XUV heating at altitudes similar to H/He atmospheres. This strongly affects the evaporation rate.
Initial stellar rotation periods for XUV scenarios = TOI-238 slow rotator 15 d at 150 Myr; TOI-1685 9.6 d at 150 Myr; fast rotator 1 d
Stellar XUV evolution is the most uncertain input. The slow rotator maximizes atmospheric lifetime for H/He; for water, both slow and fast rotators are considered.
Water-poor interior prior envelope water fraction = Gaussian mean 0.5%, sigma 0.25%
In the inside-iceline formation scenario, the volatile layer water mass fraction is sampled from this narrow prior, which drives the posterior toward nearly pure H/He envelopes of order 1e-4 percent.

assumptions (8)

domain assumption Close-in H/He envelopes with mass fractions below about 1% are evaporated within a few Myr (Owen & Wu 2017; Lopez 2017; Jin & Mordasini 2018; Kubyshkina & Vidotto 2021).
This is the physical basis for the HWW triangle upper boundary. The paper uses the 1% model as a first cut and runs target-specific evaporation models.
domain assumption BICEPS mass-radius models correctly represent bare rocky cores, Earth-like and Mercury-like cores, 1% H/He envelopes, and steam envelopes at a given equilibrium temperature.
The triangle boundaries and plaNETic interior inference rely on the BICEPS forward model (Haldemann et al. 2024) for mapping composition to radius.
domain assumption The energy-limited escape formula with constant heating efficiency captures water-rich atmospheric escape over the planet's lifetime.
Equation (1) with a single eta is used to evolve water atmospheres backward in time. The paper cannot self-consistently couple the CHAIN hydrodynamic model into the evolution due to computational cost.
domain assumption Stellar XUV luminosity evolution is described by Mors and Johnstone et al. for slow and fast rotators.
XUV history drives the evaporation. The broad age of TOI-238 and unknown initial rotation create a spread of a factor of a few.
domain assumption The known exoplanet catalog used for the demographic study is complete enough for the quoted counts of planets inside the triangles.
The query from the PlanetS catalog has precision cuts (mass below 20%, radius below 5%) and may miss real members, as the paper notes for GJ 9827 d.
domain assumption The planets' orbital semi-major axes have not changed since disk dispersal.
Used for evaporation evolution; the paper assumes the median semi-major axis and no migration, which could change irradiation history.
domain assumption Primordial water mass fractions above 50% are unlikely.
The backward evolution is truncated at a water mass fraction of 50%, citing formation model predictions. This truncation limits inferred initial water fractions.
domain assumption Interior model layering with iron core, silicate mantle, and volatile layer, with no water dissolution into the mantle, is adequate.
plaNETic and BICEPS assume a layered structure; the paper acknowledges that dissolved water reservoirs are not included.

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Cite this review

Pith. "Pith review of Searching for Hot Water World Candidates with CHEOPS: Refining the radii and analysing the internal structures and atmospheric lifetimes of TOI-238 b and TOI-1685 b." pith.science (2026). https://pith.science/paper/LIQF3Q64

@misc{pith2026250207887,
  author       = {Pith},
  title        = {Pith review of: Searching for Hot Water World Candidates with CHEOPS: Refining the radii and analysing the internal structures and atmospheric lifetimes of TOI-238 b and TOI-1685 b},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LIQF3Q64}},
  note         = {Machine review of arXiv:2502.07887}
}

read the original abstract

Studying the composition of exoplanets is one of the most promising approaches to observationally constrain planet formation and evolution processes. However, this endeavour is complicated for small exoplanets by the fact that a wide range of compositions is compatible with their bulk properties. To overcome this issue, we identify triangular regions in the mass-radius space where part of this degeneracy is lifted for close-in planets, since low-mass H/He envelopes would not be stable due to high-energy stellar irradiation. Planets in these Hot Water World triangles need to contain at least some heavier volatiles and are therefore interesting targets for atmospheric follow-up observations. We perform a demographic study to show that only few well-characterised planets in these regions are currently known and introduce our CHEOPS GTO programme aimed at identifying more of these potential hot water worlds. Here, we present CHEOPS observations for the first two targets of our programme, TOI-238 b and TOI-1685 b. Combined with TESS photometry and published RVs, we use the precise radii and masses of both planets to study their location relative to the corresponding Hot Water World triangles, perform an interior structure analysis and study the lifetimes of H/He and water-dominated atmospheres under these conditions. We find that TOI-238 b lies, at the 1-sigma level, inside the corresponding triangle. While a pure H/He atmosphere would have evaporated after 0.4-1.3 Myr, it is likely that a water-dominated atmosphere would have survived until the current age of the system, which makes TOI-238 b a promising hot water world candidate. Conversely, TOI-1685 b lies below the mass-radius model for a pure silicate planet, meaning that even though a water-dominated atmosphere would be compatible both with our internal structure and evaporation analysis, we cannot rule out the planet to be a bare core.

Figures

Figures reproduced from arXiv: 2502.07887 by the authors.

**Figure 1.** Definition of the Hot Water World triangles (light blue) in the mass-radius space. The left panel shows mass-radius models generated using the BICEPS forward model (Haldemann et al. 2024), for a fixed equilibrium temperature of 900 K. We generated models for three different core compositions, an iron-less, purely rocky core (in purple), an Earth-like core (33% inner iron core, 67% silicate mantle, in pink), and a Me… view at source ↗

**Figure 2.** Currently known exoplanets falling inside the Hot Water World triangles. Shown are confirmed planets listed in the PlanetS exoplanet catalogue (Parc et al. 2024; Otegi et al. 2020), with a precision in mass of at least 20% and at least 5% in radius, with equilibrium temperatures of more than 600 K. The depicted mass-radius curves for bare cores are the same as in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Mass-radius diagrams for TOI-561 b (left), TOI-238 b (middle) and TOI-1685 b (right), showcasing the corresponding Hot Water World triangles. The mass-radius models are the same as in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (12 more)

**Figure 4.** Figure 4: Detrended TESS (top row) and CHEOPS (bottom row) light curves for TOI-238 b (left) and TOI-1685 b (right), phase-folded to the orbital periods of the respective planets. All panels show relative flux normalised to 0. can be found in Table A.1, while the undetrended lig…

**Figure 5.** Figure 5: Comparison of the different values in the literature for the stellar radius, radius ratio and planetary radius of TOI-238 b. to reduce contamination by background stars, cosmic ray hits, or hot pixels. Additionally, chexoplanet models the impact of systematics by mode…

**Figure 6.** Figure 6: Results of the internal structure analysis for TOI-238 b. Depicted are the posterior distributions for the mass fractions of the inner core, the mantle and the volatile layer with respect to the whole planet, as well as the water mass fraction in the volatile layer, Ze…

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: The primordial atmospheric (water vapour) mass fraction of TOI-238 b against present-day mass and radius of the planet, as given by the observational constraints. Four panels correspond to different values of the heating efficiency parameter η: 0.01 (a), 0.05 (b), 0.1 …

**Figure 10.** Figure 10: Atmospheric mass loss rates of TOI-238 b in dependence on the water mass fraction in the atmosphere. 0 0.2 0.4 0.6 0.8 1 zH2O 1.5 2 2.5 3 3.5 4 4.5 5 R/Rpl R s RHion [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

**Figure 11.** Figure 11: Radial location R of the sonic radius RS and ionisation front RHion (maximum of the H+ number density) in the upper atmosphere of TOI-238 b in dependence on the water mass fraction in the atmosphere. of characteristic distances) and the heating is significant up to th…

**Figure 12.** Figure 12: Comparison of the different values in the literature for the stellar radius, radius ratio and planetary radius of TOI-1685 b. differences in both the stellar radius as well as the radius ratio, as is visualised in [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]

**Figure 13.** Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]

**Figure 14.** Figure 14: Influence of choosing different values for the intrinsic luminosity of the planet on the upper boundary of the Hot Water World triangles, for a planetary equilibrium temperature of 1000 K (top, similar to the conditions of TOI-1685 b) and 1400 K (bottom, similar to …

**Figure 15.** Figure 15: Theoretical spectra of TOI-238 b for three water-rich cases with different water mass fractions ZH2O and one case with scaled solarelement abundances. For the latter case, Z refers to the masses of the metals in the element mixture. All spectra are normalised, such t…

**Figure 16.** Figure 16: Histograms of the water content of the planets in the synthetic NGPPS population for solar mass stars, generated using the Bern Model of planet formation and evolution. The top panel shows the water mass fraction with respect to the mass of the volatile envelope layer…

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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