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Potential Interior Structures and Habitability of Super-Earth Exoplanets LHS 1140 b, K2-18 b, TOI-1452 b and TOI-1468 c

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper argues that K2-18 b and TOI-1468 c are likely water worlds with thick ice layers, while TOI-1452 b and LHS 1140 b may have rocky surfaces, and that tidal heating alone cannot make them habitable.

desk verdict Useful comparative survey, but the headline classification is more assumption-dependent than the abstract admits. read the letter →

arxiv 2412.08476 v1 pith:GPGGQPVJ submitted 2024-12-11 astro-ph.EP astro-ph.SR

Mangesh Daspute , Amri Wandel , Ravi Kumar Kopparapu , Volker Perdelwitz , Jerusalem Tamirat Teklu , Lev Tal-Or This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords super-EarthexoplanetswaterworldsinteriorstructureBayesianinferencetidalheatinghabitablezoneM-dwarfstarsLHS1140b
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 classify the interiors of four nearby super-Earths, all within 40 parsecs and orbiting M-dwarf stars in the habitable zone. It claims that, assuming no or only thin atmospheres, the low-density pair K2-18 b and TOI-1468 c are most likely water worlds with thick water-ice layers, whereas TOI-1452 b and LHS 1140 b retain a real, though small, chance of having rocky surfaces. It also claims that tidal heating adds negligibly to the planets' heat budgets, so the only way they become warm enough for liquid water is through greenhouse heating, and that among the four, LHS 1140 b has the widest room for habitable conditions. The stakes are practical: these are prime targets for atmospheric follow-up, so knowing which planets have solid surfaces and moderate temperatures guides where to look for life.

What carries the argument

The argument runs on three coupled models. First, MAGRATHEA, an open-source interior solver with up-to-date equations of state, computes mass-radius-composition relations, and Bayesian inference with a Gaussian likelihood over measured mass and radius produces posterior probability distributions for core, mantle, and ice mass fractions, with the Valencia et al. formation constraints (MMF/IMF > 0.2346 and MMF/CMF > 0.5625) acting as priors that rule out tiny mantles. Second, a constant-quality-factor tidal heating formula converts each planet's eccentricity, radius, and tidal Love number into a heat flux that can be compared with instellation. Third, the Wandel (2018) analytical model of a tidally locked planet uses two parameters, an atmospheric heating factor H and a heat transport factor f, to give the surface temperature range and the biohabitable window. The combination lets the paper assign relative probabilities of rocky versus water-rich surfaces and then ask what atmospheric conditions would make each planet habitable.

What would settle it

Measure the tidal Love number k2 of K2-18 b through orbital-decay or transit-timing observations: a value implying a large core mass fraction would contradict the nearly pure-ice interior (IMF near 81%) that the paper's classification rests on. Alternatively, a JWST phase curve of LHS 1140 b revealing a thick H2 atmosphere, with strong day-night heat redistribution and spectral features, would falsify the thin-atmosphere rocky-surface scenario.

Watch

Extended reading notes

Core claim

The central discovery is a comparative Bayesian classification. With no atmosphere or a thin one, the posterior mass-fraction distributions for K2-18 b and TOI-1468 c are pushed to very high ice mass fractions; for K2-18 b, the formation constraints force the ice mass fraction near 81%, while LHS 1140 b and TOI-1452 b have nonzero probability of an ice mass fraction below 1%, leaving open a rocky surface. Tidal heating rates, computed with a constant quality factor model, are orders of magnitude below stellar instellation; even a five-fold upper limit raises K2-18 b's global mean temperature by only about 2 K. Using the one-dimensional locked-planet temperature model, the paper shows that only atmospheric greenhouse heating can move the planets' substellar or nightside temperatures into the liquid-water range, and that for thick, well-transporting atmospheres K2-18 b, TOI-1468 c, and TOI-1452 b would become too hot, whereas LHS 1140 b keeps a wider habitable margin.

Load-bearing premise

The whole classification assumes that the host stars' elemental abundances, taken as roughly solar, match the planets' bulk compositions, and that the Valencia formation limits on core-mantle-ice fractions apply to these worlds; if those priors are wrong, the posterior probabilities and the water-world versus rocky labels shift.

Editorial extensions

If this is right

  • K2-18 b and TOI-1468 c are unlikely to have surfaces available for a rocky biosphere if they lack thick atmospheres, so atmospheric follow-up should treat them as water-world candidates.
  • A thin H-He atmosphere raises the chance of a rocky surface for LHS 1140 b and TOI-1452 b, meaning that transmission spectroscopy that limits the hydrogen abundance also sharpens the interior classification.
  • Tidal heating is not a viable warming mechanism for these planets; any liquid water requires greenhouse warming, making atmospheric composition the decisive habitability factor.
  • For thick, well-mixed atmospheres, three of the four planets would be too hot for liquid water at the substellar or nightside extremes, leaving LHS 1140 b as the most promising target for biosignature searches.

Reading between the lines

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

  • If the Valencia formation constraints were relaxed, the posterior for K2-18 b would likely spread toward lower ice fractions, making the water-world classification less certain; this can be tested by comparing interior models that drop the MMF/IMF bounds.
  • The same Bayesian-interior plus tidal-heating framework could be applied to the growing sample of M-dwarf habitable-zone super-Earths to produce a ranked list of rocky-surface candidates for follow-up, extending the paper's comparative method beyond four objects.
  • The conclusion that greenhouse heating dominates tidal heating could be sharpened by computing tidal dissipation with a frequency-dependent rheology instead of a constant quality factor, which would replace the order-of-magnitude tidal heat estimate with a physically motivated range.
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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

3 major / 6 minor

Summary. The paper presents a comparative study of interior structure and habitability for four nearby super-Earth exoplanets (LHS 1140 b, K2-18 b, TOI-1452 b, TOI-1468 c). The authors use the open-source interior solver MAGRATHEA within a Bayesian MCMC framework, impose formation constraints from Valencia et al. (2007) as hard cuts, and derive posterior distributions for core, mantle, and ice mass fractions under no-atmosphere and thin-atmosphere assumptions. They then compute tidal heating with a constant-Q model and apply the one-dimensional analytical atmosphere model of Wandel (2018) to map biohabitable parameter ranges as functions of atmospheric heating and heat transport. The central claims are that, for no or thin atmospheres, K2-18 b and TOI-1468 c are likely water worlds, while LHS 1140 b and TOI-1452 b have non-negligible probability of rocky surfaces; that tidal heating alone cannot raise the global mean surface temperature but greenhouse heating can; and that LHS 1140 b has the largest parameter space for potentially habitable conditions.

Significance. If the classification is robust, the paper provides a useful comparative framework for target prioritization: it identifies LHS 1140 b as the most promising for rocky-surface habitability among the four and flags K2-18 b and TOI-1468 c as water worlds. The methods are largely transparent, rely on a publicly available interior solver, and present posterior distributions rather than point solutions. However, the water-world classification is sensitive to the adopted formation-constraint priors, and the manuscript itself acknowledges in Section 4 that the most probable solution for K2-18 b is physically questionable under pebble accretion and that the 1D model may be insufficient for that planet. The central comparative claim therefore needs a robustness check before it can be fully credited.

major comments (3)
  1. [§2.1.2, §3.1, §4] The water-world classification of K2-18 b and TOI-1468 c in the abstract and Section 3.1 depends on applying the Valencia et al. (2007) formation constraints MMF/IMF > 0.2346 and MMF/CMF > 0.5625 as hard rejection cuts in the MCMC. These cuts place K2-18 b's posterior on the boundary CMF -> 0, MMF -> 0.19, IMF -> 0.81, and produce the 'virtually zero probability' of IMF < 1% for both planets. Because the constraints are calibrated for solar-composition formation and are applied without propagating the host-star [Fe/H] uncertainties (Table 1 shows deviations up to about 0.15 dex), the zero-probability statements are prior-driven rather than data-driven. This is not merely a philosophical concern: Section 4 itself states that the CMF = 0 solution is unlikely under pebble accretion and that the 1D modelling may be insufficient for K2-18 b. Please rerun the MCMC without the Valencia cuts or with soft priors and report how the probabilities of rocky surfaces (IMF < 1%) change for all four planets; the abstract's central claim must be accompanied by this robustness check or rephrased accordingly.
  2. [Table 3 and Table 1] For K2-18 b, the instellation listed in Table 1 is S = 1.005 S⊕, but the power 1.4718 × 10^18 W in Table 3 is inconsistent with this value. Using R_p = 2.61 R⊕ and the solar constant, the incident power at 1.005 S⊕ is about 1.19 × 10^18 W, and the absorbed power after a 0.3 albedo is about 8.3 × 10^17 W; the Table 3 value corresponds instead to roughly 1.24 S⊕ if interpreted as incident power. Please state whether ˙Eins is incident or absorbed power and reconcile the two tables. Because the GMT in Table 3 and the positions in Figure 4 rely on this quantity, the discrepancy affects the quantitative habitability conclusions.
  3. [Abstract and §4] The abstract's classification of K2-18 b as a likely water world is conditional on 'no or only thin atmospheres,' but the manuscript itself cites the JWST detection of a H2-rich atmosphere on K2-18 b (Madhusudhan et al. 2023) and states in Section 4 that a massive atmosphere is needed to explain its observed mass and radius. Thus the no-atmosphere interior solution that drives the 'water world' label is not representative of the actual planet. Please state explicitly that the no/thin-atmosphere interior inference for K2-18 b is an illustrative end-member, and discuss qualitatively or quantitatively how a thick H2 envelope would shift the inferred core and ice mass fractions. Without this, the comparative statement in the abstract overstates the applicability of the model to K2-18 b.
minor comments (6)
  1. [§2.1.3, Eq. (1)] The hat notation in the likelihood function is not defined consistently: \hat{M}_p is described as a free parameter and \hat{R}_p as the calculated radius, while the unhatted M_p and R_p denote the observed values; please define all symbols in one place.
  2. [§3.1] The statement that there is 'virtually zero probability that their IMF is between 0% and 1%' for K2-18 b and TOI-1468 c refers to a single 1%-wide bin in the posterior sampling; this should be phrased as the probability of the bin rather than a continuous range to avoid overstating the resolution of the calculation.
  3. [Table 2] For LHS 1140 b, the ice thickness for the 2% water-vapor atmosphere (2.0+0.8/-1.0) is identical to the no-atmosphere value, while the 1% case is 1.0+0.6/-0.7; please verify these entries to rule out a copy-paste error.
  4. [Figure 4] Figure 4 is crowded: the green instellation stripes for the four planets overlap with the blue reference lines for Earth, Mars, and Venus, and the caption does not identify which green stripe corresponds to which planet; consider using distinct marker styles and a legend with point identifiers.
  5. [§2.2.1 and Table 3] The derived quality factors Q in Table 3 span more than an order of magnitude (8 to 170), and the paper should note explicitly that k2 and Q are coupled to the assumed interior structure and are not independent observational quantities, so the tidal heating estimates carry additional model dependence beyond the stated 0.5–5 factor.
  6. [General] The paper does not include a data availability statement or specify the exact versions of MAGRATHEA and the MCMC sampler used; since MAGRATHEA is open-source, please provide version numbers and, if possible, a link to a repository with configuration files to make the analysis reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the interior PDFs, tidal heating limits, and biohabitability ranges are forward-model outputs conditioned on measured masses/radii, external formation constraints, and scanned atmospheric parameters rather than fitted to the four targets.

full rationale

The paper's central classification (K2-18 b and TOI-1468 c as likely water worlds; LHS 1140 b and TOI-1452 b as possibly rocky) is produced by a Bayesian forward model: the likelihood in Eq. (1) compares MAGRATHEA-computed radii against measured mass and radius, with sampling over CMF, MMF, and IMF subject to the externally published Valencia et al. (2007) formation inequalities MMF/IMF > 0.2346 and MMF/CMF > 0.5625. No fitted parameter is later renamed as a prediction; the Valencia cuts are imported priors, not outputs of this paper, and the authors explicitly acknowledge their limiting role in Section 4. The tidal-heating result uses the standard constant-Q expression (Eq. 2) with k2 and Q from Tobie et al. (2019), and the 'tidal heating not enough' conclusion is a comparison of computed heating rates to instellation, not a construction. The habitability analysis applies Wandel (2018), co-authored by one of the present authors, but as a published analytical model with the atmospheric heating factor Hatm and heat transport factor f scanned over ranges rather than fitted to the four targets; Eqs. (4)-(6) are the model's own definitions, and the paper uses them to map allowed parameter ranges. The self-citations to Perdelwitz et al. (2021, 2024) concern the derivation of log R'HK activity indices, which are auxiliary stellar inputs, not load-bearing predictions. The possible fragility of the classification under the Valencia abundance/formation priors is a validity concern, not circularity: the prior assumptions are independently citable and stated, and the MCMC likelihood is not equivalent to them.

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

The central claims rest on standard interior-structure assumptions (differentiation, hydrostatic equilibrium, MAGRATHEA EOS), stellar-abundance priors from Valencia et al. (2007), and the Wandel (2018) analytical climate model. No new physical entities are introduced. The main hand-chosen parameters are the atmospheric mass fractions, the eccentricity e=0.01 for two planets, and the factor-of-five tidal-heating bounds.

free parameters (7)
  • Core mass fraction (CMF) = posterior per planet (e.g., K2-18 b peaks near 0)
    Sampled via MCMC; constrained by measured mass and radius and stellar abundance priors.
  • Mantle mass fraction (MMF) = posterior per planet
    Sampled via MCMC alongside CMF; IMF derived as 1-CMF-MMF.
  • Atmospheric mass fraction = 0%, 1%, 2% (also 0.1% and 10%)
    Chosen by hand in Section 3.1 to test sensitivity.
  • Eccentricity for TOI-1452 b and TOI-1468 c = 0.01
    Adopted as more physical because the discovery papers fixed e=0 in their fits (Section 3.2).
  • Tidal heating uncertainty factor = 0.5 and 5 times calculated value
    Hand-chosen bounds to account for unknown mantle viscosity and Andrade rheology (Section 2.2.1).
  • Heat transport factor f = 0 to 1 (Figure 4: 0.2, 0.5, 1)
    Free parameter of the Wandel 2018 model; not fitted to data.
  • Atmospheric heating factor Hatm = scanned over range
    Free parameter combining albedo, greenhouse, and screening; not fitted to data.
assumptions (7)
  • domain assumption Planets are fully differentiated, radially symmetric, and in hydrostatic equilibrium
    Stated in Section 2.1; required by MAGRATHEA.
  • domain assumption Host star relative elemental abundances (assumed solar) are a proxy for planet bulk composition
    Section 2.1.2; used to set prior constraints.
  • ad hoc to paper Valencia et al. (2007) formation constraints MMF/IMF > 0.2346 and MMF/CMF > 0.5625
    Section 2.1.2; these bounds shape the posterior, particularly for K2-18 b where the PDF is pushed to the constraints.
  • domain assumption MAGRATHEA equations of state (Vinet core, perovskite mantle, Ice VII/X hydrosphere) are valid at super-Earth pressures
    Section 2.1.1; the central interior results depend on these EOS.
  • domain assumption Constant Q tidal model with k2 and Q from Tobie et al. (2019) captures the tidal heating rate to order of magnitude
    Section 2.2.1; the paper qualifies this as an order-of-magnitude estimate.
  • domain assumption Wandel (2018) 1D temperature formulae and habitability range (Eqs. 4-6) are adequate for comparative biohabitability
    Section 2.2.2; the conclusions on too hot or habitable rely on these expressions.
  • domain assumption Biohabitable zone is defined as liquid water surviving on at least part of the surface
    Section 2.2; this definition drives the H range used.

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Cite this review

Pith. "Pith review of Potential Interior Structures and Habitability of Super-Earth Exoplanets LHS 1140 b, K2-18 b, TOI-1452 b and TOI-1468 c." pith.science (2026). https://pith.science/paper/GPGGQPVJ

@misc{pith2026241208476,
  author       = {Pith},
  title        = {Pith review of: Potential Interior Structures and Habitability of Super-Earth Exoplanets LHS 1140 b, K2-18 b, TOI-1452 b and TOI-1468 c},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GPGGQPVJ}},
  note         = {Machine review of arXiv:2412.08476}
}
read the original abstract

We analyze four super-Earth exoplanets, LHS 1140 b, K2-18 b, TOI-1452 b, and TOI-1468 c, which orbit M-dwarf stars in the habitable zone. Their relative proximity, within 40 parsecs, makes them prime candidates for follow-up observations and atmospheric and habitability studies. This paper aims to assess their internal structure and habitability, considering their tidal heating, atmospheric heating, and global transport. We model the interior structure of the planets by applying Bayesian inference to an exoplanet's interior model. A constant quality factor model is used to calculate the range of tidal heating, and a one-dimensional analytical model of tidally locked planets is used to assess their surface temperature distribution and habitability. Assuming no or only thin atmospheres, K2-18 b and TOI-1468 c are likely to be water worlds. However, TOI-1452 b and LHS 1140 b may have rocky surfaces. We find that tidal heating is not enough to raise the global mean surface temperature, but greenhouse heating can effectively do so. If the considered planets have retained thick atmospheres, K2-18 b, TOI-1468 c, and TOI-1452 b may, for significant atmospheric heating and heat transport factors, be too hot to sustain liquid water on their surface. However, the lower instellation of LHS 1140 b and the non-zero probability of it having a rocky surface give more space for habitable conditions on the planet.

Figures

Figures reproduced from arXiv: 2412.08476 by the authors.

Figure 1
Figure 1. Ternary diagrams for LHS 1140 b, K2-18 b, TOI-1452 b, and TOI-1468 c based on a code by Zeng & Seager (2008). Each point on the ternary diagram represents a unique composition. Horizontal, positive-slope, and negative-slope lines describe the planet’s water-ice, iron, and mantle mass fractions, respectively. The blue curve shows compositions that explain the observed mass and radius of the exoplanet. Green, brown, a… view at source ↗
Figure 2
Figure 2. Posterior probability density functions of core mass fraction (red dash-dot curve), mantle mass fraction (black dash curve) and water-ice mass fraction (blue solid curve) of exoplanets LHS 1140 b (upper left), K2-18 b (upper right), TOI-1452 b (lower left) and TOI-1468 c (lower right), considering no atmosphere. Since for TOI-1452 b (Cadieux et al. 2022) and TOI￾1468 c (Chaturvedi, P. et al. 2022) the authors only c… view at source ↗
Figure 3
Figure 3. Median sizes of layers of LHS 1140 b (upper left), K2-18 b (upper right), TOI-1452 b (lower left) and TOI-1468 c (lower right) as a function of the atmosphere mass fraction. Triangles and circles represent the sizes of layers considering a water vapor and a H-He atmosphere, respectively. Typical error bars are shown on the right. and 0.75 (Wandel 2018). Their actual Hatm values are represented by blue dots in [PITH… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Maximal (red) and minimal (blue) atmospheric heating factor vs instellation, for three values of the heat re￾distribution parameter: f = 0.2 (solid), 0.5 (dashed), and 1 (dotted). The locations of the four planets in [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

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