{"id":"79119e5a-b3ac-418d-8b8c-a95cf6e4df8b","arxiv_id":"2412.08476","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Using interior and climate models, the authors find K2-18 b and TOI-1468 c are probably water worlds, while LHS 1140 b and TOI-1452 b may have rocky surfaces, and tidal heating is negligible for surface temperature.","lead":"This paper models the interiors and surface temperatures of four nearby super-Earths and asks which ones could hold liquid water. It finds that two are likely water worlds, one or two may be rocky, and tidal heating alone is too weak to warm any of them, so thick atmospheres matter most.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Water-world classification rests on hard Valencia formation cuts; rerun MCMC without them to test whether the zero-probability rocky claims are data-driven or prior-driven.","rationale":"I read the paper's central claim as a conditional comparative classification: under no or only thin atmospheres, K2-18 b and TOI-1468 c are likely water worlds, while LHS 1140 b and TOI-1452 b may have rocky surfaces. The most load-bearing condition for that classification is the prior structure imposed on the interior inversion, specifically the Valencia et al. (2007) inequalities. The mass-radius data are highly degenerate, and the paper's own ternary diagrams show wide composition ranges for all planets. The zero-probability statements for low IMF that separate water worlds from rocky worlds are exactly the kind of output that hard priors can create even when the likelihood is smooth. This concern is sharpened by the paper's own Section 4 admission that the K2-18 b posterior mode is physically unlikely, which signals that the boundary solution is not independently supported. The proposed MCMC re-run is a direct, feasible check using the already-published MAGRATHEA code and likelihood, and it would settle whether the classification is data-driven or prior-driven. The reader's weakest assumption identifies the same issue, and I agree that the paper should be accepted only conditionally on this premise being checked. A secondary internal inconsistency in Table 3's instellation values for K2-18 b and LHS 1140 b is also worth correcting, but it mainly affects the habitability-temperature comparison rather than the interior classification, so it is less load-bearing for the central claim. With the prior-sensitivity test added as a condition, the conditional verdict remains appropriate; no change to the reader's verdict is needed.","tokens_in":22152,"tokens_out":18396,"duration_ms":199399,"concrete_test":"Re-run the MCMC of Section 2.1.3 with MAGRATHEA under three prior schemes: (A) the paper's hard Valencia cuts as a control; (B) no composition cuts, uniform on CMF and MMF; (C) soft Gaussian priors centered on the compositions implied by each host star's measured [Fe/H] with its uncertainty, instead of the solar-calibrated hard inequalities. For each planet, report P(IMF<1%), the posterior mode, and 68% credible intervals. Additionally evaluate the pure-mantle endpoint (CMF=0, IMF=0) likelihood for TOI-1468 c and K2-18 b. If the no-cut posterior still gives P(IMF<1%) < 1e-3 for both planets, the water-world classification is robust. If not, the hard boundaries are the load-bearing assumption, and the abstract's classification should be reworded as conditional on those priors.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The water-world versus rocky classification in Section 3.1 and the abstract depends on applying the Valencia et al. (2007) formation constraints as hard cuts in the MCMC: MMF/IMF > 0.2346 and MMF/CMF > 0.5625, as described in Section 2.1.2. These cuts, rather than the mass-radius likelihood alone, push K2-18 b's posterior to the boundary CMF->0, MMF~0.19, IMF~0.81, and produce the tiny probabilities that LHS 1140 b and TOI-1452 b have IMF<1%. The inequalities are calibrated for solar-composition formation and are applied without propagating the host stars' measured [Fe/H] uncertainties; Table 1 shows deviations from solar by up to about 0.15 dex. Moreover, Section 4 itself argues that the CMF->0 solution dominating K2-18 b is unlikely under pebble accretion, so the paper internally acknowledges that its most probable solution is physically questionable. If these priors are too rigid, the headline classification is an artifact of the prior boundary. This is a correctness risk, not merely a disagreement with consensus: the strong statements of 'virtually zero probability that IMF is between 0% and 1%' can only follow from hard prior boundaries, not from the continuous likelihood alone.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":22448,"tokens_out":7713,"duration_ms":73604,"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":[{"comment":"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.","section":"§2.1.2, §3.1, §4"},{"comment":"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.","section":"Table 3 and Table 1"},{"comment":"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.","section":"Abstract and §4"}],"minor_comments":[{"comment":"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.","section":"§2.1.3, Eq. (1)"},{"comment":"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.","section":"§3.1"},{"comment":"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.","section":"Table 2"},{"comment":"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.","section":"Figure 4"},{"comment":"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.","section":"§2.2.1 and Table 3"},{"comment":"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.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript relies heavily on the Wandel (2018) one-dimensional habitability model, of which one of the present authors is the sole author, and this relationship is not flagged in the text. I do not see evidence that the model is being fitted to the target planets, so this is not a circularity problem, but an explicit acknowledgment of the self-citation would improve transparency. The comparative framing is well suited to an ApJ-style journal; the main concern is the robustness of the prior-driven water-world classification, which I have detailed in the major comments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Useful comparative survey, but the headline classification is more assumption-dependent than the abstract admits. There is also a concrete numerical inconsistency in the K2-18 b instellation that needs fixing.\n\nWhat is actually new: the paper runs one consistent pipeline (MAGRATHEA Bayesian interiors, constant-Q tidal heating, and the Wandel biohabitability model) across four nearby HZ super-Earths with updated masses, radii, and JWST-era atmospheric constraints. It also contributes new log R'HK activity measurements for three of the four host stars. The methods are transparent, errors are propagated, and the paper explicitly owns its limitations—it admits the 1D model is insufficient for K2-18 b and that the CMF=0 solution is unlikely under pebble accretion. That honesty is worth crediting.\n\nSoft spots, in proportion:\n\nFirst, K2-18 b's instellation is listed as 1.005 S⊕ in Table 1, but the absorbed power in Table 3 (1.47e18 W) implies about 1.24 S⊕ for the adopted radius. That is a ~23% discrepancy, and it shifts the planet's location in Figure 4 and its reported 270 K global mean temperature. This needs to be reconciled before the comparative habitability plot is used.\n\nSecond, the 'virtually zero probability that IMF < 1%' phrasing is too strong. The posterior is truncated by the Valencia et al. (2007) relative-abundance inequalities, and the paper's own discussion says the most probable K2-18 b solution (CMF→0) is physically questionable. So the 'water world' label is partly prior-driven. However, the stress-test claim that the non-rocky classification is entirely a prior artifact does not hold up. K2-18 b and TOI-1468 c have bulk densities (2.67 and 4.15 g/cc) that a purely rocky composition cannot match at their radii, so the mass-radius likelihood alone already rules out IMF<1% at any meaningful confidence. The cuts shape the detailed fractions, not the broad water-world vs rocky split.\n\nThird, the abstract's 'assuming no or only thin atmospheres' caveat is fair, but the body notes K2-18 b likely needs a massive atmosphere anyway. Readers will take 'water world' at face value; it should be softened to 'water-rich, conditional on a thin atmosphere.'\n\nWho this is for: exoplanet interior and habitability modelers, JWST follow-up planners. It is a competent comparative study, not a breakthrough. It deserves a serious referee, and I would accept it after minor-to-moderate revision.","headline":"Useful comparative survey, but the headline classification is more assumption-dependent than the abstract admits.","tokens_in":23032,"tokens_out":6851,"would_cite":true,"duration_ms":64393,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["super-Earth exoplanets","water worlds","interior structure","Bayesian inference","tidal heating","habitable zone","M-dwarf stars","LHS 1140 b"],"falsifier":"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.","tokens_in":21913,"feed_emoji":"🪐","tokens_out":5223,"duration_ms":46540,"temperature":0.7,"pith_summary":"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.","feed_headline":"Two super-Earths may be water worlds, two may have rocky surfaces","feed_subtitle":"Tidal heating barely warms these four planets; greenhouse heating decides, and LHS 1140 b has the widest habitable margin.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the formation constraints (MMF/IMF > 0.2346, MMF/CMF > 0.5625) that push the posterior mass fractions to their allowed limits.","marker":"Valencia et al. (2007)"},{"why":"Provides MAGRATHEA, the open-source interior solver and default equations of state used to map mass and radius to core, mantle, and ice fractions.","marker":"Huang et al. (2022)"},{"why":"Provides the Bayesian likelihood framework, a Gaussian in measured mass and radius, that produces the posterior PDFs.","marker":"Rogers & Seager (2010)"},{"why":"Supplies the one-dimensional tidally locked planet model with heating factor H and heat transport factor f that defines the biohabitable window.","marker":"Wandel (2018)"},{"why":"Supplies the constant-quality-factor tidal heating formula used to compute the tidal heat rates for the four planets.","marker":"Henning et al. (2009)"},{"why":"Provides the measured mass, radius, and instellation of LHS 1140 b used as input to the interior and habitability inference.","marker":"Cadieux et al. (2024a)"},{"why":"Provides the measured mass, radius, and instellation of K2-18 b used as input to the interior and habitability inference.","marker":"Benneke et al. (2019)"},{"why":"Provides the measured mass, radius, and instellation of TOI-1452 b used as input to the interior and habitability inference.","marker":"Cadieux et al. (2022)"},{"why":"Provides the measured mass, radius, and instellation of TOI-1468 c used as input to the interior and habitability inference.","marker":"Chaturvedi et al. (2022)"}],"fun_headline_variants":["Tidal heating too weak; greenhouse gases decide super-Earth habitability","LHS 1140 b may host rocky surface, best chance for life","K2-18 b and TOI-1468 c likely water worlds, new model shows","Super-Earth interiors: two icy, two rocky, one habitable?","Greenhouse effect key for super-Earth surface water, not tides"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Tidal heating too weak; greenhouse gases decide super-Earth habitability","LHS 1140 b may host rocky surface, best chance for life","K2-18 b and TOI-1468 c likely water worlds, new model shows","Super-Earth interiors: two icy, two rocky, one habitable?","Greenhouse effect key for super-Earth surface water, not tides"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000934,"raw_usage":{"total_tokens":4069,"prompt_tokens":1089,"completion_tokens":2980,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":705,"completion_tokens_details":{"reasoning_tokens":2878}},"tokens_in":705,"tokens_out":2980,"duration_ms":18520,"temperature":1.0,"reasoning_tokens":2878,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T17:44:47.603180+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}