{"id":"d1154a2c-e763-4bd9-b622-d3610eb46f77","arxiv_id":"2506.24100","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Misaligned Neptune-sized planets show stronger tidally induced radius inflation than aligned ones, based on structure-model fits and statistical tests.","lead":"A study of 24 Neptune-sized exoplanets finds that those in tilted, misaligned orbits show more signs of tidal heating and inflated radii than aligned ones. The result connects a planet's dynamical history to its physical size, and offers a way to interpret observations of puffy planets like WASP-107 b.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Propagating Table 3 uncertainties and excluding model-unconstrained planets likely removes the claimed ≥90% confidence; the p-values are point-estimate artifacts.","rationale":"The reader's verdict is already CONDITIONAL, and my concern reinforces that condition rather than shifting it. The paper's central claim is explicitly a statistical one: 'at least 90% confidence' from the tests in Table 4. The weakest link is not the tidal model itself—which is internally consistent and openly approximate—but the step from model outputs to a confidence statement. The tests input one point estimate per planet, ignore the reported dispersions, and include planets whose no-tide fits are outside the model grid, while other such planets are excluded. A quick estimate shows that dropping the four fenv,0>50 planets shrinks the mean difference enough that the t-test p-value likely rises above 0.1. This is checkable, and the check should be a required part of revision. I do not think the paper should be rejected: the population trend may survive, and the WASP-107 b case study is a useful demonstration independent of the population claim. But the 'at least 90% confidence' wording should not stand until the tests are rerun with proper uncertainty propagation and a consistent model-boundary rule.","tokens_in":25831,"tokens_out":12572,"duration_ms":143112,"concrete_test":"Rerun all four statistical tests on (a) full posterior draws: for each planet, sample Rp,t/Rp,0 from its MCMC posterior at Q'=10^4 (or, if unavailable, from the reported mean plus the standard deviation in Table 3) and compute the distribution of p-values; (b) a pre-registered sensitivity set that excludes all planets with fenv,0>50% (WASP-107 b, HAT-P-12 b, HAT-P-18 b, Kepler-9) or treats fenv,0 with a 50% cap; and (c) the same tests at Q'=3×10^3 and 3×10^4. If fewer than 90% of Monte Carlo draws yield p<0.1, or if the fenv,0>50 exclusions raise the p-values above 0.1, the headline claim is not supported by the present analysis.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 5.3 applies KS, t, Welch, and Mann-Whitney tests to the single Rp,t/Rp,0 point estimates in Table 3, with no propagation of the quoted standard deviations or of the MCMC/measurement uncertainty. The quoted 'error' is only the standard deviation of Rp,t/Rp,0 across the Q' bin [3.8,4.2] (§4.2), not the posterior uncertainty at fixed Q', so the true uncertainty is larger. Several of the largest values are fragile: GJ 436 b is explicitly identified as not reaching Q'=10^4 and is linearly extrapolated (§4.1), and WASP-107 b, HAT-P-12 b, HAT-P-18 b, and Kepler-9 have fenv,0 > 50%, meaning the no-tide model cannot fit them within the simulation grid. These planets are retained in the statistical sample while TOI-1842 b and HD 148193 b are excluded for a domain limitation (§4.1), so the treatment of the model boundary is non-uniform. Excluding the three fenv,0>50 misaligned planets and Kepler-9 reduces the mean difference from about 0.25 to about 0.13, which would plausibly push the t-test p above 0.1. With 24 planets and four tests, a p-value near 0.022 is not robust evidence of 'at least 90% confidence' unless the tests are rerun with full posterior draws and a pre-specified model-boundary rule.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates whether misaligned (including polar) Neptune-sized and sub-Saturn-sized planets are more tidally inflated than aligned planets. Using 12 misaligned and 12 aligned planets with stellar obliquity measurements, the authors apply a MESA-based thermal evolution model with and without tidal heating, fix the reduced tidal quality factor at Q'=10^4, and infer envelope mass fractions (fenv,0 and fenv,t) and a dimensionless degree of inflation Rp,t/Rp,0. The reported mean inflation is about 1.4 for misaligned planets and 1.1 for aligned planets; four statistical tests (KS, Student t, Welch, Mann-Whitney) give p-values of 0.099, 0.022, 0.024, and 0.046, which the authors interpret as at least 90% confidence that misaligned planets are more inflated. The paper also presents a case study of WASP-107 b, coupling tidal orbital evolution with radius evolution, and derives Q' in the range 10^4-10^6, said to agree with JWST-based internal temperature constraints.","tokens_in":26222,"tokens_out":7054,"duration_ms":76336,"significance":"If the population-level claim is correct, it would establish a direct observational connection between a planet's dynamical history (spin-orbit misalignment and eccentricity excitation) and its present-day interior heat budget, with consequences for formation and migration theories. The assembled catalog of aligned and misaligned Neptune/sub-Saturn planets with obliquity measurements is a useful community resource, and the WASP-107 b coupled orbital-radius evolution model provides a concrete methodological advance by showing that radius feedback can slow tidal circularization. The paper also makes a falsifiable prediction: misaligned Neptunes should show systematically larger tidally-induced radius inflation under equilibrium-tide models. However, the statistical evidence as presented is not yet robust enough to support the stated confidence level, because the key tests ignore the quoted uncertainties and the sample treatment at the model boundary is inconsistent.","major_comments":[{"comment":"The four statistical tests are applied to single point estimates of Rp,t/Rp,0 with no propagation of the quoted uncertainties. The errors in Table 3 are standard deviations of Rp,t/Rp,0 over the log10 Q' bin [3.8,4.2] (Sections 4.1 and 4.2), not the full posterior or measurement uncertainties at fixed Q', so the effective noise is larger than reported. The p-values (especially the t-test p=0.022 and Welch p=0.024) would need to be recomputed using draws from the posterior distributions, or at least using Monte Carlo resampling from the individual standard deviations, before the claim of 'at least 90% confidence' is supported.","section":"Section 5.3 and Table 3"},{"comment":"The treatment of planets whose no-tide fits require fenv,0 > 50% is internally inconsistent: TOI-1842 b and HD 148193 b are excluded for this reason, while WASP-107 b, HAT-P-12 b, HAT-P-18 b, and Kepler-9 b are retained with fenv,0 > 50% in Table 3. Three of the four retained planets are misaligned and have some of the largest inflation ratios (Rp,t/Rp,0 between 1.68 and 1.89), so the exclusion rule directly affects the group means and the statistical comparison. The authors should specify a uniform, pre-selected boundary criterion and report results both with and without the fenv,0 > 50% planets.","section":"Section 4.1 and Table 3"},{"comment":"The assumption of e = 0.05 ± 0.02 for planets without measured eccentricities, combined with setting the planetary obliquity to ϵ = 0 for all planets, is not sufficiently stress-tested. The reported sensitivity analysis using only planets with measured eccentricities is reassuring in direction, but the subsample is small and no p-values are given. Because the inferred Rp,t/Rp,0 values depend strongly on the assumed eccentricity through equation (8), a quantitative sensitivity study (for example, comparing e = 0.05 vs e = 0.1, and including obliquity tides for polar planets) is needed to establish that the population difference is not an artifact of these choices.","section":"Section 3.3 and Table 3"},{"comment":"In the WASP-107 b case study, the authors fix fenv,t = 0.49 at Q' = 10^6 because the simulation grid ends at fenv = 50%, even though the MCMC fit at Q' = 10^4 gives fenv,t ≈ 24%. This clipping is a strong modeling assumption, and the resulting conclusion that Q' ≈ 10^4-10^6 for WASP-107 b should be labeled as conditional on that cap. A dedicated exploration of the sensitivity of the inferred Q' range to the fenv ceiling, or an extension of the simulation grid, would make the dynamical constraints more convincing.","section":"Section 6.2.1"},{"comment":"Multiple testing is not accounted for. Four separate tests are presented and the paper selects the 'at least 90% confidence' framing based on the ensemble. The KS p-value of 0.099 is the weakest, and the t-test p-value of 0.022 would not survive a strict 95% Bonferroni correction (0.022 × 4 = 0.088, though still below 0.1). The tests are also not independent because they are computed from the same point estimates. The authors should either pre-specify a primary test or report adjusted p-values; at present the evidence for the population difference is suggestive but not as strong as the abstract claims.","section":"Section 5.3 and Table 4"}],"minor_comments":[{"comment":"The caption contains a doubled word: 'Impact of of tidal inflation'; please correct.","section":"Figure 4 caption"},{"comment":"The abbreviation for the Kolmogorov-Smirnov test appears as both 'K-S Test' and 'KS test'; please standardize to one form.","section":"Throughout"},{"comment":"The Ltide column lists values without uncertainties; if these are point estimates computed at Q' = 10^4, please clarify, or provide errors consistent with the other columns.","section":"Table 3"},{"comment":"The sentence 'we determine the value of fenv,t corresponding to this Q′ to be ≥ 50%' would be clearer as 'to be at least 50%', and the subsequent clipping at 0.49 should be described with an explicit justification.","section":"Section 6.2.1"},{"comment":"The reference list for the sample properties is long but not keyed to individual planets; a per-row citation column would aid reproducibility.","section":"Table 1"}],"recommendation":"major_revision","confidential_remarks":"The central idea is interesting and the WASP-107 b coupled evolution analysis is a useful contribution. The main barrier to acceptance is statistical rigor: the population claim currently rests on tests that ignore the quoted uncertainties and on a non-uniform treatment of the model-boundary planets, both of which are fixable within the scope of a revision. The heavy reliance on the authors' own MESA simulation suite is not, by itself, a problem because the suite is public and the methodology is standard in the field."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper asks a good question: do misaligned sub-Neptunes show more tidally-induced radius inflation than aligned ones? The new piece is the population-level comparison itself, and the WASP-107 b coupled orbital–radius evolution is a useful demonstration of how radius inflation can slow tidal circularization. The authors are also transparent about their assumptions and openly discuss the ohmic dissipation alternative, which is more than many papers do.\n\nThat said, the central claim is not supported by the statistics as presented. The four hypothesis tests are run on point estimates from Table 3, with no propagation of the quoted uncertainties. Those uncertainties are themselves only the spread across a narrow Q' bin, not the full posterior width, so the true errors are larger. The KS p-value of 0.099 is borderline, and with four tests the chance of at least one p<0.1 is higher than the nominal 90%. The t-test and Mann-Whitney p-values around 0.02–0.05 are fragile to small sample changes.\n\nThe bigger problem is the inconsistent treatment of the model boundary. TOI-1842 b and HD 148193 b are excluded because the no-tide model requires fenv,0>50%, but WASP-107 b, HAT-P-12 b, HAT-P-18 b, and Kepler-9 are retained despite having the same issue. Excluding those four reduces the mean inflation difference from about 0.25 to about 0.13, which would likely push the t-test p above 0.1. That is exactly the sort of pre-specified boundary rule a reader needs to see. GJ 436 b is also linearly extrapolated to Q'=10^4 and has a large inflation value; the paper does not test sensitivity to that.\n\nI do not think these problems are fatal to the underlying idea. The physical narrative—misaligned planets are dynamically excited, get eccentric, and therefore tidally heat more—is plausible, and the case study gives some support. But the paper overclaims when it says 'at least 90% confidence'. Right now this is a suggestive population trend, not a demonstrated statistical effect.\n\nI would send this to peer review. A serious referee can push for a proper statistical treatment: propagate posterior uncertainties, use a consistent rule for model-boundary planets, adjust for multiple testing, and report the eccentricity-only subsample in full. With those revisions the paper could be publishable, but only with a much more careful claim.","headline":"The population comparison is a good idea and the case study is interesting, but the statistical evidence for 'at least 90% confidence' does not survive contact with the model-boundary and uncertainty problems.","tokens_in":26700,"tokens_out":4580,"would_cite":true,"duration_ms":45156,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper's statistical tests show misaligned Neptune-sized planets are more tidally inflated than aligned ones, at at least 90% confidence.","keywords":["exoplanets","tidal heating","radius inflation","spin-orbit misalignment","polar planets","Neptune-sized planets","planetary evolution","WASP-107 b"],"falsifier":"A larger sample of Neptune/sub-Saturn planets with measured eccentricities, ages, and 3D obliquities could settle it: if the inflation excess among misaligned planets disappears once eccentricity and age are controlled, or if equally inflated planets appear at low obliquity, the central claim fails.","tokens_in":1665,"feed_emoji":"🪐","tokens_out":2724,"duration_ms":94655,"temperature":0.7,"pith_summary":"The paper tries to establish that the unusually large radii of many Neptune-sized exoplanets are tied to their orbital histories: planets whose orbits are misaligned with their host star's spin are more inflated by tidal heating than aligned planets. It compares 12 misaligned and 12 aligned planets, fitting each with and without tidal heating in a structural-evolution model, and measures the degree of inflation $R_{p,t}/R_{p,0}$, the factor by which tides enlarge the planet beyond the radius its envelope would have without tides. Four statistical tests separate the two populations at $\\geq 90\\%$ confidence, with average inflation of roughly 1.4 for misaligned planets versus 1.1 for aligned ones. If the result holds, a planet's observable size and internal energy budget carry information about its dynamical past, not just its composition.","feed_headline":"Tidal inflation is stronger for misaligned Neptunes","feed_subtitle":"Comparing 24 planets, misaligned worlds show roughly 30% more tidal radius inflation than aligned ones.","key_machinery":"The central object is the degree of inflation, $R_{p,t}/R_{p,0}$: the ratio of the radius a tidal-heating model assigns to a planet (matching the observed radius) to the radius the same envelope mass fraction would have if tides were absent. It is extracted from a grid of about 15,000 two-layer thermal-evolution models by fitting each observed planet twice, once with and once without tidal heating, and comparing the inferred envelope fractions at a fixed reduced tidal quality factor $Q' = 10^4$. The tidal luminosity law used sets the heating from eccentricity tides with planetary obliquity set to zero, so the machinery isolates eccentricity-driven inflation rather than obliquity-driven tides.","core_discovery":"For a sample of 24 Neptune-to-sub-Saturn planets with measured stellar obliquities, the paper finds that misaligned planets ($|\\lambda| > 40^\\circ$) have average tidally induced radius inflation $\\langle R_{p,t}/R_{p,0}\\rangle_m \\approx 1.4$, compared with $\\langle R_{p,t}/R_{p,0}\\rangle_a \\approx 1.1$ for aligned planets, evaluated at a fixed reduced tidal quality factor $Q' = 10^4$. The inferred envelope mass fraction drops by roughly 12% for misaligned planets when tides are included, versus about 5% for aligned planets. The Kolmogorov-Smirnov, Student's t, Welch's t, and Mann-Whitney U tests reject the null hypothesis that the two populations are drawn from the same inflation distribution at the 90%, 97%, 97%, and 95% confidence levels respectively. The paper interprets this as evidence that misaligned planets' dynamically excited histories, which place them in close-in, eccentric, highly inclined orbits, deposit more tidal heat into their envelopes and puff them up.","pith_inferences":["A testable extension would be to measure internal temperatures across a larger sample with infrared emission spectroscopy; the model predicts misaligned planets should show systematically higher internal heat at fixed mass, radius, and incident flux.","If eccentricity tides are the driver, the inflation signal should weaken as orbits circularize, predicting a correlation between current eccentricity and inflation among misaligned planets and a deficit of inflated low-eccentricity misaligned planets at old ages.","The paper's exclusion of Jupiter-mass planets leaves open whether a similar alignment trend exists among hot Jupiters, where tidal inflation is also common but the dominant formation channels differ."],"forward_implications":["Observed radii of misaligned Neptune/sub-Saturn planets should be interpreted with tidal inflation in mind; otherwise their envelope mass fractions are overestimated.","Low densities among misaligned planets can be read as a signature of past high-eccentricity migration or scattering, not necessarily of unusually massive envelopes.","Population studies of sub-Neptune and sub-Saturn composition should treat aligned and misaligned planets separately rather than combining them.","Dynamical modeling of close-in planets should couple radius evolution to orbital evolution; ignoring radius changes overestimates the tidal circularization rate.","The WASP-107 b case study favors $Q' \\approx 10^4$-$10^6$, consistent with internal heat constraints from recent infrared observations."],"supporting_citations":[{"why":"Supplies the tidal-heating simulation grid and MCMC inference routine used to estimate envelope fractions and the degree of inflation.","marker":"S. Millholland et al. (2020)"},{"why":"Establishes the tidal radius-inflation model for sub-Neptunes and the dependence of inflation on tidal luminosity.","marker":"S. Millholland (2019)"},{"why":"Provides the tidal luminosity and orbital-evolution equations used to compute $L_{\\rm tide}$ and to model WASP-107 b's tidal evolution.","marker":"J. Leconte et al. (2010)"},{"why":"Provides the planetary thermal-evolution framework that the tidal-heating models are built on.","marker":"H. Chen & L. A. Rogers (2016)"},{"why":"Compiles 3D stellar obliquity measurements and identifies the polar-planet population that motivates the aligned/misaligned comparison.","marker":"S. H. Albrecht et al. (2021)"},{"why":"Supplies the compiled transiting-planet data, including obliquities, used to build the sample.","marker":"J. Southworth (2011)"},{"why":"Provides JWST-based constraints on WASP-107 b's core mass that the case study compares against its $Q'$ predictions.","marker":"D. K. Sing et al. (2024)"},{"why":"Infers a high internal heat flux for WASP-107 b, used to check the tidal-heating interpretation.","marker":"L. Welbanks et al. (2024)"}],"fun_headline_variants":["Misaligned Neptunes puff up more from tidal heating","Polar orbits inflate Neptune-sized planets more","Tides puff up misaligned Neptunes ~30% more","Misaligned planets show ~30% more tidal inflation"],"cache_read_input_tokens":28800,"weakest_assumption_plain":"The result stands on the assumption that the tidal-heating model with zero planetary obliquity, its simulation grid, and a linear extrapolation to a common tidal quality factor estimate inflation without a bias that tracks misalignment.","fun_headline_variants_meta":{"raw":{"variants":["Misaligned Neptunes puff up more from tidal heating","Polar orbits inflate Neptune-sized planets more","Tides puff up misaligned Neptunes ~30% more","Misaligned planets show ~30% more tidal inflation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000626,"raw_usage":{"total_tokens":2897,"prompt_tokens":943,"completion_tokens":1954,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":559,"completion_tokens_details":{"reasoning_tokens":1885}},"tokens_in":559,"tokens_out":1954,"duration_ms":15254,"temperature":1.0,"reasoning_tokens":1885,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:24:34.019802+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A larger sample of Neptune/sub-Saturn planets with measured eccentricities, ages, and 3D obliquities could settle it: if the inflation excess among misaligned planets disappears once eccentricity and age are controlled, or if equally inflated planets appear at low obliquity, the central claim fails.","supporting_citations":[],"review_version":1}