{"id":"c984ad1b-9f01-4f35-8beb-49de72267fac","arxiv_id":"2411.11452","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Low-viscosity protoplanetary discs produce wider resonant chains (4:3, 3:2, 2:1) matching observed super-Earth chains, while high-viscosity discs match the broader Kepler period-ratio distribution.","lead":"This paper uses planet formation simulations to show that planets forming in low-viscosity discs get trapped in wider orbit resonances, matching observed resonant chains like TRAPPIST-1, while higher-viscosity discs match the overall period ratio distribution of Kepler super-Earths. The result suggests that observed systems formed in discs with a range of viscosities.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper never tests the proposed mixed-viscosity population against the full Kepler period-ratio distribution; the central diversity claim is inferred from two separate subset matches, not demonstrated.","rationale":"The reader's weakest assumption is the unmodified Cresswell & Nelson damping at low viscosity. That is a legitimate model uncertainty and could shift resonance capture outcomes. I do not dispute it. However, I judge the more load-bearing gap to be logical: the headline claim is population-level, and the paper never constructs the proposed mixed-viscosity population. Even with perfect damping, the central claim would remain unsupported because the full Kepler period-ratio distribution, which includes the observed chains, is a single dataset. Explaining chains with one simulation set and the rest of the distribution with another does not demonstrate that the two populations can coexist in the required proportions. The low-viscosity runs' known deficits—low masses (Appendix E), overall over-tight packing after instabilities (Sect. 3.3), and a stable-chain fraction of only ~5%—make it plausible that no mixture will match the full data. This is directly testable with the authors' existing output. Because the paper is honest about its failures and the missing test is fixable, I keep the reader's CONDITIONAL verdict; the concern strengthens the condition rather than changing the verdict.","tokens_in":23815,"tokens_out":15095,"duration_ms":149693,"concrete_test":"Combine the synthetic transit detections from the low-viscosity runs (this paper) and the high-viscosity runs (Izidoro et al. 2021) with a mixing weight w on the low-viscosity sample, stepping w from 0 to 1. For each w, compute the cumulative period-ratio distribution of adjacent planets and run a two-sample Anderson-Darling test against the full Kepler period-ratio sample (R < 4 R_Earth) and against the observed chain subsample separately. Also record the fraction of adjacent pairs in the 3:2 and 2:1 resonances. If no w simultaneously passes the full-sample test (e.g., AD p > 0.05) and reproduces the observed chain resonance fractions, the paper's central diversity claim is not supported by the presented simulations and would need a revised or more qualified conclusion.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that diversity of disc viscosities explains the period ratios of resonant and non-resonant systems—requires showing that some mixture of low- and high-viscosity populations reproduces the full Kepler period-ratio distribution. The paper instead offers two separate comparisons: low-viscosity chains match the observed chain period ratios (Sect. 3.3, Fig. 6), and high-viscosity simulations match the overall distribution (Sect. 3.3, Fig. 5, from Izidoro et al. 2021). These are different subsets of the same observed sample, and the paper never combines the two simulation sets. Appendix F only mixes 2% stable with 98% unstable low-viscosity runs, not low- and high-viscosity populations. This omission is consequential: the low-viscosity runs, by the authors' own analysis, remain too tightly packed overall (Sect. 3.3) and are too low in mass (Appendix E), while only ~5% of low-viscosity runs produce stable chains. Adding low-viscosity systems to the high-viscosity sample could therefore degrade the good overall fit. Without a joint mixture test, the diversity conclusion is an inference from the failures of each population alone, rather than a demonstrated explanation of the observed period-ratio data.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper uses N-body simulations of pebble-accreting planetary embryos in a low-viscosity disc (alpha = 10^-4) to study the formation of close-in super-Earth and mini-Neptune systems, and compares the outcomes with the high-viscosity (alpha = 5.4e-3) simulations of Izidoro et al. (2021). The authors find that low-viscosity discs produce wider resonant chains (4:3, 3:2, 2:1) at the end of the gas-disc phase, that about 95% of these chains become unstable after gas dispersal, and that the few surviving chains match the period ratios of observed resonant chains such as TRAPPIST-1, TOI-178, and Kepler-223 better than high-viscosity simulations do. Since low-viscosity simulations alone do not match the overall Kepler period-ratio distribution while high-viscosity simulations do, the paper proposes that a diversity of disc viscosities is needed to explain both resonant and non-resonant systems.","tokens_in":23913,"tokens_out":9342,"duration_ms":90881,"significance":"The hypothesis that disc viscosity, through partial gap opening and slower migration, sets the width of resonant chains is timely and physically plausible. The paper builds on established prescriptions (Paardekooper et al. 2011; Kanagawa et al. 2018; Johansen et al. 2015), includes synthetic transit observations, and provides valuable control experiments (Appendix G's two-planet migration test and Appendix D's embryo-number comparison) that support the causal role of viscosity rather than initial conditions. The honest presentation of the low-viscosity model's failures, such as the mass distribution and the overall period-ratio mismatch, is a strength. If the diversity-of-viscosity picture can be demonstrated with a quantitative joint fit, it would reconcile the existence of wide resonant chains with the broader Kepler period-ratio distribution and connect disc physics to the presence or absence of inner super-Earths. However, the paper's central claim is currently supported only by two separate subset comparisons and not by a combined model.","major_comments":[{"comment":"The central diversity claim is not directly tested. The paper shows that low-viscosity chains match the period ratios of observed chains (Fig. 6) and that high-viscosity simulations from Izidoro et al. (2021) match the overall Kepler period-ratio distribution (Fig. 5), but it never combines the two populations into a single mixed model and compares that model to the full Kepler sample. Appendix F mixes 2% stable with 98% unstable low-viscosity systems, not low- and high-viscosity systems, and the text states that this mixture still fails to reproduce the observed period ratios. Because the low-viscosity simulations are too tightly packed overall (Sect. 3.3) and too low in mass (Appendix E), it is not obvious that adding them to the high-viscosity sample would preserve the good overall fit. A quantitative joint fit, for example varying the low-viscosity fraction and comparing synthetic period-ratio distributions to Kepler with a two-sample test, is needed to support the title claim.","section":"§3.3, §5, Appendix F"},{"comment":"The stable-chain sample is very small: about 95% of the low-viscosity resonant chains become unstable (Sect. 3.3), leaving roughly 2-3 chains among 50 runs. The period-ratio match in Fig. 6 therefore rests on a handful of systems, and the sampling uncertainty is not quantified. Moreover, the left panel of Fig. 6 shows that low-viscosity chains contain only four or more planets, while the observed chain sample includes systems with two or three planets, so the match to the chain population is incomplete. A bootstrap or Poisson-resampling analysis and an explicit definition of the observed chain sample would make the comparison more convincing.","section":"§3.3, Fig. 6"},{"comment":"The eccentricity and inclination damping is implemented with the Cresswell & Nelson (2008) formulae without modification for partial gap opening, even though the central mechanism of the paper is partial gap opening at low viscosity. Resonance capture and the resulting period ratios depend on the balance between migration and damping, so a viscosity-dependent damping prescription, for example following Pichierri et al. (2023, 2024), could shift the chain outcomes. The paper acknowledges this in §2 but does not test the sensitivity. Please add a test, at least for a subset of runs or in the two-planet control of Appendix G, to show that the wider resonances at low viscosity are robust to the damping prescription.","section":"§2 (damping)"},{"comment":"The masses of the low-viscosity planets are systematically too low compared to the Kepler-derived masses (Fig. E.1), with most planets at or below roughly 3 Earth masses. Since the paper's target population is hot super-Earths and mini-Neptunes, the period-ratio match for the low-viscosity chains is achieved with systems that are not representative of the observed masses. The authors note this discrepancy, but the implications for the chain-match claim need to be discussed or addressed, for example by varying the pebble isolation mass prescription or including gas accretion; otherwise the low-viscosity model may explain period ratios only in a mass regime that is not the observed one.","section":"Appendix E"}],"minor_comments":[{"comment":"The high-viscosity value is written inconsistently as 5.4e-3 in Section 2, 5e-3 in Appendix D, and 0.005 in Appendix A; please unify.","section":"§2, Appendix A, Appendix D"},{"comment":"The caption states that the high-viscosity simulations produce 'wider systems' after instabilities, which seems inconsistent with the text's statement that the low-viscosity systems remain too tightly packed; please clarify the intended direction of the comparison.","section":"Fig. 5 caption"},{"comment":"Please define 'chains' more precisely and state how the observed chain sample is selected, including the number of planets and the resonance criterion, when the term is first used.","section":"§3.3"},{"comment":"The statement that the low-viscosity chains harbour only four or more planets, in contrast to the Kepler observations, needs a short explanation of why two- and three-planet chains are absent and whether this affects the period-ratio comparison.","section":"§3.3"},{"comment":"Baumann & Bitsch (2020) is cited in Section 4.1 but does not appear in the reference list; please add the reference or remove the citation.","section":"§4.1"},{"comment":"There are minor typographical issues, including 'benefitial' in Appendix B and the spacing in the caption 'Fig. F .1'; please correct them.","section":"Appendix B, Appendix F"},{"comment":"The notation 'K = 5 damping' is used without definition in this paper; please define it or refer explicitly to the relevant description in Bitsch & Izidoro (2023).","section":"Appendix D"},{"comment":"The 'better match' claims are based on visual comparison of cumulative distributions; reporting a quantitative goodness-of-fit statistic (for example a Kolmogorov-Smirnov test) would strengthen the conclusions.","section":"Figs. 4-6"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is likely to interest A&A readers. The main gap is not a technical error in the simulations but a missing joint-population test: the diversity-of-viscosity conclusion is inferred from two separate subset matches rather than demonstrated with a combined model against the full Kepler period-ratio distribution. The small number of stable chains and the mass discrepancy of the low-viscosity systems are additional risks. I believe these concerns are addressable within the scope of a revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nRead the Bitsch and Izidoro paper on disc viscosity and period ratios. Bottom line: the simulations are honest, the trend is real, and the paper is worth a serious referee, but the headline 'diversity of viscosities' claim is not tested as stated — it is inferred from two separate subset matches.\n\nWhat is actually new: this is the first low-viscosity (alpha = 1e-4) breaking-the-chains simulation without outer giants. It cleanly shows that low viscosity leads to wider resonances (3:2, 2:1) that resemble observed chains like TRAPPIST-1 and TOI-178, while high-viscosity runs produce tighter chains that fit the general Kepler period-ratio distribution. The controls in Appendix D and the two-planet experiment in Appendix G give good evidence that viscosity, not embryo number, drives this difference. I also appreciate the honesty: they report that low-viscosity systems alone remain too tightly packed and too low in mass (Appendix E), and that the damping prescription is unchanged despite partial gap opening (Sect. 2).\n\nThe soft spots are real but not fatal. First, the central 'diversity' claim is an inference, not a demonstration. The paper never combines low- and high-viscosity populations into a single mixture and compares to the full observed period-ratio distribution. Appendix F only mixes stable and unstable low-viscosity runs. This matters: adding low-viscosity systems could degrade the good overall fit of the high-viscosity runs. The abstract is careful ('may suggest'), so the paper is honest about the gap, but the title overshoots. Second, the damping treatment: using Cresswell and Nelson (2008) unchanged across viscosities is a known simplification, and resonance capture depends on the balance between migration and damping. A revised damping law could shift outcomes. Third, the chain match rests on about 5% of 50 runs — a handful of stable systems with no error bars. That is thin for the paper's centerpiece.\n\nNet: a solid contribution that advances the conversation about resonant chain formation. For publication, I would want either a joint mixture test or scaled-back language, plus a note on how the small stable-chain sample affects the chain comparison. The paper deserves peer review and likely publication with revisions.","headline":"Stated diversity claim is inferred rather than tested, but the low-viscosity chain result is new, honest, and deserves a serious referee.","tokens_in":24600,"tokens_out":2844,"would_cite":true,"duration_ms":50739,"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 the orbital spacing of hot super-Earth systems is set by disc viscosity: low-viscosity discs build wide resonance chains like TRAPPIST-1, high-viscosity discs the tighter Kepler packing.","keywords":["disc viscosity","planetary migration","mean-motion resonances","super-Earths","mini-Neptunes","pebble accretion","period ratios","resonance chains"],"falsifier":"Re-run the low-viscosity simulation suite with eccentricity and inclination damping modified by partial gap opening instead of the fixed Cresswell & Nelson (2008) formulas; if the wide 3:2 and 2:1 chains no longer form, the central mechanism fails. The paper's own caveat in Sect. 2 identifies this damping input as the step that could most plausibly change the result.","tokens_in":23459,"feed_emoji":"🪐","tokens_out":16649,"duration_ms":129549,"temperature":0.7,"pith_summary":"This paper argues that the variety of orbital spacings seen among hot super-Earths and mini-Neptunes is set by one quantity: the viscosity of the gas disc in which the planets formed. In low-viscosity discs, planets of a few Earth masses open partial gaps that slow their inward migration, so they lock into wide resonance chains with 4:3, 3:2, and 2:1 period ratios, matching observed chains like TRAPPIST-1, TOI-178, and Kepler-223. In high-viscosity discs, faster migration produces tighter chains, mostly 7:6, 5:4, and 4:3, which reproduce the overall period-ratio distribution of the Kepler sample. After the gas disperses, damping ceases and about 95% of the low-viscosity chains are destroyed by instabilities triggered by leftover outer planets, leaving roughly half of the systems without planets interior to 200 days. Because neither viscosity alone fits all observations, the authors conclude that planetary systems form in natal discs with a diversity of viscosities, and they speculate that the violent destruction of inner planets in low-viscosity systems matches the observed lack of close-in planets around many Sun-like stars.","feed_headline":"Disc viscosity sets the orbital spacing of super-Earth systems","feed_subtitle":"Low-viscosity discs yield wide chains like TRAPPIST-1; higher-viscosity discs yield the tighter Kepler packing","key_machinery":"The controlling mechanism is the migration speed of growing planets and its dependence on disc viscosity, implemented through the type-I migration torque of Paardekooper et al. (2011) with a gap-opening correction from Kanagawa et al. (2018). The correction lengthens the migration timescale by a factor $\\Sigma_{\\mathrm{up}}/\\Sigma_{\\mathrm{min}} = 1 + 0.04 K_{\\mathrm{mig}}$, where $K_{\\mathrm{mig}} \\propto (M_p/M_\\star)^2 (H/r)^{-5} \\alpha^{-1}$; at $\\alpha = 10^{-4}$ this factor becomes large, so a few-Earth-mass planet migrates slowly, while at $\\alpha = 5 \\times 10^{-3}$ it barely acts. Because resonance capture depends on the relative migration velocity of converging planets, the viscosity sets which resonances form — verified by the paper's two-planet experiment of Appendix G, where increasing $\\alpha$ monotonically tightens the final resonance ratio. The second stage of the argument is the post-gas instability: once eccentricity and inclination damping switch off, outer planets excite eccentricities and break or destroy the chains, and the different outer-planet populations in the two viscosity regimes determine how violent that destruction is.","core_discovery":"The paper's central claim is that the period ratios of close-in super-Earth and mini-Neptune systems — both the wide resonance chains and the bulk non-resonant population — are a direct readout of disc viscosity. In simulations with $\\alpha = 10^{-4}$, growing planets of a few Earth masses open partial gaps that slow their type-I migration, so converging planets trap each other into wide resonances (4:3, 3:2, and 2:1), matching the observed chains of TRAPPIST-1, TOI-178, and Kepler-223. In simulations with $\\alpha = 5 \\times 10^{-3}$, gap opening is suppressed, migration is faster, and the resulting chains are tighter (7:6, 5:4, and 4:3), which matches the overall Kepler period-ratio distribution. Once the gas disc dissipates, the low-viscosity chains become violently unstable: about 95% experience giant impacts, driven by massive leftover planets beyond $P > 200$ days, and about half of the final systems contain no planet interior to 200 days while all retain outer planets. The authors conclude that a mixture of viscosities is required in nature — low-viscosity discs for the observed resonant chains, high-viscosity discs for the bulk of the non-resonant census — and that the violent fate of low-viscosity inner systems may explain the scarcity of inner planets around a large fraction of Sun-like stars.","pith_inferences":["A testable extension: if low-viscosity formation destroys inner systems, then stars lacking close-in super-Earths should preferentially retain outer sub-Neptunes beyond about 200 days, a correlation that transit and radial-velocity surveys could check.","If gap-modified eccentricity and inclination damping is adopted — the paper flags this as future work — the wide 3:2 and 2:1 chains must persist for the viscosity-diversity interpretation to hold; otherwise the resonance ladder itself would shift.","The viscosity logic also predicts a mass signature: inner planets built in low-viscosity discs grow only to the local pebble-isolation mass (roughly 3 Earth masses here), so surviving chains should be systematically less massive than the products of high-viscosity formation, which transit-timing-variation measurements could separate."],"forward_implications":["Observed wide resonance chains — TRAPPIST-1, TOI-178, Kepler-223 — have a formation channel in low-viscosity discs, which the high-viscosity simulations cannot supply.","The overall Kepler period-ratio census remains best matched by the high-viscosity simulations, so both regimes are required to explain the full sample.","About 95% of low-viscosity resonance chains go unstable, and about half of the final systems lose all planets interior to ~200 days, offering a pathway to the observed rarity of inner planets around many Sun-like stars.","Because the outcome depends on migration speed rather than the growth pathway, the viscosity explanation should hold whether planets grow by pebble or planetesimal accretion and for a range of initial embryo configurations.","Surviving resonance chains most plausibly formed at low viscosity without nearby external perturbers, since perturbers efficiently destroy chains."],"supporting_citations":[{"why":"Supplies the high-viscosity simulations ($\\alpha = 5.4 \\times 10^{-3}$) that form the comparison baseline and best match the overall Kepler period-ratio distribution.","marker":"Izidoro et al. (2021)"},{"why":"Provides the type-I migration torque prescription whose rate the paper varies through the disc viscosity.","marker":"Paardekooper et al. (2011)"},{"why":"Gives the gap-opening correction that lengthens the migration timescale at low viscosity, the mechanism behind wider resonance chains.","marker":"Kanagawa et al. (2018)"},{"why":"Supplies the eccentricity and inclination damping formulae applied unchanged across viscosities, the paper's stated weakest input.","marker":"Cresswell & Nelson (2008)"},{"why":"Describes the FLINTSTONE N-body code with pebble accretion and migration used in all simulations.","marker":"Bitsch et al. (2019a)"},{"why":"Independent parameter study finding that viscosities $\\alpha \\leq 10^{-3}$ favour Kepler-223, corroborating the low-viscosity chain result.","marker":"Hühn et al. (2021)"},{"why":"Established the breaking-the-chains scenario, where instabilities after gas dispersal break resonance chains and shape observed multiplicities.","marker":"Izidoro et al. (2017)"},{"why":"Determined the Kepler-223 chain of 4:3, 3:2 and 4:3 resonances, one of the observed wide chains the low-viscosity models reproduce.","marker":"Mills et al. (2016)"},{"why":"Determined the TOI-178 2:4:6:9:12 Laplace chain, a wide configuration the paper attributes to low-viscosity formation.","marker":"Leleu et al. (2021)"},{"why":"Prior low-viscosity simulations with outer giant planets that already suggested 2:1 resonances are common at low viscosity and that separate viscosity from embryo-number effects.","marker":"Bitsch & Izidoro (2023)"}],"fun_headline_variants":["Disc viscosity drives super-Earth resonance widths","Wide or tight exoplanet chains? Blame disc viscosity","Super-Earth spacings trace natal disc viscosity","Viscous discs explain packed and spaced super-Earths","Diverse disc viscosities shape super-Earth orbits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that eccentricity and inclination damping has the same strength at every disc viscosity, even though the partial gaps that slow migration in the low-viscosity case should alter those damping rates, and resonance capture, which sets the period ratios, depends on the balance between migration and damping.","fun_headline_variants_meta":{"raw":{"variants":["Disc viscosity drives super-Earth resonance widths","Wide or tight exoplanet chains? Blame disc viscosity","Super-Earth spacings trace natal disc viscosity","Viscous discs explain packed and spaced super-Earths","Diverse disc viscosities shape super-Earth orbits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000534,"raw_usage":{"total_tokens":2700,"prompt_tokens":1211,"completion_tokens":1489,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":827,"completion_tokens_details":{"reasoning_tokens":1411}},"tokens_in":827,"tokens_out":1489,"duration_ms":9054,"temperature":1.0,"reasoning_tokens":1411,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:31:44.068011+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the low-viscosity simulation suite with eccentricity and inclination damping modified by partial gap opening instead of the fixed Cresswell & Nelson (2008) formulas; if the wide 3:2 and 2:1 chains no longer form, the central mechanism fails. The paper's own caveat in Sect. 2 identifies this damping input as the step that could most plausibly change the result.","supporting_citations":[{"cited_title":"J., Baruteau , C., & Kley , W","cited_arxiv_id":null,"evidence_quote":"Provides the type-I migration torque prescription whose rate the paper varies through the disc viscosity."},{"cited_title":"D., Tanaka , H., & Szuszkiewicz , E","cited_arxiv_id":null,"evidence_quote":"Gives the gap-opening correction that lengthens the migration timescale at low viscosity, the mechanism behind wider resonance chains."},{"cited_title":"& Nelson, R","cited_arxiv_id":null,"evidence_quote":"Supplies the eccentricity and inclination damping formulae applied unchanged across viscosities, the paper's stated weakest input."}],"review_version":1}