{"id":"918cf296-deae-46ca-b35c-7321f505b0d2","arxiv_id":"2505.22806","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Compact exoplanetary systems may form during late disk infall, with planet masses set by a balance between solid accretion and gas-driven inward migration.","lead":"This paper proposes that compact multi-planet systems like TRAPPIST-1 formed during the final infall of gas and dust onto their star, when planet growth was balanced by inward migration. The model naturally yields total planet masses of a few 10^-5 to 10^-4 of the stellar mass, matching observed compact systems and explaining their similar mass ratios.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central mass-ratio result hinges on the unmodeled premise that planetesimals form inside r_c before infall decays; the paper's own Methods states that grain-growth-to-planetesimal models are lacking and collapse conditions are unclear.","rationale":"The paper is a coherent, well-argued concept piece. The analytical scalings and N-body simulations are mutually consistent, and the predicted Mtot/M* range matches observations across three orders of magnitude of (alpha*epsilon/f). The treatment of inner cavities and long-term instability is thoughtful. The weakest point is not the migration physics but the input condition that planetesimals exist in the infall region during final infall. This is acknowledged in the manuscript, and it is load-bearing: without it the entire accretion-migration regulator is inert. I agree with the reader's identification. The concern is not an internal contradiction; it is an unresolved boundary condition. A dedicated dust-growth and streaming-instability calculation would settle whether the premise is plausible enough to carry the prediction. If the test fails, the model would need to be restricted to special disks where planetesimal formation is accelerated. Since the reader already returned CONDITIONAL with this as the weakest assumption, my pass does not require changing the verdict. I would not label the paper unsound; the limitation is explicit and the authors are transparent about it. Independent support includes deposited input and output files for Figure 4a share, although the modified SyMBA code is proprietary and no formal verification exists. The central claim should remain conditional on the planetesimal-formation premise until tested.","tokens_in":26511,"tokens_out":12231,"duration_ms":130265,"concrete_test":"Run a coupled dust-coagulation and streaming-instability calculation using the Methods disk state (alpha=1e-4 to 1e-3, T>1000 K, r_c<1 au, infall flux F0) to determine whether grains reach St~0.01-0.1 and midplane Z exceeds the resolution-corrected Zcrit within tau_in=3e5 yr. If collapse occurs before infall decays, the premise is supported; if the required time exceeds tau_in or Z remains below Zcrit, Eq. 4's regulated mass ratio is not established for generic conditions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that infall-produced planets survive with Mtot/M* regulated to a few 1e-5 to 1e-4 (Eq. 4)—only operates if km-sized planetesimals appear inside r_c while infall is still decaying. The paper states this explicitly: 'A premise of our model is that planetesimals form somewhere within the region of infall (i.e., at or interior to r_c) during the final infall stage.' The Methods section 'Dust-to-planetesimal accretion' then concedes that 'models that explicitly treat grain growth up to planetesimal formation are lacking, and whether conditions for collapse are actually achieved is unclear, particularly for turbulent disks.' The N-body simulations bypass the premise by injecting infalling solids as bodies of mass a few×1e-8 M* interior to r_c, and the analytical tau_acc assumes the solid infall rate limits accretion rather than the dust-to-planetesimal step. If growth to St~0.01-0.1 or streaming-instability collapse (Z>=Zcrit, with Zcrit~0.02-0.2 for alpha=1e-4-1e-3 and St=0.1-0.01) takes longer than tau_in~3e5-1e6 yr, the accretion-migration balance in Eq. 2 never establishes and Eq. 4's mass-ratio regulation does not follow. Thus the predicted universal mass ratio holds only within a regime whose accessibility is argued by plausibility, not demonstrated. The concern is about an unmodeled physical step, not an algebraic inconsistency.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that compact multi-planet systems form during the final infall phase of the circumstellar disk, rather than after infall ends. In the proposed scenario, planet masses are set by a balance between the accretion of infalling solids and increasingly rapid Type-I migration, so that the total system mass is regulated to a few times 10^-5 to 10^-4 of the stellar mass (Eq. 4). The authors derive this mass ratio analytically (Eqs. 2-4) and support it with N-body simulations that inject growing bodies into an infall-supplied disk. They argue that the weak dependence of the final mass ratio on disk and infall parameters explains the observed clustering of compact-system mass ratios, the 'peas-in-a-pod' architecture, and the weak metallicity dependence. The paper explicitly identifies as a premise that planetesimals form interior to the centrifugal radius r_c during the final infall stage, and it acknowledges that the dust-to-planetesimal growth step is not modeled.","tokens_in":26848,"tokens_out":8010,"duration_ms":86870,"significance":"If the central premise holds, the paper offers a novel and potentially important explanation for the observed common mass ratio of compact exoplanetary systems, one that naturally connects to the physics of infall and migration. The analytical derivation is internally consistent, the N-body simulations reproduce the analytical scalings across a wide parameter range, and the paper makes falsifiable predictions (weak metallicity dependence, a transition in mass-ratio behavior near r_c, and early accretion during infall). The authors also provide data for the simulations. However, the entire framework rests on the unmodeled assumption that planetesimals form efficiently inside r_c during the final infall stage; the paper itself states that models for this growth are lacking. This limits the current significance to a plausibility argument rather than a demonstrated formation pathway.","major_comments":[{"comment":"The central claim of the paper, expressed in Eq. (4) and the abstract, depends on planetesimal formation interior to r_c during the final infall stage. The paper states this as a premise in the Results and then concedes in the Methods section 'Dust-to-planetesimal accretion' that 'models that explicitly treat grain growth up to planetesimal formation are lacking, and whether conditions for collapse are actually achieved is unclear, particularly for turbulent disks.' The analytical accretion timescale (Supplemental Discussion 2, Eq. 2.2) and the N-body injection scheme assume that the solid infall rate limits accretion; they do not include the time or efficiency of the dust-to-planetesimal step. If growth to Stokes number St ~ 0.01-0.1 and streaming-instability collapse at Zcrit ~ 0.02-0.2 for alpha = 10^-4 to 10^-3 takes longer than tau_in ~ 3 x 10^5 to 10^6 yr, the tau_acc ~ tau_I balance in Eq. (2) never establishes and Eq. (4)'s mass-ratio regulation does not follow. Please either provide a quantitative estimate of the dust-to-planetesimal timescale in the inner infall region, or show that the final mass ratio is insensitive to delayed or inefficient planetesimal formation (e.g., through N-body experiments with delayed injection of solids).","section":"Results, 'A premise of our model'; Methods, 'Dust-to-planetesimal accretion'"},{"comment":"In the N-body simulations, the infalling solids are injected as bodies of mass a few x 10^-8 M_sun, which for a solar-mass star is about 3 x 10^-3 M_Earth, roughly four to five orders of magnitude more massive than km-sized planetesimals. This injection scheme bypasses not only the dust-to-planetesimal stage but also the growth from planetesimals to embryos. The simulations therefore validate the accretion-migration balance only after a population of massive embryos is assumed to exist; they do not provide independent evidence for the planetesimal-formation premise. I recommend that the authors state this limitation explicitly in the main text and, if feasible, test sensitivity to the injected mass and to the temporal and radial distribution of injection.","section":"Methods, 'Infall description' and 'N-body planet accretion simulation'"}],"minor_comments":[{"comment":"The sentence 'The flux density at different wavelengths in systems undergoing infall is indicative of grain growth [15]' appears to cite reference [15] (Tychoniec et al. 2020), which is a dust mass survey; please verify the intended citation.","section":"Introduction, paragraph 4"},{"comment":"In the definition of chi, the normalization constants '16 Myr' and '100 days' are used without explanation; a brief statement that these are dimensionless normalizations would improve readability.","section":"Results, Eq. (2)"},{"comment":"Please unify the notation for the parameter combination that appears variously as alpha epsilon / f and alpha epsilon/f; in particular, check that the x-axis label in Figure 3 matches the text.","section":"Figures 2 and 3"},{"comment":"The phrase 'few 10^{-5} to 10^{-4}' contains a missing space and is informal; consider replacing with 'approximately 10^{-5} to 10^{-4}'.","section":"Abstract"},{"comment":"The two-stage viscosity treatment for initially massive disks (setting alpha = 0.1 for the initial state and then reducing to alpha = 10^-4) is described in one sentence; a brief justification of this procedure would help the reader assess its influence on the derived beta values.","section":"Methods, 'Relative timescales of gas disk dispersal vs. infall'"}],"recommendation":"major_revision","confidential_remarks":"This is a well-written concept paper that extends the authors' satellite-formation framework to compact exoplanet systems. The main risk is the unmodeled planetesimal-formation premise, which the authors acknowledge; without a quantitative treatment or at least numerical experiments that relax the instantaneous-formation assumption, the central mass-ratio prediction remains conditional. If the authors can address this, the paper would be a strong contribution. I also note that the paper leans heavily on the authors' own prior framework (Canup & Ward 2002, 2006), and a broader discussion of alternative post-infall formation models would strengthen the presentation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper gives a physical mechanism for the observed common mass ratio of compact multi-planet systems: planets form during the final infall phase, and their mass is set by the balance between accretion of infalling solids and inward Type-I migration. That is new and worth taking seriously. The analytical derivation is transparent, and the N-body simulations reproduce the analytical predictions across a range of parameters. The weak-metallicity-dependence prediction is a nice falsifiable consequence that distinguishes the model from some alternatives.\n\nWhat it does well: the derivation is internally consistent (eqns. 2-4 are the backbone, and the supplementary derivation checks out), the simulations span two stellar masses and both with and without inner cavities, and the paper is unusually honest about its own limitations. The Methods section explicitly concedes that models for grain growth up to planetesimal formation are lacking and collapse conditions are unclear, particularly for turbulent disks.\n\nThat concession points to the real soft spot. The load-bearing premise is that km-sized planetesimals form interior to rc during the few 1e5 yr of infall. The N-body simulations bypass this by injecting solids as a few 1e-8 M* bodies, and the analytical tau_acc assumes the solid infall rate limits accretion rather than the dust-to-planetesimal step. If growth to St ~ 0.01-0.1 or streaming-instability collapse takes longer than tau_in ~ 3e5-1e6 yr, the accretion-migration balance never establishes and eqn. 4's mass-ratio regulation fails. The paper argues plausibility from high-temperature sticking, vortices, and drift pile-up, but it does not demonstrate the timescale. That is a genuine unmodeled physical step, not an algebraic inconsistency, and the paper says so.\n\nThe absolute normalization also depends on (alpha epsilon/f), H/r, and Min/M*, none of which are tightly constrained. The beta range 1.3-2 comes from a disk-evolution model with its own assumptions, though the paper checks that low-alpha fast-infall cases behave differently. The code is proprietary, but some simulation outputs are archived on Zenodo, which is at least partial credit.\n\nIf the planetesimal-formation premise holds, this explains a puzzling observational pattern that has resisted prior models. The premise is identified clearly and could be tested by dedicated dust-growth simulations. I would send this to peer review: the model is coherent, novel, and the weak spot is addressable in the literature rather than fatal. A referee should push on the premise and on whether the beta range is robust, but the paper merits serious engagement.","headline":"A genuinely new physical mechanism for the compact-system mass ratio, built on a coherent accretion-migration balance, with one large unmodeled planetesimal-formation premise that the paper honestly flags.","tokens_in":27403,"tokens_out":1503,"would_cite":true,"duration_ms":17660,"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 argues that compact multi-planet systems form during the final infall of gas and solids onto the disk, with planet masses set by a balance between solid accretion and inward Type-I migration, yielding a common system mass ratio…","keywords":["compact exoplanetary systems","planet formation","disk infall","Type-I migration","planetesimal formation","protoplanetary disks","system mass ratio","super-Earths"],"falsifier":"A survey of Class 0/I protostellar disks showing that planetesimals do not form interior to the centrifugal radius during infall would falsify the model's premise; a testable alternative is that compact-system mass ratios should be nearly metallicity-independent, so a strong metallicity trend would rule it out.","tokens_in":26252,"feed_emoji":"🪐","tokens_out":10627,"duration_ms":115023,"temperature":0.7,"pith_summary":"The paper proposes that the compact, short-period multi-planet systems seen by Kepler are relics of planet formation that happened while the circumstellar disk was still being fed by infall, not after infall ended. Inside the centrifugal radius, a growing planet's mass is capped by the point where the rate of solid infall equals the rate of inward gas-driven migration, because larger planets migrate faster. This self-regulating balance yields similar-sized planets and, integrated over the disk, a total system mass of a few $10^{-5}$ to $10^{-4}$ times the host star's mass across a wide range of disk and infall conditions. The predicted mass ratio is essentially independent of stellar mass and weakly dependent on metallicity, matching the observed 'peas-in-a-pod' compact systems and their weak metallicity bias.","feed_headline":"Infall-era accretion explains compact systems' common mass ratio","feed_subtitle":"A balance between infalling solids and inward migration fixes the system mass at a few 10^-5 to 10^-4 of the host star.","key_machinery":"The central object is the accretion-migration balance: a planet inside the centrifugal radius $r_c$ accretes infalling solids on a timescale $\\tau_{\\rm acc}\\propto M_p/(\\text{infall rate})$, while the gas disk drives inward Type-I migration on a timescale $\\tau_I\\propto (M_*/M_p)(\\Sigma_g r^2)^{-1}(H/r)^{-2}$. Setting $\\tau_{\\rm acc}=\\tau_I$ gives the critical mass $M_{\\rm crit}$ (eqn. 2); the mass density of critical-mass planets, integrated over the infall region, gives the system mass ratio (eqn. 3); and evaluating it when migration slows ($\\tau_I\\sim10\\tau_g$) gives the final ratio (eqn. 4). The analysis also uses a gas disk model with infall, viscous spreading, and photoevaporation to estimate $\\beta\\equiv \\tau_g/\\tau_{\\rm in}$ in the range $1.3$ to $2$ for compact ($r_c<1$ au) disks.","core_discovery":"On the paper's own terms, the central discovery is that the common mass ratio of compact exoplanetary systems is not an accident of initial conditions but a self-regulating outcome of accreting during infall. Equating the solid-infall-limited accretion timescale with the Type-I migration timescale yields a critical planet mass $M_{\\rm crit}$ (eqn. 2) that varies weakly with infall rate; planets near $M_{\\rm crit}$ migrate inward and are replaced by newly accreting ones, so the integrated system mass ratio $M_{\\rm tot}/M_*$ (eqn. 3) stays near a narrow band. When gas dispersal makes migration slow compared with the disk lifetime, the surviving systems retain a final mass ratio (eqn. 4) of a few $10^{-5}$ to $10^{-4}$, consistent with observations. The mechanism also produces the observed uniformity of planet sizes within each system.","pith_inferences":["If infall-era accretion is real, young Class 0/I disks should show dynamical or dust-continuum evidence of embedded massive bodies near $r_c$; searching for such signatures with ALMA would test the proposed timing of planet formation.","The model predicts that the innermost planet orbit traces the inner edge of the planetesimal formation region, so comparing minimum orbital periods with condensation-temperature radii across compact systems would provide a test.","The same accretion-migration balance may operate in any infall-fed disk, including circumplanetary disks, and the difference in the ratio of disk-dispersal to infall timescales may explain why satellite systems peak at a somewhat lower mass ratio than compact exoplanetary systems."],"forward_implications":["Compact systems should show a total mass ratio of a few $10^{-5}$ to $10^{-4}$ times the host star, nearly independent of stellar mass and of the specific infall rate or disk viscosity.","The system mass ratio depends on stellar metallicity only weakly, as a power of about $0.2$ to $0.3$, so compact systems should be found around stars of widely varying metallicity.","Systems with estimated mass ratios below the predicted range may host additional, as-yet-undetected planets, since the model sets a system-wide mass budget rather than a per-planet one.","After the gas disperses, dynamical instabilities can reshape the period-ratio distribution toward the observed, non-resonant configuration while changing the system mass ratio by only a few percent."],"supporting_citations":[{"why":"Provides the standard model of infalling gas and grains spreading in a viscous disk that the paper adopts for the gas surface density evolution.","marker":"[20]"},{"why":"Supplies the Type-I migration timescale (eqn. 1) that defines the critical mass and the whole accretion-migration balance.","marker":"[39]"},{"why":"Provides experimental evidence for enhanced grain stickiness at high inner-disk temperatures, supporting the premise that planetesimals form interior to $r_c$.","marker":"[25]"},{"why":"Gives streaming-instability thresholds that make planetesimal collapse plausible in the inner disk.","marker":"[29]"},{"why":"Updates streaming-instability criteria including turbulence, used to argue that inner-disk conditions may exceed the critical solid-to-gas ratio.","marker":"[30]"},{"why":"Models dust growth and radial drift, delivering solids inward and concentrating them near the star.","marker":"[23]"},{"why":"Provides prior N-body models of compact super-Earth formation via migration and resonant chains, used for comparison and for the post-dispersal instability evolution.","marker":"[6]"},{"why":"Presents the alternative narrow-ring planetesimal model that this paper contrasts with by forming planets interior to $r_c$ during infall.","marker":"[7]"}],"fun_headline_variants":["Infall-era planet growth sets compact systems' mass ratio","Compact exoplanets: a self-regulating infall accretion story","Disk infall balance explains uniform compact system masses","How infall-born planets survive to form compact systems"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that km-sized planetesimals form inside the centrifugal radius during the final infall stage, on a timescale shorter than the infall decay; the paper argues this is plausible from high-temperature sticking, streaming instability, and particle concentration, but does not model it.","fun_headline_variants_meta":{"raw":{"variants":["Infall-era planet growth sets compact systems' mass ratio","Compact exoplanets: a self-regulating infall accretion story","Disk infall balance explains uniform compact system masses","How infall-born planets survive to form compact systems"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000162,"raw_usage":{"total_tokens":1232,"prompt_tokens":934,"completion_tokens":298,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":232}},"tokens_in":550,"tokens_out":298,"duration_ms":4223,"temperature":1.0,"reasoning_tokens":232,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:00:17.579770+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A survey of Class 0/I protostellar disks showing that planetesimals do not form interior to the centrifugal radius during infall would falsify the model's premise; a testable alternative is that compact-system mass ratios should be nearly metallicity-independent, so a strong metallicity trend would rule it out.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides prior N-body models of compact super-Earth formation via migration and resonant chains, used for comparison and for the post-dispersal instability evolution."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Presents the alternative narrow-ring planetesimal model that this paper contrasts with by forming planets interior to $r_c$ during infall."}],"review_version":1}