{"id":"bb32d0e5-4d36-4f96-bb9a-c55c89e8fc52","arxiv_id":"2608.05661","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In convectively stable envelopes of embedded Earth-like planets, the dust-to-gas ratio falls by 2 to 4 orders of magnitude toward the core, because small grains are blocked by the recycling flow and large grains settle quickly.","lead":"Simulations of gas and dust around an Earth-mass planet in a protoplanetary disk show that the planet's envelope becomes heavily depleted of dust inward, with dust-to-gas ratios dropping by orders of magnitude near the core. Because dusty envelopes control how fast gas giant planets form, this depletion could speed up envelope cooling and change how planets get their atmospheres.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Concern: the prescribed beta=1 cooling time is the load-bearing assumption; if real envelopes cool faster or slower, the buoyancy barrier and the 2-4 dex depletion at 0.1 R_B may weaken or shift inward.","rationale":"The reader's weakest_assumption correctly identifies the prescribed beta=1 thermal structure as the most load-bearing element. The paper is explicitly framed as an idealized radiative end-member, and it depends on an in-press companion paper for the physical justification of this regime. The numerical results themselves are internally consistent and supported by 2D/3D convergence tests, but the generality of the '2-4 dex depletion' claim for disk-embedded planets rests on whether such nearly isothermal, convectively stable envelopes actually occur with beta around unity. A secondary caveat, noted by the reader, is that the abstract's St~1e-3 statement overlaps the range flagged in Appendix B as increasingly affected by numerical artifacts; this is worth correcting but does not dislodge the main depletion trend, which is robust at larger Stokes numbers. No code or data release was provided, which limits reproducibility but is not an internal flaw. The appropriate verdict remains CONDITIONAL, with the condition being a demonstration that the beta=1 regime is physically realized or a clear qualification of the claim to that regime. Since the reader already reached this verdict, no adjustment is proposed.","tokens_in":22137,"tokens_out":4691,"duration_ms":54122,"concrete_test":"Re-run the fiducial 3D case with beta=0.1 and beta=10, and, if available, with a radially varying beta(r) profile computed from the KL26c 1D envelope model at 10 au with kappa=1e-3 cm^2/g. Measure the recycling-radiative boundary radius and the shell-averaged dust-to-gas ratio at 0.1 R_B. If the depletion at 0.1 R_B weakens by more than 1 dex or the steep-decline radius moves inward to roughly 0.1 R_B, the beta=1 assumption is the load-bearing condition for the central claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central simulation result, a radially inward dust-to-gas ratio decrease of 2-4 dex in convectively stable envelopes, depends on the envelope being shielded from the recycling flow by a positive entropy gradient. That shielding is created by the imposed beta=1 cooling time (Sect. 2, Eq. 3), and the paper itself acknowledges that this corresponds to a restricted opacity range (kappa ~ 1e-3 cm^2/g at 10 au; KL26c) and that the isothermal limit lacks the buoyancy barrier (Appendix A). Since the recycling-radiative boundary moves inward as beta decreases (Sect. 5, Eq. 36; Appendix D), a real envelope with a shorter or longer cooling time could have a much deeper recycling flow and a correspondingly weaker or displaced dust-depletion profile. The manuscript frames this as an idealized end-member rather than a self-consistent thermal model, so the concern is about external applicability, not internal consistency. The claim that dust-depleted convectively stable envelopes are a robust outcome of planet formation is therefore only as strong as the beta=1 regime's representativeness.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents two- and three-dimensional multifluid (gas and dust) hydrodynamical simulations of an Earth-mass planet embedded in a protoplanetary disk, with a prescribed dimensionless cooling time beta=1 that maintains a nearly isothermal, convectively stable envelope. The central result is that the dust-to-gas density ratio decreases radially inward within the envelope, by more than two to four orders of magnitude at radii below 0.1 Bondi radius relative to the envelope outer edge. The proposed mechanism is that small grains (St <= 1e-3) remain entrained in the outer recycling flow and are shielded from entering the envelope, while larger grains (St >= 1e-2) penetrate but settle rapidly onto the core. The authors also construct a one-dimensional semi-analytic model based on a constant dust mass flux and a collision-rate prescription, and they discuss implications for envelope opacity, the onset of runaway gas accretion, and atmospheric metallicity.","tokens_in":22284,"tokens_out":14250,"duration_ms":155181,"significance":"If the result holds for realistic radiative envelopes, it is significant: it directly links envelope-scale gas dynamics to the dust opacity that regulates envelope cooling, and it provides a plausible pathway to sub-stellar atmospheric metallicities through dust filtering in the outer envelope. The paper benefits from a consistent demonstration of the depletion trend in both 2D and 3D, resolution and inner-boundary sensitivity tests in Appendix A, additional tests of headwind, adiabatic index, and cooling time in Appendix D, and unusually transparent statements of its limitations. In particular, the paper explicitly identifies the restricted opacity range needed for the beta=1 regime and the non-convergence of the smallest-grain run. The central depletion result is a direct simulation outcome and does not depend on the analytic model; however, the quantitative headline is conditional on the prescribed beta=1 radiative end-member.","major_comments":[{"comment":"The quantitative headline, namely a dust-to-gas reduction of more than two to four orders of magnitude at <0.1 R_B, is established only for the prescribed cooling time beta=1 (Sect. 2, Eq. 3). The paper's own analysis shows that this result is beta-dependent: Eq. (36) states that the recycling-radiative boundary scales as beta^0.22, and Appendix D (Fig. D.1c) states that the radius where the dust-to-gas ratio starts to decline moves inward as beta decreases. Because Sect. 2 further restricts the regime to a narrow opacity range (kappa ~ 1e-3 cm2/g at 10 au, from the companion paper KL26c), the abstract's unqualified statement that the depletion occurs in 'convectively stable envelopes' overreaches the presented support. I request either a quantitative statement of the depletion at 0.1 R_B as a function of beta (for example for beta=1, 0.1, and 0.01) or an explicit restriction of the abstract and conclusions to the beta=1 radiative end-member.","section":"Abstract; Sect. 5; Appendix D"}],"minor_comments":[{"comment":"The value xi=0.08m is introduced as 'chosen to match our numerical results', and the same 3D simulations are then used to validate the 1D model in Sect. 4 and Conclusions. The agreement shown in Fig. 5b is therefore partly a calibration rather than an independent test; this should be stated explicitly at the point where the model is described as reproducing the numerics.","section":"Appendix C, Eq. (C.10)"},{"comment":"The beta column for the fiducial runs appears to read '100' rather than '1', which is inconsistent with Table 1 and with the text of Sect. 2; this should be corrected.","section":"Table D.1"},{"comment":"The term 'nearly isothermal' is used for the beta=1 envelope, but with gamma=1.43 and a finite cooling time the gas is not strictly isothermal. Please quantify the temperature variation or clarify that 'nearly isothermal' refers to the small fractional temperature change in the simulation.","section":"Sect. 2, after Eq. (3)"},{"comment":"The high-resolution 3D convergence run (N_r,N_theta,N_phi)=(256,64,256) is integrated only for t_end=10 Omega^-1, much shorter than the fiducial 100 Omega^-1. Since the convergence claim in Fig. A.5 compares against this run, the authors should justify that this integration time is sufficient for a steady-state comparison.","section":"Appendix A, Table 1"},{"comment":"The discussion of micron-sized grains estimates settling times of order 10^3 Omega^-1 from the terminal-velocity approximation, which exceeds the simulated duration; the text should state explicitly that the abundance of such grains is an extrapolation rather than a simulated outcome.","section":"Sect. 6.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of A&A and the simulations appear carefully executed. My major concern is scope rather than internal correctness: the headline claim is demonstrated for a prescribed beta=1 end-member, and the paper's own beta-dependence tests weaken the unqualified abstract statement. The authors are transparent about the restricted opacity regime and the calibration of xi in the 1D model, so I see this as a fixable revision rather than a rejection. I would be willing to review a revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look, and I mean that. The genuinely new thing is that these are the first local multifluid simulations of a planet envelope that let dust leave through the inner boundary, and they show a clear inward depletion of the dust-to-gas ratio by 2-4 orders of magnitude in a convectively stable envelope. The result is robust across 2D and 3D, with convergence tests, and the mechanism is clean: small grains stay entrained in the recycling flow, large grains penetrate and settle. Prior studies missed this because they either lacked the inner sink or didn't quantify the depletion.\n\nI believe the central simulation result. The 1D analytic model reproduces the numerics, though with one fitted parameter (xi=0.08m in the 3D collision rate), so that part is partly circular. But the depletion is a direct simulation outcome, not an artifact of the model.\n\nThe soft spots are real but not fatal. The beta=1 cooling time is load-bearing: the positive entropy gradient that shields the envelope comes from the prescribed cooling, and the paper itself admits the isothermal limit lacks the buoyancy barrier and that this regime needs a restricted opacity range (kappa ~ 1e-3 cm^2/g at 10 au, from the companion paper). So the applicability to real envelopes is conditional, and the abstract overstates it a little. The abstract's claim about St<=1e-3 also goes below the range that Appendix B actually establishes; the smallest-grain run didn't converge, and there's a residual radial gas velocity issue at the St~1e-4 level. That should be qualified. The discrepancy with Johansen & Nordlund's nearly constant dust-to-gas ratio is acknowledged but not quantitatively explained. And there is no code or data release, so the runs can't be independently reproduced from the paper alone.\n\nBottom line: this deserves a serious referee. The core result is credible, and the caveats are revision-level, not rejection-level. Anyone modeling envelope cooling or interpreting sub-stellar atmospheric metallicities will want to see this.","headline":"Solid, genuinely new simulations show strong inward dust depletion in convectively stable envelopes; the main caveat is that the result depends on the prescribed beta=1 thermal regime.","tokens_in":22945,"tokens_out":5210,"would_cite":true,"duration_ms":46144,"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":"The envelope of an embedded Earth-mass planet becomes strongly depleted in dust, by two to four orders of magnitude in the deep interior, because small grains are screened out by the recycling gas flow while large grains settle and…","keywords":["protoplanetary disks","planet formation","dust transport","envelope recycling flow","dust-to-gas ratio","gas accretion","multifluid hydrodynamics","convectively stable envelope"],"falsifier":"Run the same standard runs with a shorter cooling time (β=$10^{-2}$) or with self-consistent radiative cooling: if small grains then penetrate the envelope and the dust-to-gas ratio at 0.1 R_B stays within a factor of ten of its value at the Bondi radius, the central depletion claim fails.","tokens_in":21823,"feed_emoji":"🪐","tokens_out":6598,"duration_ms":62041,"temperature":0.7,"pith_summary":"The paper argues that the gaseous envelope around an embedded Earth-mass planet, when it is nearly isothermal and convectively stable, becomes strongly depleted in dust. In 2D and 3D multifluid simulations, the dust-to-gas ratio falls monotonically inward, reaching values two to four orders of magnitude below the envelope's outer edge inside 0.1 Bondi radius. The reason is size-selective delivery: small grains stay locked to the recycling gas flow and never enter the envelope, while large grains enter but settle onto the core too quickly to accumulate. This matters because dust is the main source of envelope opacity; a dust-depleted envelope cools faster and may trigger runaway gas accretion sooner, and it sets a stringent route for enriching the deep envelope with volatiles.","feed_headline":"Envelope dust drops by up to four orders of magnitude","feed_subtitle":"Small grains are screened out; large grains sink fast, clearing the envelope's opacity and speeding gas accretion.","key_machinery":"The central object is the radial dust-to-gas density ratio profile inside the Bondi sphere, and the mechanism that sets it is a two-population filter. A buoyancy barrier (positive entropy gradient) near the Bondi radius, maintained by a prescribed short cooling time β=1, stops the polar recycling inflow from penetrating the inner envelope; this is the gate that excludes small grains. For grains that do enter, the key identity is the constant inwards dust mass flux F_d = 4π $r^{2}$ v_in(r) ρ_d(r) (or 2π r ... in 2D), which, together with an infall speed v_in = min(v_term, v_ff) and a collision-rate prescription P_col(St) for grains entering from the disk, yields the 1D analytic formula for the dust density. The Stokes number St = t_s Ω_0 is the dimensionless stopping time that separates the two behaviours: St≲$10^{-3}$ grains track the gas and are screened out, St≳$10^{-2}$ grains decouple and sediment.","core_discovery":"On the paper's own terms: in a convectively stable (nearly isothermal) envelope around a low-mass planet, dust depletion is a robust outcome of the gas–dust dynamics, not a boundary artifact. The simulations resolve an outer recycling flow that is blocked from the inner envelope by a positive entropy (buoyancy) barrier near the Bondi radius, and an inner envelope that is therefore shielded from incoming small grains. Grains with Stokes number St≲$10^{-3}$ remain entrained in the recycling flow and do not cross into the envelope; grains with St≳$10^{-2}$ do enter but sediment rapidly onto the core along the midplane. The result is that the envelope is depleted of both small and large grains, with the dust-to-gas ratio reduced by more than two to four orders of magnitude at r<0.1 R_B compared with the value at the envelope edge. The depletion is robust across 2D and 3D simulations, across Stokes numbers from $10^{-3}$ to $10^{-1}$, and across fixed-size runs, and it is reproduced by a simple 1D model equating a radially constant dust mass flux with an infall velocity set by the smaller of the terminal and free-fall speeds.","pith_inferences":["If the depletion persists in self-consistent thermal models, published envelope-cooling timescales that assume a constant dust-to-gas ratio may be overestimates, and population syntheses should treat the dust-to-gas ratio as a radially decreasing function of the local envelope structure.","The same size-selective filtering should operate for other volatile carriers: only solids that arrive as large pebbles and disaggregate deep inside can enrich the atmosphere, which predicts a link between the pebble size distribution in the disk and the atmospheric metallicity of the planet.","The 1D collision-rate framework could be extended to predict depletion as a function of planet mass and disk location, offering a testable scaling before full 3D runs are done."],"forward_implications":["A convectively stable envelope is depleted of dust throughout most of its volume, so the interior dust opacity is far below the ISM-like value often assumed; envelope cooling is faster and the onset of runaway gas accretion can occur earlier, especially in the outer disk (≳10 au).","Because small grains are screened out, the deep envelope (<0.1 R_B) can only be enriched in dust or volatiles by large pebbles that fragment or sublimate once they have penetrated that deep.","The depletion profile is insensitive to the assumed Stokes number or grain size over the tested range, so the result is a generic expectation for radiative envelopes rather than a fine-tuned outcome.","The 1D analytic model (constant dust mass flux with terminal/free-fall infall speed and a collision rate P_col) reproduces the simulated profiles, giving a cheap tool for modelling dust distributions in envelope evolution calculations.","The dust-to-gas ratio is anisotropic in 3D, peaking at the midplane, which allows polar radiation escape and may further enhance cooling."],"supporting_citations":[{"why":"Presents the grid-based hydrodynamics code used for all gas and dust simulations.","marker":"Stone et al. 2020"},{"why":"Provides the multifluid dust framework that couples gas and dust via drag in the simulations.","marker":"Huang & Bai 2022"},{"why":"Identifies the recycling flow structure and the inner bound atmosphere that the paper resolves.","marker":"Ormel et al. 2015b"},{"why":"Gives the specific collision rate P_col of pebbles in non-Keplerian flow, used to close the 1D dust-density model.","marker":"Okamura & Kobayashi 2021"},{"why":"Provides the convectively-stable envelope structure and the recycling-radiative boundary fitting formula that justify the β=1 setup.","marker":"Kuwahara & Lambrechts 2026a"},{"why":"Shows that a positive entropy gradient (buoyancy) blocks polar inflow, the barrier that shields the envelope from small grains.","marker":"Kurokawa & Tanigawa 2018"},{"why":"Previously found little particle accumulation in a convectively stable envelope, consistent with the depletion reported here.","marker":"Popovas et al. 2018"}],"fun_headline_variants":["Envelope dust drops up to four orders of magnitude","Small grains bounce, large grains sink: envelope dust cleared","Dust-free envelopes speed gas accretion in planet formation","Envelope dust depletion: up to 10^4 inward drop","Convectively stable envelopes starve of dust"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the envelope really is convectively stable with a sharp buoyancy barrier, which is imposed by hand through a short cooling time (β=1); if real opacity or accretion heating sets a different thermal structure, the recycling flow can penetrate deeper and the strong dust depletion can shrink or disappear.","fun_headline_variants_meta":{"raw":{"variants":["Envelope dust drops up to four orders of magnitude","Small grains bounce, large grains sink: envelope dust cleared","Dust-free envelopes speed gas accretion in planet formation","Envelope dust depletion: up to 10^4 inward drop","Convectively stable envelopes starve of dust"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000918,"raw_usage":{"total_tokens":4001,"prompt_tokens":1070,"completion_tokens":2931,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":686,"completion_tokens_details":{"reasoning_tokens":2851}},"tokens_in":686,"tokens_out":2931,"duration_ms":20669,"temperature":1.0,"reasoning_tokens":2851,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T04:33:34.048243+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same standard runs with a shorter cooling time (β=$10^{-2}$) or with self-consistent radiative cooling: if small grains then penetrate the envelope and the dust-to-gas ratio at 0.1 R_B stays within a factor of ten of its value at the Bondi radius, the central depletion claim fails.","supporting_citations":[],"review_version":1}