{"id":"f3f140b0-3c07-4da9-bdea-fbe408883c4c","arxiv_id":"2505.07937","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The sign of the disk's radial temperature gradient decides which Lagrange point, L4 or L5, collects more gas around an embedded planet, breaking the classical symmetry of the restricted three-body problem.","lead":"Hydrodynamic simulations of a planet inside a gas disk show that gas piles up at the leading or trailing co-orbital Lagrange point depending on whether the disk gets warmer or cooler with distance from the star. If real crescents in protoplanetary disks follow the same rule, their shape and position can reveal the disk's local temperature structure and help estimate the planet mass.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed physical origin is not derived: the symmetry-breaking beta dependence is entirely contained in delta_v_r imported from the simulations, so the mechanism may be a restatement of the asymmetry rather than an explanation.","rationale":"The reader's weakest_assumption and my concern coincide: Section 4 never derives the beta-dependence of delta_v_r. Inspecting Eqs. (8)-(9) shows that the only beta-dependent term in the analytical field is axisymmetric; the L4/L5 selection must come from delta_v_r, which is read off the same simulations whose asymmetry it is supposed to explain. This does not invalidate the empirical result—the beta-sign trend is tested with controlled parameter variations and is consistent with earlier L5-dominated crescents in negative-gradient disks—but it makes the 'origin' claim in the title and abstract conditional on a non-circular, non-numerical delta_v_r. I also note the 'solely' language is stronger than the explored grid: positive beta is tested only at the fiducial mp,hp, while the 83-run grid uses beta=-0.1. That is a secondary concern about amplitude/universality, not about the sign-selection result. The concrete test of extracting delta_v_r at t=10 orbits and feeding it into the model would establish causal direction and separate a genuine beta-controlled background from a co-evolving response. If the test succeeds, the mechanism is credible; if not, Section 4 should be reframed as a phenomenological fit rather than the origin. Either way the empirical finding merits publication, so I keep the reader's CONDITIONAL verdict.","tokens_in":14138,"tokens_out":7063,"duration_ms":78424,"concrete_test":"Extract the corotation-radius delta_v_r profile from the fiducial beta=+/-0.1 runs at t=10 orbits—well before the L4/L5 overdensities appear—and feed it into Eqs. (8)-(9). If the model then predicts the late-time L4-enhancement for beta>0 and L5-enhancement for beta<0, the imported velocity field acts as a causal driver and the mechanism is supported; if the delta_v_r asymmetry appears only after the density contrast grows, or predicts the wrong point, the Section 4 explanation is circular or incomplete.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weak point is the causal mechanism in Section 4. The only explicit beta term in the semi-analytical model, h_p^2 beta/2 in Eq. (8), is azimuthally symmetric and thus cannot by itself distinguish L4 from L5. The symmetry-breaking agent is entirely the delta_v_r term added to Eq. (9), and the paper states 'by taking this delta_v_r component from our simulations we can effectively deform the libration region.' The model therefore imports the simulation's outcome rather than deriving the beta-dependence. If delta_v_r is a response to the growing density contrast rather than a pre-existing perturbation set by beta, the causal arrow is backwards; if delta_v_r is a numerical artifact of the 2D locally isothermal setup, fixed smoothing length epsilon=0.6 H_p, or the chosen resolution (no convergence tests are shown), the claimed physical origin fails even though the empirical beta-sign trend may survive. No independent derivation of delta_v_r from the linearized equations or from a 3D/adiabatic run is provided, so the core explanatory claim is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses 2D FARGO3D hydrodynamic simulations of a non-migrating, circularly orbiting planet in a locally isothermal disk to study the gas distribution near the co-orbital Lagrange points L4 and L5. The authors vary the radial temperature exponent beta, the surface density exponent alpha, the planet mass m_p, and the disk aspect ratio h_p. They report that the asymmetry between L4 and L5 is controlled by the sign of beta: positive beta enhances L4, negative beta enhances L5, and beta=0 gives a symmetric distribution. They also find that the azimuthal locations of the density peaks deviate from the classical 60-degree RTBP positions, following the empirical relation of Eq. (7) in terms of Q=m_p/M_th. To explain the asymmetry, they propose a semi-analytical model based on the Ogilvie and Lubow (2006) co-orbital velocity field plus a radial velocity perturbation delta_v_r taken from their simulations; this perturbation deforms the libration region around the favored Lagrange point. The results are applied to observations of PDS 70, HD 163296, and LkCa 15, and the paper argues that the sign of the asymmetry constrains the disk temperature gradient.","tokens_in":14356,"tokens_out":4199,"duration_ms":42370,"significance":"If the empirical beta-sign trend holds, this is a useful and simple diagnostic: the L4/L5 asymmetry direction would directly indicate the sign of the radial temperature gradient in a protoplanetary disk, and the offset relation in Eq. (7) could help constrain planet mass and disk aspect ratio. The controlled parameter study is a real strength: beta, m_p, h_p, and alpha are varied in a systematic way, the time evolution of the contrast is quantified for many runs, and the comparison with observed systems is explicit. The paper is also careful to distinguish the gas behavior from that of decoupled dust. The main weakness is that the proposed mechanism in Section 4 is not an independent derivation: it imports the symmetry-breaking radial velocity perturbation from the very simulations it is meant to explain, so the causal origin of the beta-dependence remains, at present, a restatement of the simulation outcome rather than a closed physical explanation. The 'solely controlled' claim is also stronger than the tested parameter space, which includes only one viscosity, one equation of state, 2D geometry, and no resolution study.","major_comments":[{"comment":"The explanatory model is not derived from beta: the only explicit beta term, h_p^2 beta/2 in Eq. (8), is azimuthally symmetric and cannot by itself distinguish L4 from L5. The symmetry-breaking agent is entirely the delta_v_r term added to Eq. (9), which is imported from the simulations, as stated in the text: 'By taking this delta_v_r component from our simulations we can effectively deform the libration region as a function of the temperature gradient beta.' The model therefore reproduces the asymmetry by using the simulation output it is meant to explain, rather than by deriving the beta-dependence of delta_v_r. To support the causal claim in Section 6 that the asymmetry is 'caused by' delta_v_r, the authors should provide an independent derivation of delta_v_r from the linearized equations, or test the model by prescribing a synthetic delta_v_r with a known beta-dependence in a separate calculation. Without such a test, the mechanism is a restatement of the simulation result.","section":"Section 4, Eqs. (8)-(9)"},{"comment":"The claim that the asymmetry is 'solely controlled' by the sign of beta is stronger than the evidence presented. The simulations use a single viscosity (alpha_ss = 10^-4), a single equation of state (locally isothermal), 2D geometry with a fixed smoothing length epsilon = 0.6 H_p, and no resolution convergence tests. The parameter exploration varies alpha, m_p, and h_p but not these numerical and physical choices. I request at least resolution tests and one higher/lower viscosity run; a 3D or adiabatic comparison would further strengthen the claim. If these are not feasible, the wording should be softened to 'for the explored parameter range' in the abstract and conclusions.","section":"Abstract, Section 3, and Section 7"},{"comment":"The gap-depth selection criterion is stated as '0.2 < Sigma_gap/Sigma_0 < 0.02', which is an empty interval; the intended inequality is presumably 0.02 < Sigma_gap/Sigma_0 < 0.2. Please correct this. In addition, the threshold for the chaotic regime is given as 'm_p > 185M_sun' in several places but as 'above 240M_sun' in Section 3.2; the inconsistency should be resolved and the criterion for the threshold explained.","section":"Section 2.2 and Section 5"}],"minor_comments":[{"comment":"The text and the Figure 3 caption give different mass thresholds for the chaotic outliers (m_p > 240M_sun in the text versus m_p ≳ 185M_sun in the caption); please reconcile these values.","section":"Figure 3 and Section 5.1"},{"comment":"The fitting formula for the azimuthal offset is presented with a single coefficient 0.18 and no uncertainty or description of the fitting procedure; please specify the fit range, the treatment of the excluded outliers, and the scatter around the relation.","section":"Equation (7)"},{"comment":"The caption does not explain why the region |phi - phi_p| < 0.7 is masked for the radial velocity cuts outside co-rotation; please add a sentence describing the reason for this mask.","section":"Figure 4, top-right panel"},{"comment":"There are typographical errors in this section: 'decouples species' should be 'decoupled species' and 'whide range' should be 'wide range'.","section":"Section 6.4"}],"recommendation":"major_revision","confidential_remarks":"The empirical beta-sign result is promising and likely of interest to the planet-disk community, but the semi-analytical mechanism in Section 4 is currently circular in an important way: it explains the asymmetry by importing the simulated delta_v_r, which is the very quantity whose beta-dependence needs explanation. This can be addressed with an independent derivation or a prescribed-delta_v_r test, and the 'solely' claim needs to be tempered or supported by viscosity and resolution tests. I recommend major revision rather than rejection because the central empirical trend is well documented and the requested additions are within the scope of the manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid numerical study with a clear, testable claim—the sign of the radial temperature gradient selects which Lagrange point accumulates gas (L4 for beta>0, L5 for beta<0, symmetric at beta=0). The controlled beta variation is the real new thing; earlier simulations saw similar asymmetries but no one isolated the controlling parameter. The offset formula Eq 7 is a useful fitting relation, and the comparison with HD 163296 and PDS 70 is sensible. Deserves a serious referee.\n\nWhat I like: the parameter sweep is honest, with 83 runs over mp and hp for fixed beta, plus the beta experiments and the alpha checks. The trend is consistent with Rodenkirch and Garrido-Deutelmoser, which is good context. The paper also notes the eccentricity and migration caveats itself, which is more than many do.\n\nSoft spots: the \"solely\" in the abstract and Section 3 outruns the evidence. You have one viscosity, one equation of state, 2D geometry, no resolution tests. That is fine for a first look, but it does not license \"solely.\" The semi-analytical model in Section 4 is the bigger issue: the symmetry-breaking term is delta_v_r, which is taken from the simulations. The stress-test note is right that the mechanism is not derived. The paper is transparent about this, but transparent circularity is still circularity. If delta_v_r is itself a response to the density contrast, the causal arrow could point the other way. That does not invalidate the empirical result, but it means the paper explains the asymmetry in terms of a velocity perturbation it does not explain. I would ask for a linear derivation or a test with a prescribed delta_v_r, or at least a clear statement that the model is phenomenological.\n\nMinor: Eq 7 is a fit used as a prediction; give uncertainties. No data release or parameter files mentioned.\n\nBottom line: the central claim about beta sign is well-supported and will be useful to observers and simulators. The mechanism section needs more work. Send it to review; it will get the right pushback.","headline":"The beta-sign result looks real and useful; the proposed mechanism is more of a demonstration than a derivation, but that does not sink the paper.","tokens_in":14896,"tokens_out":1863,"would_cite":true,"duration_ms":17939,"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":"This paper claims that the sign of a protoplanetary disk's radial temperature gradient alone determines whether more gas accumulates at the L4 or the L5 Lagrange point of an embedded planet, and that the effect is caused by a…","keywords":["protoplanetary disks","planet-disk interactions","Lagrange points","co-orbital dynamics","temperature gradient","hydrodynamic simulations","gap-opening planets","crescent structures"],"falsifier":"Run the fiducial simulation with a substantially different smoothing length (e.g., ε=0.3H_p) or with a 3D energy equation in which the temperature gradient is not prescribed, and check whether the L4/L5 asymmetry still follows the sign of β and whether δv_r retains the same azimuthal structure. If the asymmetry reverses, disappears, or decouples from β, the central claim and its mechanism are falsified; conversely, finding an observed disk with a measured positive temperature gradient that still shows a brighter L5 clump would contradict the claimed trend.","tokens_in":13916,"feed_emoji":"🪐","tokens_out":10771,"duration_ms":91922,"temperature":0.7,"pith_summary":"The paper asks why hydrodynamic simulations of a planet embedded in a gaseous protoplanetary disk so often pile up more material at one of the Trojan Lagrange points, L4 or L5, even when the planet is not migrating. Using a suite of 2D simulations, it claims to isolate a single controlling parameter: the sign of the disk's radial temperature gradient, with temperature rising outward (β>0) favoring L4, falling outward (β<0) favoring L5, and an isothermal disk (β=0) giving perfect symmetry. The result is robust across variations in planet mass, disk aspect ratio, and surface-density profile. If it holds, the crescents and clumps observed inside dust gaps—in PDS 70, HD 163296, and LkCa 15—become readable diagnostics of which way the local disk temperature changes with radius, a quantity that is otherwise very hard to pin down. The paper ends with a semi-analytical mechanism: the planet sets up a small, azimuthally varying radial velocity that enlarges the libration region around the favored Lagrange point, letting it hold onto more gas.","feed_headline":"Temperature gradient decides which Trojan point traps gas","feed_subtitle":"If true, observed L4/L5 crescents in PDS 70 and HD 163296 reveal whether the disk cools or warms outward.","key_machinery":"The load-bearing mechanism is the co-orbital velocity field: an analytic description of the radial and azimuthal gas velocities in the planet's co-rotating frame, extended with a small azimuthally varying radial velocity term δv_r that the authors extract from their simulations. This δv_r carries the signature of the temperature gradient—its azimuthal profile steepens near the Lagrange point favored by the sign of β. When that profile is fed into the analytic streamlines, the libration region around the favored point expands in radius and azimuth while the other region stays roughly unchanged, which is exactly the pattern seen in the density maps. The mechanism works without invoking planet migration: the symmetry breaking comes from the background flow the planet itself creates, with the temperature gradient fixing which side of the co-orbital region that flow opens up.","core_discovery":"The central claim is that the asymmetry of gas between the co-orbital Lagrange points of an embedded, non-migrating planet is solely controlled by the radial temperature gradient β of the locally isothermal disk. In a globally isothermal disk the distribution is symmetric; for β>0 the L4 region retains more gas, for β<0 the L5 region does. The same trend appears across the full parameter survey of 83 simulations spanning planet masses 30–300 Earth masses and aspect ratios 1/30 to 2/15, independent of the surface-density exponent, planet mass, and aspect ratio. The paper also documents that the azimuthal location of the accumulated gas shifts away from the classical ±60° of the restricted three-body problem, following φ_max≈±60°[1+0.18 $Q^{{-2/3}}$], with Q the planet mass in units of the thermal mass; systems where the planet dominates its vicinity approach the classical positions. Finally, the paper offers a causal mechanism: the planet-induced, azimuthally varying radial velocity background δv_r expands the libration region around the favored point, allowing it to retain more gas, and this mechanism reproduces the simulated asymmetry in the semi-analytical model.","pith_inferences":["The proposed mechanism predicts that the radial gas velocity near co-rotation, not just the density, should show a measurable azimuthal asymmetry tied to β; high-resolution molecular-line observations of gap edges might be able to test this directly.","The strong suppression of the asymmetry for planet eccentricity above one disk scale height means that interpreting a null asymmetry as β≈0 requires independent knowledge that the planet's orbit is nearly circular.","A clean numerical falsification is available: re-running the same setup with a different smoothing length or with a 3D non-isothermal energy equation would show whether the imported δv_r is physical or a 2D artifact, and whether the β-sign rule survives.","The same mechanism should amplify in dust: well-coupled dust (St≪1) traces the gas and shows even stronger Lagrange-point overdensities, so the observed dust crescents may be magnified gas asymmetries whose amplitude as a function of Stokes number remains to be quantified."],"forward_implications":["A crescent or clump observed at L5 (as reported for HD 163296 and PDS 70) would imply that the local temperature decreases with radius, β<0.","A gap showing comparable clumps at both L4 and L5 would point to a locally isothermal region, β≈0.","Measuring the angular offset of a crescent gives an estimate of Q=m_p/M_th, the planet mass in units of the disk thermal mass, through the formula φ_max≈±60°[1+0.18 Q^{-2/3}].","Long-lived, high-contrast Lagrange-point structures require gap depths with log K≳2, i.e., Σ_gap/Σ0≲0.2, so the persistence of observed crescents constrains the combination of planet mass, disk aspect ratio, and viscosity.","Because the asymmetry appears for non-migrating planets, a bright L5 clump should not by itself be read as evidence of planet migration or of a radial drift of gas."],"supporting_citations":[{"why":"Supplies the analytic co-orbital velocity field that the semi-analytical model extends with the planet-induced δv_r.","marker":"Ogilvie & Lubow 2006"},{"why":"Original FARGO code from which the hydrodynamic solver descends.","marker":"Masset 2000"},{"why":"The hydrodynamic solver used to run all of the paper's 2D simulations.","marker":"Benítez-Llambay & Masset 2016"},{"why":"Gives the horseshoe half-width x_s used to set the radial measurement box for the L4/L5 contrast.","marker":"Jiménez & Masset 2017"},{"why":"Provides the K parameter that predicts gap depth and defines the regime where the asymmetry is long-lived.","marker":"Kanagawa et al. 2017"},{"why":"Earlier simulation that showed a strong L4/L5 asymmetry for a non-migrating planet, the puzzle this paper explains.","marker":"Garrido-Deutelmoser et al. 2022"},{"why":"HD 163296 model with β<0 that accumulates dust at L5, used as a consistency check for the claimed trend.","marker":"Rodenkirch et al. 2021"},{"why":"Reports the PDS 70 L5 clump that the authors use to infer a negative temperature gradient.","marker":"Balsalobre-Ruza et al. 2023"}],"fun_headline_variants":["Temperature slope tips the scales at L4/L5","Disk's radial heat gradient picks Trojan gas pile","Which Trojan traps gas? Thermal slope decides","Gas at L4 vs L5? Check the temperature gradient","Planet's Trojans: Asymmetry from disk's thermal slope"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The causal story depends on a small radial velocity perturbation δv_r that is imported from the simulations rather than derived from β; if that perturbation is an artifact of the 2D locally isothermal setup or of the chosen smoothing length (ε=0.6H_p), the proposed physical origin would fail even if the empirical β-sign trend survives.","fun_headline_variants_meta":{"raw":{"variants":["Temperature slope tips the scales at L4/L5","Disk's radial heat gradient picks Trojan gas pile","Which Trojan traps gas? Thermal slope decides","Gas at L4 vs L5? Check the temperature gradient","Planet's Trojans: Asymmetry from disk's thermal slope"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000177,"raw_usage":{"total_tokens":1384,"prompt_tokens":1125,"completion_tokens":259,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":741,"completion_tokens_details":{"reasoning_tokens":180}},"tokens_in":741,"tokens_out":259,"duration_ms":3621,"temperature":1.0,"reasoning_tokens":180,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:07:47.131994+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the fiducial simulation with a substantially different smoothing length (e.g., ε=0.3H_p) or with a 3D energy equation in which the temperature gradient is not prescribed, and check whether the L4/L5 asymmetry still follows the sign of β and whether δv_r retains the same azimuthal structure. If the asymmetry reverses, disappears, or decouples from β, the central claim and its mechanism are falsified; conversely, finding an observed disk with a measured positive temperature gradient that still shows a brighter L5 clump would contradict the claimed trend.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The hydrodynamic solver used to run all of the paper's 2D simulations."},{"cited_title":"M., & Dong , R","cited_arxiv_id":null,"evidence_quote":"Earlier simulation that showed a strong L4/L5 asymmetry for a non-migrating planet, the puzzle this paper explains."},{"cited_title":", de Gregorio-Monsalvo, I","cited_arxiv_id":null,"evidence_quote":"Reports the PDS 70 L5 clump that the authors use to infer a negative temperature gradient."}],"review_version":1}