{"id":"7e40aab1-e237-454d-b16c-4e7fe64422d1","arxiv_id":"2607.15923","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":14,"one_line_summary":"Dynamical rotation-curve fits give M_disk ≈ 0.30 M_sun for HD 97048 and ≈ 0.21 M_sun for WaOph 6, and indicate disks with mm-dust spirals have systematically lower Toomre Q.","lead":"Astronomers used ALMA gas-motion observations to weigh two planet-forming disks, finding disk masses of roughly 0.3 and 0.2 times the Sun's mass—heavier than typical estimates. The result strengthens the case that spiral arms seen in the millimeter dust emission of one disk arise from the disk's own gravity.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Axisymmetric/HSE rotation-curve model applied to strongly non-axisymmetric WaOph 6 can bias M_d and R_c; since WaOph 6 is one of only three spiral disks, this directly threatens the Q_min separation.","rationale":"The reader's weakest assumption identifies the axisymmetric/HSE model as the main vulnerability. I agree and sharpen it: the paper's most novel claim is the Q_min separation between spiral and non-spiral disks, and that claim depends on the mass of WaOph 6, a strongly non-axisymmetric disk that is one of only three spiral sources. Because the rotation-curve extraction uses a restricted azimuthal wedge on one side, the spiral's non-axisymmetric velocity field is not azimuthally averaged away, so the fitted disk mass and scale radius can be biased. A ~20% bias in M_d for WaOph 6 would shift its Q_min enough to weaken the Anderson-Darling separation. The proposed synthetic recovery test directly settles whether the axisymmetric model is adequate. I do not raise a stronger objection because the mass estimates themselves show reasonable agreement with literature, and the bootstrapping treatment of geometry and temperature is careful. The reader's CONDITIONAL verdict therefore remains appropriate.","tokens_in":28281,"tokens_out":11366,"duration_ms":133656,"concrete_test":"Run a controlled recovery test: take a 3D hydro simulation of a self-gravitating disk (M*=0.96 M_sun, M_d=0.21 M_sun, R_c=650 au) and a matched planet-driven spiral simulation, post-process both with RADMC-3D to produce 12CO/13CO ALMA cubes at WaOph 6 resolution/SNR including foreground absorption, and run the exact discminer/disksurf/DySc pipeline with the same red-side masking. Check whether the recovered M_d, R_c, and Q_min are within 1σ of input for both. If the pipeline is biased for the GI run but not the planet run, the inferred Q_min separation is an artifact of the model assumption; if recovery is unbiased for both, the axisymmetry objection is retired.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Sec. 4.2's conclusion that mm-spiral disks have lower Q_min rests on Q_min values for three disks, including WaOph 6. The rotation-curve fit for WaOph 6 assumes an axisymmetric, steady-state, vertically hydrostatic LBP disk with a barotropic EOS (Sec. 3.2), but WaOph 6 has a strong m=2 spiral (Sec. 2.2). The rotation curves are not a full azimuthal average: they are extracted from a [-30°,30°] wedge on the red-shifted side only to avoid cloud absorption (Sec. 3.1.1, App. C). An m=2 spiral produces non-axisymmetric velocity perturbations that are not averaged out by this procedure; the DySc self-gravity term is computed for an axisymmetric potential, so a spiral can bias the fitted M_d and R_c. The claimed systematic uncertainty is ~20%, and all three spiral disks have Q_min between 4 and 6, so a moderate bias in WaOph 6 could move it into the non-spiral Q distribution and remove the statistical separation. A second issue is that Q_min~5 is well above the canonical GI threshold (~1.5-2), but the paper only claims a relative lowering; the axisymmetry bias is the more direct threat to that relative claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents dynamical mass measurements for the disks around HD 97048 and WaOph 6 by fitting CO rotation curves with a thermally stratified, self-gravitating disk model. The analysis includes a careful treatment of cloud absorption (using red-shifted-side extraction within a narrow azimuthal wedge), a beam-smearing correction based on a convolved Keplerian model, and a bootstrap procedure over disk geometry and thermal structure that yields ~19–20% systematic uncertainties on the disk masses. The reported values are M_star = 2.226^{+0.054}_{-0.049} M_sun, M_d = 0.300^{+0.055}_{-0.061} M_sun, R_c = 172^{+24}_{-14} au for HD 97048 and M_star = 0.956^{+0.006}_{-0.006} M_sun, M_d = 0.210^{+0.045}_{-0.038} M_sun, R_c = 647^{+193}_{-155} au for WaOph 6. In the final section, the authors combine these results with literature dynamical masses to compare the minimum Toomre parameter Q_min for disks with and without mm-dust spirals, concluding that spiral-hosting disks have systematically lower Q_min and that this supports gravitational instability as the origin of the spirals.","tokens_in":28776,"tokens_out":6925,"duration_ms":79512,"significance":"If the dynamical masses hold, this is a valuable extension of rotation-curve-based disk weighing to embedded, absorbed sources, and WaOph 6 is a particularly important target because it is a young, massive disk with clear mm-dust spiral structure that had no previous dynamical mass measurement. The paper uses multiple CO isotopologues, makes the analysis code public, and attempts a more systematic treatment of uncertainties than many earlier dynamical mass studies. The comparison of Q_min across dynamically weighed disks is interesting, but the strength of that conclusion is limited by the small number of spiral disks (three) and by the fact that one of them, WaOph 6, is also the source for which the axisymmetric model assumption is most questionable.","major_comments":[{"comment":"The rotation-curve model assumes an axisymmetric, vertically hydrostatic, barotropic disk, but WaOph 6 is strongly non-axisymmetric, with a prominent m=2 dust spiral (Sec. 2.2). The rotation curves are extracted only from a [-30°, 30°] wedge on the red-shifted side (Sec. 3.1.1, App. C), so an m=2 kinematic perturbation is not azimuthally averaged out. The DySc self-gravity term is computed for an axisymmetric potential, so the fitted M_d and R_c for WaOph 6 could be biased. Since WaOph 6 is one of only three spiral disks in the Q_min comparison, a moderate bias could remove the claimed statistical separation. Please quantify this: either fit the WaOph 6 data with an explicit non-axisymmetric perturbation, or compare with a full-azimuth rotation curve where the data allow, and test how a plausible M_d/R_c bias shifts Q_min relative to the non-spiral sample.","section":"Secs. 3.2, 3.1.1, 4.2"},{"comment":"The beam-smearing correction factor is defined as the ratio of a pure Keplerian rotation curve to the beam-convolved Keplerian model based on the discminer stellar mass. This correction is applied before the self-gravity fit and is not iterated with the final best-fit model. Since the correction changes the inferred disk mass by ~46% for HD 97048 and ~38% for WaOph 6, the choice of reference model is not a minor detail. The final M_star differs from the discminer M_star,dm by ~7–8%, and the disk self-gravity term is absent from the reference curve. Please test the sensitivity of the fitted parameters to using the best-fit total model rotation curve in the correction, or otherwise propagate an uncertainty on the correction factor itself.","section":"Sec. 3.1.2, Eq. (1)"},{"comment":"The Anderson–Darling test is applied to bootstrap realizations that resample the input parameters of the fixed 15-source sample, but it does not resample the sample of sources. Averaging p-values over these parameter realizations is not a standard valid test, and the claim of \">3σ significance\" is therefore overstated. With only three spiral disks, the separation should be assessed with a permutation test on the observed point estimates or with a small-sample rank test, and the sensitivity to removing WaOph 6 should be reported.","section":"Sec. 4.2"}],"minor_comments":[{"comment":"The bootstrap procedure does not include the distance uncertainty, although the quoted distance enters the conversion from angular to physical scales and thus affects M_star and M_d. Please state the adopted distances and justify that their uncertainties are negligible compared to the ~20% disk-mass systematics.","section":"Sec. 3.3"},{"comment":"Typo: \"HD 90748\" should be \"HD 97048\".","section":"Sec. 3.3, last paragraph"},{"comment":"The notation H/R|_mid is ambiguous; please define the midplane aspect ratio explicitly and state whether H/R is evaluated at the radius in question or at the midplane height.","section":"Sec. 4.2, Eq. (3)"},{"comment":"Teague et al. 2025a and 2025b are listed with identical bibliographic information; if these are two distinct papers, the entries should be corrected.","section":"References"},{"comment":"The word \"prove\" is too strong for a set of numerical demonstrations; consider \"show\" or \"demonstrate\".","section":"Abstract and Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The paper is well executed and likely publishable after the robustness concerns are addressed. The main risk is the WaOph 6 axisymmetry assumption; if the requested non-axisymmetric test shows a significant bias in M_d or R_c, the Q_min separation should be softened or removed. I do not see citation, novelty, or scope issues."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The useful core of this paper is the two first dynamical mass measurements: HD 97048 (M_star = 2.226, M_d = 0.300, R_c = 172 au) and WaOph 6 (0.956, 0.210, 647 au). The analysis is careful: beam smearing correction, bootstrapping over geometry and thermal structure, and a believable treatment of absorption in embedded sources. The WaOph 6 stellar mass resolves a literature discrepancy by showing a massive disk contributes to the observed kinematics. The HD 97048 mass agrees with independent stellar estimates. This is a genuine extension of the established method, not a new framework.\n\nThe comparative Toomre Q analysis is suggestive, but the weakest part of the paper. The claim that mm-spiral disks have lower Q_min rests on three disks: Elias 2-27, IM Lup, and WaOph 6. The stress-test concern is real: WaOph 6 has a strong m=2 spiral, yet the rotation curve fit assumes an axisymmetric, vertically hydrostatic model, and the curve is extracted from a [-30,30] wedge on the red-shifted side. A non-axisymmetric velocity perturbation can bias the fitted M_d and R_c, and the paper's own systematic uncertainty is ~20%. With all three spiral Q_min values between 4 and 6, a moderate bias in WaOph 6 could plausibly move it into the non-spiral distribution and erase the statistical separation. The Anderson-Darling p=0.001 is therefore over-claimed for a 3-vs-12 sample with one fragile point. Additionally, Q_min ~5 is well above the canonical GI threshold (~1.5-2); the paper only claims a relative lowering, but the phrase \"likely driven by gravitational instability\" goes beyond what the data support. The HD 97048 and WaOph 6 individual Q_min values (4.7 and 5.4, respectively) are not near instability on their own.\n\nThe axisymmetry concern also applies to the primary WaOph 6 disk mass, so that result should be treated with more caution than HD 97048's. In contrast, the stellar masses are less sensitive to the disk modeling assumptions.\n\nWho this is for: anyone working on dynamical disk masses, disk stability, or spiral-driven GI. The paper deserves a serious referee. The method application is clean, the mass measurements are useful, and the comparative Q sample is a good addition. The authors should be asked to temper the GI conclusion, address the non-axisymmetric bias for WaOph 6, and ideally test how sensitive the AD result is to removing or reweighting that one disk.\n\nSend it to peer review. With moderate revisions on the stability discussion, it would be a solid contribution.","headline":"Solid dynamical masses for two disks, but the Toomre Q separation rests on three spiral disks and one of them (WaOph 6) is the least well-modeled.","tokens_in":29267,"tokens_out":1820,"would_cite":true,"duration_ms":22018,"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":"Dynamical disk masses link millimeter-dust spirals to gravitational instability.","keywords":["protoplanetary disks","dynamical mass measurement","disk self-gravity","Toomre Q","gravitational instability","rotation curves","beam smearing","CO kinematics"],"falsifier":"Measure the proper motion of the millimeter-dust spiral arms in WaOph 6: if they orbit at the local Keplerian speed, gravitational instability is supported; if the pattern speed is slower or the arms are static, a planet or another mechanism is likely. Alternatively, compare the predicted rotation curves against a new, independent tracer not used in the fit at higher angular resolution; a mismatch in the inner few beams beyond the modeled pressure-gradient and self-gravity terms would indicate the axisymmetric hydrostatic model is incomplete.","tokens_in":28235,"feed_emoji":"🪐","tokens_out":5806,"duration_ms":62378,"temperature":0.7,"pith_summary":"This paper tries to establish that protoplanetary disk masses can be measured from gas rotation alone, even for embedded disks whose CO lines are partly absorbed, and that the resulting masses reveal a dynamical fingerprint of gravitational instability. It fits the rotation curves of multiple CO lines with a thermally stratified, self-gravitating disk model to obtain stellar masses, disk masses, and scale radii for HD 97048 and WaOph 6, and it applies the same machinery to all disks with dynamical masses measured so far. The central comparative result is that disks showing millimeter-dust spirals have systematically lower minimum Toomre Q values than disks without spirals, with the two groups separated at high statistical significance. If this holds, spiral morphology in the millimeter continuum is a reliable signpost of ongoing gravitational instability, and the dynamical method becomes a tracer-independent way to weigh disks across a wider range of environments.","feed_headline":"Spiral-hosting disks sit closest to gravitational instability","feed_subtitle":"Weighing 15 disks by gas motion shows spiral-bearing disks have lower stability margins, pointing to gravity as the spiral's driver.","key_machinery":"The central object is the rotation curve model: a self-similar, exponentially tapered surface density profile for a barotropic gas in vertical hydrostatic equilibrium, with the azimuthal velocity built from stellar gravity, pressure gradients (including vertical thermal stratification), and disk self-gravity. Emission from several CO isotopologues is used to reconstruct the 2D temperature structure and emitting surfaces; an empirical correction factor derived from beam-convolved Keplerian models removes the spatial-resolution bias in the inner disk. The Toomre Q parameter, computed from the fitted masses, temperatures, and scale radius, is the diagnostic that ties the mass measurements to sp","core_discovery":"The authors show that the rotation curves of two disks can be simultaneously fit with a model that includes stellar gravity, pressure gradients from a vertically stratified temperature structure, and disk self-gravity, recovering M_star = 2.226 +/- 0.054 Msun and M_disk = 0.300 Msun for HD 97048, and M_star = 0.956 Msun and M_disk = 0.210 Msun for WaOph 6. They extend the method to sources with foreground cloud absorption by excluding contaminated channels and extracting velocities from the unabsorbed side, and they show that ignoring beam smearing biases disk masses by up to about 45%. When the minimum Toomre Q is computed for all 15 disks with dynamical mass measurements, disks with millim","pith_inferences":["If the Q-spiral correlation holds, disks with low Q_min but no detected millimeter spirals become prime targets for deep high-resolution continuum searches for faint or suppressed spiral arms; their absence would favor a planet-disk interaction that washes out gravitational-instability spirals.","A testable extension: in the gravitational-instability scenario, spiral arms should rotate at approximately the local Keplerian speed, so measuring the proper motion of the spiral arms in WaOph 6 could distinguish that mechanism from a planet-driven spiral.","The method's success on absorbed sources suggests it can be pushed to embedded Class I disks, where CO absorption is common; if so, disk-to-star mass ratios can be measured at earlier evolutionary stages and compared with the values reported here.","The reported gas-to-dust ratios (about 640 and 1500) likely overestimate the true ratios if dust masses are underestimated by the optically thin assumption; longer-wavelength continuum observations could test this without invoking dynamical models."],"forward_implications":["Embedded, cloud-contaminated disks can now be weighed dynamically by masking absorbed channels and fitting the unabsorbed side of the emission, extending the method to earlier-stage sources.","Beam smearing must be corrected in rotation-curve fits: leaving it out shifts disk mass estimates by up to about 45%, comparable to the standard systematic uncertainty budget.","Bootstrapping over disk geometry and thermal structure puts realistic uncertainty estimates of roughly 20% on dynamical disk masses, dominated by the temperature structure rather than the number of fitted lines.","The two disks have high disk-to-star mass ratios (0.13 and 0.22), consistent with the expectation that massive disks are the ones developing spirals.","Across all dynamically weighed disks, lower minimum Toomre Q values track the presence of millimeter-dust spirals, so spiral morphology is a candidate observable signpost of ongoing gravitational instability."],"fun_headline_variants":["Spiral disks sit closest to gravitational instability","Beam smearing can bias disk mass estimates by 45%","New dynamical masses for HD 97048 and WaOph 6","Spiral-bearing disks show lower Toomre stability margins","Gravitational instability likely drives mm-dust spirals"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The fit assumes an axisymmetric, steady-state, vertically hydrostatic disk with a self-similar surface density profile and a barotropic equation of state; if a disk is strongly non-axisymmetric—as WaOph 6's spiral suggests—or out of hydrostatic equilibrium, the inferred disk mass and scale radius could be biased.","fun_headline_variants_meta":{"raw":{"variants":["Spiral disks sit closest to gravitational instability","Beam smearing can bias disk mass estimates by 45%","New dynamical masses for HD 97048 and WaOph 6","Spiral-bearing disks show lower Toomre stability margins","Gravitational instability likely drives mm-dust spirals"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000312,"raw_usage":{"total_tokens":1723,"prompt_tokens":965,"completion_tokens":758,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":709,"completion_tokens_details":{"reasoning_tokens":675}},"tokens_in":709,"tokens_out":758,"duration_ms":34194,"temperature":1.0,"reasoning_tokens":675,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T21:54:08.818627+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the proper motion of the millimeter-dust spiral arms in WaOph 6: if they orbit at the local Keplerian speed, gravitational instability is supported; if the pattern speed is slower or the arms are static, a planet or another mechanism is likely. Alternatively, compare the predicted rotation curves against a new, independent tracer not used in the fit at higher angular resolution; a mismatch in the inner few beams beyond the modeled pressure-gradient and self-gravity terms would indicate the axisymmetric hydrostatic model is incomplete.","supporting_citations":[],"review_version":1}