{"id":"c276174c-da61-43b1-9810-6b552b104d29","arxiv_id":"2501.04411","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A disc evolution model with a 40 au centrifugal radius and weak viscous heating best reproduces the flux-size relation of young protoplanetary discs, while older discs are mostly optically thin at 1.3 mm.","lead":"This paper models how protoplanetary discs change size and brightness as they evolve, and compares the predictions to telescope surveys of young stars. It finds that discs with lots of initial spin and weak internal heating best match the youngest observed discs, and that dust mass estimates are mostly reliable after 0.5 million years.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The class 0/I model preference rests on comparing model 95% flux radii with Gaussian-fitted observed sizes, an estimator mismatch the paper itself concedes could be a factor of 2 and could erase the claimed discrimination.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the comparison between model 95% flux radii and observed Gaussian-fitted class 0/I disc sizes. My stress-test confirms this is the most serious threat to the central claim, because the claimed preference for high angular momentum and weak viscous heating is established by matching those observed sizes, and the paper's own Sec. 5.3 admits that a factor-of-2 systematic in the observed sizes would make the preference unclear. The concern is not an internal inconsistency or a disagreement with disciplinary consensus; it is a measurable estimator-mapping issue. The proposed forward-modeling test would settle whether the mapping between Eq. (6) radii and Gaussian-fitted radii preserves the model ordering. Since the reader already assigned CONDITIONAL based on this same weakest assumption, no verdict adjustment is needed. The secondary claims about optically thin discs and dust-mass evolution are supported by internal diagnostics (Fig. 3, Fig. 7) and are not the main point of failure.","tokens_in":18152,"tokens_out":3196,"duration_ms":34685,"concrete_test":"Use the preferred model (mod-a-3-r40) and the alternative (mod-a-2-r10) to produce synthetic 1.3 mm continuum images over the full disc formation phase. Degrade them to the angular resolution, sensitivity, and uv-coverage of the eDisk survey and run the same Gaussian-fitting pipeline used by Ohashi et al. (2023) to measure sizes. Compare the recovered Gaussian sizes with the model's true R95 from Eq. (6) for both models. If the bias between the two size estimators differs by a factor approaching 2, or if after applying the same Gaussian-fitting procedure to both models the preferred model no longer brackets the observed flux-radius distribution better than the alternative, the central discrimination in Sec. 3.2 is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that class 0/I discs prefer R1=40 au with alpha_vh=1e-3 (abstract, Sec. 3.2) is established only by overlaying model tracks in the flux-radius plane (Figs. 4-6). The model tracks use the 95% flux radius defined by Eq. (6), integrated from the model intensity profile; the observed eDisk/VANDAM sizes used for comparison are obtained from single-Gaussian fits to the continuum (Ohashi et al. 2023; Tobin et al. 2020). These are not the same estimator. The paper itself states in Sec. 5.3 that Gaussian fitting of embedded objects can overestimate disc sizes by up to a factor of 2 (Tung et al. 2024) and concedes that 'if the true disc sizes of the class 0/I sample we compare to were smaller by a factor of 2, it would not be so clear that the model discs with reduced viscous heating would match the observed sample better.' Because the discrimination between the 40 au/weak-heating and 10 au/strong-heating models rests on reproducing observed class 0/I radii, an unresolved estimator mismatch of this size is load-bearing. The comparison also lacks any quantitative goodness-of-fit; 'best agreement' is visual, so the factor-2 systematic cannot be separated from model preference.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a one-dimensional model of protoplanetary disc formation and viscous evolution, coupled to dust growth and radial drift, and uses it to compute the millimeter flux, flux radius, and optically thin dust mass of young discs. Two model variants are compared: one with high angular momentum (R1=40 au) and weak viscous heating (alpha_vh=1e-3), and one with low angular momentum (R1=10 au) and strong viscous heating (alpha_vh=1e-2). The authors report that the first variant best matches the observed fluxes and radii of class 0/I discs, that class II discs are consistent with both models, and that after about 0.5 Myr discs are largely optically thin at 1.3 mm, so standard dust mass estimates are accurate to within a factor of about two. A population synthesis with the preferred parameters reproduces the cumulative dust mass distributions of young star-forming clusters.","tokens_in":18429,"tokens_out":6997,"duration_ms":65792,"significance":"If the conclusions hold, the paper would establish the flux-size plane as a practical diagnostic for the angular momentum budget and viscous heating efficiency of protoplanetary discs, and would strengthen the case that viscous heating is inefficient in embedded discs. The model is clearly described, with explicit equations for the intensity and flux radius and a transparent discussion of parameter choices. The paper is also commendably candid about its limitations, especially the factor-of-two uncertainty in observed disc sizes and the simplifications of the model. The second claim, that discs are optically thin at 1.3 mm for most of their evolution, is a robust output of the model and is useful for the interpretation of dust mass surveys. However, the central model-preference claim is currently supported only by a visual overlay of model tracks on observed data, without a quantitative goodness-of-fit measure or treatment of upper limits, and the paper itself concedes that the factor-of-two size uncertainty could erase the apparent preference. These issues need to be addressed before the central claim can be considered established.","major_comments":[{"comment":"The abstract and Sec. 3.2 state that the model with R1=40 au and alpha_vh=1e-3 is 'best able to match' the observed class 0/I flux and radius data. However, this conclusion is drawn by eye from overlaying model tracks on the observed points in Figs. 4-6; no goodness-of-fit statistic, confidence interval, or treatment of measurement errors is provided. The comparison also excludes discs with upper limits on their size, which biases the observed sample toward larger radii and may favor the high-angular-momentum model. The authors should either (i) quantify the agreement (e.g., the fraction of observed points within a given distance of the model track, or a likelihood-based comparison) and show the sensitivity to the excluded upper limits, or (ii) soften the claim to state that the model is 'consistent with' rather than 'best able to match' the data.","section":"Sec. 3.2, Figs. 4-6"},{"comment":"The model flux radius defined in Eq. (6) is the radius containing a given fraction of the integrated model intensity. The observed class 0/I sizes from Ohashi et al. (2023) and Tobin et al. (2020) are derived from single-Gaussian fits to the continuum emission. These are different estimators, and the paper acknowledges in Sec. 5.3 that Gaussian fitting of embedded objects can overestimate true sizes by up to a factor of two (Tung et al. 2024). This is in tension with the statement in Sec. 2.2 that the differences between the two methods 'should be small'. Because the discrimination between the two models in Sec. 3.2 rests on matching the observed 95% radii, the factor-of-two systematic directly affects the central claim. The authors should either compute synthetic observations from the model (including appropriate resolution and fitting procedures) or, at minimum, propagate the factor-of-two uncertainty into the stated model preference.","section":"Sec. 2.2, Eq. (6) vs Sec. 5.3"},{"comment":"The preferred values R1=40 au and alpha_vh=1e-3 are not derived from independent constraints; they are selected because the resulting model tracks pass through the observed class 0/I points in the flux-radius plane. Only two values of each parameter are explored (Table 1 and Fig. 6), and no systematic parameter search or quantitative selection metric is presented. The abstract's claim to be 'best able to match' therefore overstates the evidence. The conclusion should be rephrased as 'among the model variants we consider' unless a broader parameter exploration or a statistical model-comparison test is added.","section":"Sec. 2.1, Table 1"},{"comment":"The flux-size tracks are computed for face-on discs, with no dust diffusion, and using only absorption (Eq. 3) with no scattering. As the authors note in Sec. 5.3, dust diffusion can increase the 90% flux radius by up to a factor of two (Pinilla et al. 2021), scattering can reduce the flux from optically thick regions (Zhu et al. 2019), and inclination affects the measured size. The argument that the effect of diffusion on the 95% radius would still leave the agreement 'good' is not demonstrated. Given that the central discrimination depends on the radii of the class 0/I discs, a test with at least one of these effects included (or a clear justification for ignoring them) is needed to establish robustness.","section":"Sec. 5.3, Eq. (3)"}],"minor_comments":[{"comment":"The phrase 'the evolution of the cumulative evolution of the observable dust masses' contains a duplicated word; it should be something like 'the evolution of the cumulative distribution of observable dust masses'.","section":"Abstract"},{"comment":"The caption states that the class 0/I discs report the 95% flux radius, but the text in Sec. 3.2 says the eDisk sizes were estimated from Gaussian fitting; please clarify how the reported 95% radius relates to Gaussian-derived sizes, or refer to the observed quantity as 'reported size' rather than '95% flux radius'.","section":"Sec. 3.2, Fig. 4 caption"},{"comment":"There is a typo: 'Viscous heating as also been inferred' should be 'Viscous heating has also been inferred'.","section":"Sec. 5.1"},{"comment":"The agreement between the model and observed cumulative dust mass distributions is assessed visually. A two-sample Kolmogorov-Smirnov test or a similar quantitative comparison would strengthen the statement that the model 'agrees well' with the observations.","section":"Sec. 4, Fig. 7"}],"recommendation":"major_revision","confidential_remarks":"The paper is honest about its limitations and the central claim is timely, but the lack of quantitative comparison and the acknowledged factor-of-two estimator mismatch make the current version unsuitable for acceptance. The authors should be encouraged to add a quantitative fit statistic and to test the effect of the size systematics. The appendix correcting a parameter error in A23 is useful but tangential to the main narrative; it could be shortened or moved to an erratum."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: this paper uses a disc formation/evolution model with dust drift to compute flux-size tracks and compares them to eDisk/VANDAM class 0/I and class II samples. The headline result is that class 0/I discs favour high angular momentum (R1=40 au) and weak viscous heating (alpha_vh=1e-3); class II discs are consistent with both variants. The supporting claim that discs are optically thin at 1.3 mm after 0.5 Myr, so standard mass estimates are good to factor ~2, is the better-established part.\n\nWhat is new: the optical-depth-corrected population synthesis, the explicit flux-size tracks for two parameter combos, and the separate examination of angular momentum and heating effects. The paper is honest: it openly notes the size-estimator problem in Sec. 5.3 and includes an appendix correcting a parameter error in A23, which is the kind of transparency you want.\n\nSoft spots: the central discrimination between the two models rests on a visual overlay of model 95% flux radii on Gaussian-fitted observed sizes. The paper itself concedes that a factor-of-2 size overestimate would make the preference unclear. There is no statistical comparison, no error bars, and no parameter exploration beyond the two hand-picked combinations. Since R1 and alpha_vh were chosen to reproduce the data, the agreement in Sec. 3.2 is partly a fit, not an independent prediction. The population synthesis check is useful but uses the same model. Also, the observed sample excludes upper limits, which may bias the comparison toward larger sizes.\n\nBottom line: this is a readable, useful paper for people comparing disc evolution models to mm continuum surveys. It deserves peer review, but the authors should be pushed to quantify the model-data comparison and, ideally, to test the size estimator directly. The optically-thin mass claim and the class II consistency will likely survive; the class 0/I preference should be treated as tentative.","headline":"A plausible but visually-staked model-data comparison that deserves review, with the central class 0/I preference stronger than the evidence supports.","tokens_in":19036,"tokens_out":2137,"would_cite":true,"duration_ms":21905,"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 observed class 0/I disc fluxes and radii are best matched by a model where cloud-core angular momentum gives a 40 au centrifugal radius and viscous heating is weak, while class II discs tolerate both 40 au and 10 au…","keywords":["protoplanetary discs","flux-size relation","viscous disc evolution","radial drift","dust mass estimates","class 0/I discs","class II discs","disc population synthesis"],"falsifier":"Measure a sample of class 0/I disc sizes with radiative-transfer modelling instead of single-Gaussian fitting; if the resulting 95% flux radii are systematically about a factor of two smaller than the Gaussian radii, the claimed preference for the 40 au, weak-viscous-heating model would weaken or vanish.","tokens_in":17927,"feed_emoji":"🪐","tokens_out":7561,"duration_ms":65654,"temperature":0.7,"pith_summary":"This paper asks whether the observed relation between millimetre flux and disc size can tell apart different assumptions about how protoplanetary discs form and evolve. It argues that embedded class 0/I discs, the youngest objects, are best matched by a model in which the parent cloud core carries enough angular momentum to place material at a centrifugal radius of 40 au around a solar-like star, and in which viscous heating is only 10% as efficient as the angular-momentum transport coefficient. Older class II discs are reproduced about equally well by 40 au and 10 au cores and by both heating efficiencies, so the embedded phase is the discriminating one. The paper also claims that discs older than about 0.5 Myr are optically thin at 1.3 mm, so standard optically-thin dust mass estimates are accurate to within a factor of about two, and that a population of such discs reproduces the observed decline of dust mass with cluster age. If these claims hold, the flux-size plane becomes a direct probe of the angular momentum budget and heating physics of protoplanetary discs.","feed_headline":"Class 0/I discs point to 40 au cores and weak viscous heating","feed_subtitle":"Model matches young-disc fluxes and radii; dust masses accurate to a factor of 2 after 0.5 Myr.","key_machinery":"The central object is the flux-size relation: the 1.3 mm continuum flux $F_\\nu$ plotted against the flux radius, defined as the radius containing 68% or 95% of the total integrated intensity. The machinery is a one-dimensional model in which a Bonnor-Ebert sphere collapses to form a viscous $\\alpha$-disc, with angular-momentum transport coefficient $\\alpha_\\nu = 10^{-2}$ and a separate viscous-heating coefficient $\\alpha_{\\rm vh}$, while dust grows to the fragmentation limit and drifts radially inward under the Weidenschilling drift prescription. Emission is computed from the Birnstiel et al. (2018) opacity tables using $I_\\nu = B_\\nu(1-e^{-\\tau_\\nu})$, so the flux radius is a direct prediction. The 95% flux radius is the discriminating quantity because it traces the faint outer disc, hence the physical size set by the core's angular momentum, while the total flux carries the temperature and mass information affected by viscous heating.","core_discovery":"On its own terms, the paper's discovery is that the flux-radius plane separates disc formation physics: a disc evolving from a high-angular-momentum core with a centrifugal radius $R_1 = 40$ au and inefficient viscous heating, $\\alpha_{\\rm vh} = 10^{-3}$, passes through the observed fluxes and 95% flux radii of the eDisk and VANDAM class 0/I samples during its embedded buildup, whereas a low-angular-momentum core with $R_1 = 10$ au and full viscous heating, $\\alpha_{\\rm vh} = 10^{-2}$, produces discs that are too small and too bright at that stage. For class II discs both models are compatible, so the claim is specifically that the youngest discs carry the information. A second discovery is that radial drift makes discs optically thin at 1.3 mm for most of their lifetime, so the standard optically-thin mass formula traces true dust mass within a factor of about two after 0.5 Myr, with a factor of about three underestimate during the embedded phase.","pith_inferences":["If Gaussian fitting overestimates embedded disc sizes by the factor of two cited in the paper, then the claimed preference for the 40 au, weak-heating model would probably become a weaker preference for an intermediate or 10 au model; radiative-transfer size measurements of the same targets would settle this directly.","The model omits dust diffusion, which the paper notes can enlarge 90% flux radii by up to a factor of two; including diffusion could let lower-angular-momentum cores reproduce the same observed sizes, making the 40 au requirement an upper bound on core angular momentum.","If angular momentum transport is dominated by MHD winds rather than viscosity, discs may not viscously expand, so reproducing large class 0/I radii may require even higher initial angular momentum or an additional expansion mechanism.","The model's spectral index rises to about 3.25 at 1 Myr, above typical observed values, suggesting that fragmentation-limited growth makes mm-sized grains too scarce; allowing grain growth past the fragmentation barrier or dust trapping would raise the mm opacity and could change the inferred dust masses."],"forward_implications":["The flux-radius plane can discriminate between formation models: the embedded class 0/I phase rejects low-angular-momentum cores with efficient viscous heating.","For discs older than about 0.5 Myr, standard 1.3 mm dust masses trace true masses to within roughly a factor of two, so cluster-age dust-mass trends can be interpreted as radial-drift depletion rather than opacity artefacts.","Very young and massive embedded discs can have their 1.3 mm dust masses underestimated by up to a factor of about three, making those estimates lower limits.","A population model with 40 au centrifugal radii and weak viscous heating reproduces the observed cumulative dust-mass decline across clusters aged about 0.5 to 5 Myr.","With photoevaporation, discs retain a narrow dusty ring outside the gap, keeping flux radii large while total fluxes drop as the inner disc is cleared."],"supporting_citations":[{"why":"Supplies the base gas-disc formation and viscous evolution model plus the population synthesis framework that this paper modifies.","marker":"A23"},{"why":"Provides the collapse solution that sets how the disc forms from a Bonnor-Ebert sphere.","marker":"Takahashi et al. (2013)"},{"why":"Defines the alpha-viscosity prescription used for angular momentum transport and viscous heating.","marker":"Shakura & Sunyaev (1973)"},{"why":"Gives the radial drift velocity used to evolve the dust component.","marker":"Weidenschilling (1977)"},{"why":"Sets the fragmentation-limited maximum particle size that controls the dust size distribution.","marker":"Birnstiel et al. (2012)"},{"why":"Supplies the wavelength- and size-dependent opacity tables used to compute optical depth and continuum emission.","marker":"Birnstiel et al. (2018)"},{"why":"Provides the eDisk class 0/I fluxes and 95% flux radii that the model must reproduce.","marker":"Ohashi et al. (2023)"},{"why":"Provides the larger VANDAM Orion class 0/I sample used as a second comparison for the flux-size relation.","marker":"Tobin et al. (2020)"},{"why":"Defines the standard optically-thin dust mass estimator and opacity scaling law that the model tests.","marker":"Ansdell et al. (2016)"},{"why":"Supplies the X-ray photoevaporation prescription used in the population synthesis models.","marker":"Picogna et al. (2021)"}],"fun_headline_variants":["Young discs reveal core angular momentum via flux-radius relation","Flux-radius plane pins down disc formation physics","40 au cores and weak heating shape youngest discs' fluxes","Discs turn optically thin early, making dust masses reliable","Dust mass evolution matches young clusters across ages"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The comparison assumes that the Gaussian-fit sizes of embedded class 0/I discs can stand in for the model's 95% flux radius, although the paper cites evidence that such fits can overestimate sizes by up to a factor of two.","fun_headline_variants_meta":{"raw":{"variants":["Young discs reveal core angular momentum via flux-radius relation","Flux-radius plane pins down disc formation physics","40 au cores and weak heating shape youngest discs' fluxes","Discs turn optically thin early, making dust masses reliable","Dust mass evolution matches young clusters across ages"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00081,"raw_usage":{"total_tokens":3587,"prompt_tokens":1011,"completion_tokens":2576,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":627,"completion_tokens_details":{"reasoning_tokens":2500}},"tokens_in":627,"tokens_out":2576,"duration_ms":16943,"temperature":1.0,"reasoning_tokens":2500,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:34:14.650933+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure a sample of class 0/I disc sizes with radiative-transfer modelling instead of single-Gaussian fitting; if the resulting 95% flux radii are systematically about a factor of two smaller than the Gaussian radii, the claimed preference for the 40 au, weak-viscous-heating model would weaken or vanish.","supporting_citations":[{"cited_title":"P., van der Marel , N., et al","cited_arxiv_id":null,"evidence_quote":"Defines the standard optically-thin dust mass estimator and opacity scaling law that the model tests."},{"cited_title":"Z., Inutsuka , S.-i., & Machida , M","cited_arxiv_id":null,"evidence_quote":"Provides the collapse solution that sets how the disc forms from a Bonnor-Ebert sphere."},{"cited_title":"J., Sheehan , P","cited_arxiv_id":null,"evidence_quote":"Provides the larger VANDAM Orion class 0/I sample used as a second comparison for the flux-size relation."}],"review_version":1}