{"id":"442a7f73-fdd9-46c1-98e5-2cbf945dff17","arxiv_id":"2608.11984","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A unified evolutionary model of disk-instability planets, from pre-collapse clump to multi-Gyr cooling, reproduces the dynamical masses of four directly imaged planets and shows metallicity can shift inferred masses by up to 1.5 Jupiter masses.","lead":"This paper simulates the full evolution of giant planets born from collapsing gas clumps, from the bloated pre-collapse stage to billions of years of cooling. It shows that these models match the measured masses of four directly imaged exoplanets, and that unknown metallicity can shift inferred masses by up to 1.5 Jupiter masses.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The viability claim rests on an untested assumption that dynamical collapse conserves total entropy; shock heating during collapse could shift inferred masses enough to break the marginal agreement for Beta Pic b and AF Lep b.","rationale":"I examined the central claim: disk-instability cooling tracks are consistent with dynamical masses, so the formation path remains viable. The weakest link is the adiabatic-collapse assumption, which sets the initial post-collapse entropy and thereby the entire long-term luminosity evolution. The reader flagged this same assumption. The paper's own Appendix A demonstrates that the EoS-induced 50% radius mismatch at fixed entropy does not persist beyond ~1 Myr, but no test addresses the possibility that the entropy itself changes during collapse. In a genuine dynamical collapse, shock dissipation in the infalling envelope or non-homologous compression can alter the entropy profile, and the paper provides no reason to expect the change to be small. Because the inferred masses in Section 6 are sensitive to the luminosity normalization of the cooling tracks, and because the agreement with Beta Pic b and AF Lep b is already marginal, an entropy shift of ~0.5 kB/baryon could be consequential. The test I propose is a straightforward sensitivity study using the existing code: a grid of initial entropies. If the inferred masses remain within the dynamical constraints, the concern is resolved; if not, the paper's claim that disk instability cannot be ruled out would require additional support. The paper has independent support from its agreement with ATMO 2020 and Sonora Bobcat hot-start models, and the comparisons with dynamical masses are a genuine prediction with no free parameter tuned to the observations. Thus I do not think the paper should be rejected; the conditional verdict is appropriate, but it should explicitly require the entropy-sensitivity analysis.","tokens_in":18534,"tokens_out":12287,"duration_ms":111754,"concrete_test":"Use the authors' MESPA/modified MESA setup to recompute post-collapse cooling tracks for 4, 8, and 12 MJ models with initial total entropy shifted by -1.0, -0.5, -0.25, +0.25, +0.5, and +1.0 kB/baryon relative to the fiducial adiabatic value. Then re-derive the inferred masses for HR 8799 e, AF Lep b, Beta Pic b, and Beta Pic c using the age and luminosity inputs of Table 2. If any planet's inferred mass range no longer overlaps the 1-sigma dynamical mass range, the adiabatic assumption is load-bearing for the viability claim; if all four remain consistent across the full entropy grid, the concern is mitigated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the disk-instability tracks are consistent with all dynamical mass measurements, so disk instability remains viable. The most load-bearing step is the treatment of dynamical collapse in Section 2: the collapse is not simulated but replaced by an adiabatic jump, with the post-collapse radius selected from a table mapping mass, composition, and total entropy to radius, requiring total entropy to be the same before and after collapse. The post-collapse entropy is the dominant parameter controlling luminosity evolution, so if the true collapse is not adiabatic, the entire cooling track shifts. The paper does not test this: Appendix A only quantifies the EoS-dependent radius mismatch at fixed entropy, not uncertainty in the entropy itself. This matters because the agreement with dynamical masses is marginal for two of four planets: Beta Pic b has inferred mass >11.85 MJ vs dynamical 9.3+2.6-2.5 (overlap only in the 1-sigma tail), and AF Lep b has inferred 4.11-6.94 vs 3.75±0.5. A modest entropy change (e.g., from shock dissipation in the infalling envelope) could shift inferred masses by ~1 MJ, potentially pushing these planets out of consistency and weakening the viability conclusion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents self-consistent evolutionary tracks for giant planets formed by disk instability, using the MESPA extension of MESA. The authors follow a gas clump from an extended pre-collapse phase, through an assumed adiabatic dynamical collapse, into long-term contraction for masses 1-12 Jupiter masses and metallicities 0.5-2 times proto-solar. They compute cooling curves, study the metallicity dependence of inferred masses, compare their tracks to established hot-start and core-accretion models, and apply the tracks to infer masses of directly imaged planets with dynamical constraints (HR 8799 e, AF Lep b, Beta Pic b, Beta Pic c). The central claim is that the disk-instability tracks, without tuning to observations, yield masses consistent with all four dynamical mass measurements, so disk instability remains a viable formation pathway; they also argue that luminosity alone cannot distinguish disk instability from core accretion.","tokens_in":18768,"tokens_out":6469,"duration_ms":67477,"significance":"If the tracks are substantiated, this is a valuable unified framework that connects the pre-collapse clump phase to the post-collapse long-term evolution, a step that has been largely missing for disk instability. The paper explicitly quantifies the EoS-induced initial-radius uncertainty in Appendix A, compares with multiple published hot-start models and core-accretion models, and provides falsifiable mass predictions for benchmark directly imaged planets. The finding that metallicity can change inferred masses by up to 1.5 Jupiter masses is a useful caution for mass inference in the direct-imaging community. The main caveat is that the central consistency claim rests on a model assumption (adiabatic collapse with conserved total entropy) that is not stress-tested in the manuscript, and the agreement for two of the four planets is marginal rather than strong.","major_comments":[{"comment":"The adiabatic-collapse assumption is load-bearing: the post-collapse model is constructed by conserving total entropy, and the initial entropy controls the subsequent luminosity evolution. Appendix A quantifies the radius mismatch between the SCvH and CMS equations of state at fixed entropy, but it does not test the sensitivity of the tracks to the entropy itself. A non-adiabatic collapse with modest shock heating could shift the inferred masses in Table 2 by an amount comparable to the margin of agreement for Beta Pic b and AF Lep b. Please add a quantitative sensitivity test (for example, perturb the post-collapse entropy by plus or minus 1-2 k_B per baryon and recompute the cooling tracks and inferred masses), or cite published hydrodynamical evidence demonstrating that total entropy is conserved to the required precision during clump collapse.","section":"Section 2, Figure 2, Table 2"},{"comment":"The text states that Beta Pic b is consistent with the disk-instability tracks, but the inferred mass is >11.85 MJ while the dynamical mass is 9.3 +2.6/-2.5 MJ. The 1-sigma dynamical interval extends only to about 11.9 MJ, so the overlap is at the extreme tail. Calling this 'consistent' without a quantitative confidence statement overstates the agreement and is central to the paper's main claim. Please report the probability content of the overlap (e.g., by propagating the age and luminosity uncertainties into M_evol and computing the joint overlap) or phrase the result as marginal consistency.","section":"Table 2, Beta Pic b row; Section 6.3"},{"comment":"The mass ranges in Table 2 appear to reflect the metallicity variation only (plus the age interval for HR 8799 e), and the full age uncertainty for the Beta Pic group is not propagated. For Beta Pic b and c, the age is 18.5 +2.0/-2.4 Myr; a younger age within this range would lower the inferred masses, possibly improving agreement for Beta Pic b, while an older age would worsen it. The paper demonstrates the age sensitivity for AF Lep b, but does not apply the same propagation to Beta Pic. Please propagate the age (and luminosity) uncertainties into the quoted M_evol ranges, or explicitly state that the ranges include only the metallicity variation.","section":"Section 6.3 and Table 2"}],"minor_comments":[{"comment":"The text says 'the MESPA code' as if it were a standalone code; MESPA is an extension to MESA. Please write 'MESA with the MESPA extension' (or similar) for precision.","section":"Abstract and Section 2"},{"comment":"The caption says 'The sharp transitions in each panel corresponds to the dynamical collapse.' The verb should agree: 'correspond'.","section":"Section 3, Figure 1 caption"},{"comment":"The table is titled 'Synthetic observations with inferred masses,' but the table lists synthetic observations and the resulting inferred masses; consider renaming it 'Synthetic observations and inferred masses' to avoid ambiguity.","section":"Table 1 caption"},{"comment":"The target name 'WISPIT 2' appears in the sentence about multi-planet systems; this is likely a typo or malformed name. Please verify and correct.","section":"Section 6.1"},{"comment":"The phrase 'a 1.09 ± 0.06 Solar mass star' uses a capital S; for consistency with journal style, use 'solar'.","section":"Section 6.2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within A&A scope and the numerical machinery appears sound. The main risk is that the headline claim ('consistent with all dynamical mass measurements') is somewhat stronger than the marginal overlaps in Table 2 actually support, and the adiabatic-collapse assumption is not stress-tested. I recommend requesting an entropy-sensitivity test and a more quantitative treatment of the consistency statement; neither should require major new code, so the revisions are feasible within a revision cycle."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nHere's my take on Bussmann & Helled. The new thing is a single numerical framework, built on MESPA, that follows a gas clump from the pre-collapse phase through the dynamical collapse and into gigayear cooling tracks, for masses 1–12 MJ and metallicities 0.5–2 Zproto. Previous work treated the pre-collapse contraction and the long-term evolution separately; this paper connects them and makes the comparison to directly imaged planets with dynamical masses. That comparison—four objects, HR 8799 e, AF Lep b, β Pic b, β Pic c—is the useful part. The paper does not oversell: the conclusion is that disk instability remains viable, not that it is the pathway, and they explicitly show that luminosity alone cannot distinguish DI from hot-start core accretion.\n\nThe metallicity grid is a genuine plus. They show that for a fixed age and luminosity the inferred mass can shift by ~1.5 MJ depending on assumed Z, which matters for interpreting direct imaging surveys. That is an actionable result.\n\nThe soft spots are real but not fatal. The load-bearing assumption is that the collapse conserves total entropy: they replace the dynamical collapse with a jump to a tabulated radius at fixed entropy. The stress-test note is right that shock heating during collapse would change the post-collapse entropy and, with it, the inferred masses. The paper acknowledges the approximation in Section 2 and in the summary, but it never quantifies the sensitivity. A simple test—running the post-collapse tracks with initial entropy varied by a few percent—would have told them how robust the mass predictions are. I suspect it would not break the overall viability claim, because the sample is small and the dynamical mass uncertainties are broad, but for two of the four planets (β Pic b and AF Lep b) the agreement is already in the 1-sigma tail. For β Pic b, raising the entropy would actually lower the inferred mass and improve the agreement; for AF Lep b it would push the lower edge down, potentially weakening it. So the effect is not one-directional, and the authors should show it rather than leave it.\n\nThe EoS switch from SCvH to CMS is handled carefully in Appendix A: the 50% radius difference disappears after a few Myr, and the choice of EoS matters more than the initial radius. That is good. The simple grey atmosphere is a limitation, but the comparison with non-grey models (ATMO, Sonora) suggests it is not driving the results. On reproducibility, MESPA is public but the paper does not pin a version; a versioned release would help. The self-citations to the group's own code are appropriate given the code is open.\n\nOverall: this is a solid, honest paper. It deserves a proper peer review. A good referee should ask for an entropy-sensitivity test and a versioned code snapshot, but neither request is grounds for rejection. I'd cite it and I'd bring it to the group.","headline":"A genuinely unified set of disk-instability tracks with a fair comparison to the four dynamical-mass planets; the adiabatic collapse assumption is the main soft spot, but the paper deserves a serious referee.","tokens_in":19279,"tokens_out":4217,"would_cite":true,"duration_ms":41321,"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":"Disk-instability cooling tracks reproduce the measured masses of directly imaged giant planets.","keywords":["disk instability","giant planet formation","planetary evolution","cooling tracks","dynamical collapse","metallicity","directly imaged exoplanets","age-luminosity relation"],"falsifier":"A directly imaged planet in the $1$–$12\\,M_{\\rm J}$ range whose dynamical mass lies outside the mass range implied by its measured age and luminosity for every metallicity between $0.5$ and $2$ times protosolar would contradict the tracks; a concrete version is a benchmark planet whose dynamical mass disagrees with the inferred mass by more than the model's $1.5\\,M_{\\rm J}$ metallicity spread. A direct calculation that would also settle the matter is a 3D radiation-hydrodynamic collapse simulation showing that the total entropy before and after collapse differs by more than a few percent.","tokens_in":18313,"feed_emoji":"🪐","tokens_out":12475,"duration_ms":105752,"temperature":0.7,"pith_summary":"This paper builds a unified evolutionary model of giant planets born by disk instability, following a gas clump from its extended, cold pre-collapse state through dynamical collapse and into billions of years of contraction and cooling. The aim is to see whether such tracks, without tuning to observed luminosities, can match the age–luminosity–mass relations of directly imaged exoplanets. For the four planets with measured dynamical masses in the model's $1$–$12\\,M_{\\rm J}$ range—HR 8799 e, AF Lep b, Beta Pic b, and Beta Pic c—the inferred masses agree with the dynamical measurements. The authors also find that assumed metallicity shifts inferred masses by up to $1.5\\,M_{\\rm J}$ at the ages typical of directly imaged planets, and that luminosity evolution alone cannot distinguish disk instability from core accretion. If the tracks are right, disk instability remains a viable formation pathway for these objects, and composition must be included when deriving masses from luminosity.","feed_headline":"Disk-instability tracks match masses of imaged planets","feed_subtitle":"A unified clump-to-planet model reproduces dynamical masses for HR 8799 e, AF Lep b, and Beta Pic b and c.","key_machinery":"The carrying object is a set of cooling tracks for $1$–$12\\,M_{\\rm J}$ protoplanets computed in one numerical framework that spans three phases: a slow Kelvin–Helmholtz contraction of an extended, low-density gas clump (radii of order AU, surface temperatures below 100 K, modeled with low-temperature opacities down to 10 K); a dynamical collapse triggered when molecular hydrogen begins to dissociate at central temperatures of roughly 2000 K; and long-term contraction and cooling lasting several gigayears. The collapse itself is not simulated: the post-collapse radius is read from a precomputed table that maps mass, composition, and total entropy to radius under the assumption that the collapse is adiabatic, so the initial post-collapse entropy is fixed by the clump's pre-collapse evolution rather than chosen by hand. Metallicity enters through opacity scaling and through the resulting initial structure, and the same tracks are then inverted to turn measured age and luminosity into inferred mass.","core_discovery":"The central claim is that the initial entropy of a disk-instability planet is not an arbitrary hot-start parameter but is set by the preceding clump evolution, and that cooling tracks built on that entropy reproduce the observed luminosities of all currently known directly imaged giant planets with dynamical mass constraints. For a protosolar composition, the tracks imply masses of $8.42$–$10.90\\,M_{\\rm J}$ for HR 8799 e (dynamical mass $9.6^{+1.9}_{-1.8}\\,M_{\\rm J}$), $4.11$–$6.94\\,M_{\\rm J}$ for AF Lep b ($3.75\\pm0.5\\,M_{\\rm J}$), $6.21$–$8.10\\,M_{\\rm J}$ for Beta Pic c ($8.3\\pm1.0\\,M_{\\rm J}$), and above $11.85\\,M_{\\rm J}$ for Beta Pic b ($9.3^{+2.6}_{-2.5}\\,M_{\\rm J}$). Metallicity between $0.5$ and $2$ times protosolar changes the inferred mass of a given object by up to $1.5\\,M_{\\rm J}$, with the largest spread at ages of tens of megayears. The authors conclude that disk instability cannot be ruled out by current observations, and that luminosity is not a discriminator between formation pathways because core accretion with hot accretion, and even cold accretion with massive cores, can produce nearly identical cooling curves.","pith_inferences":["If more dynamical masses arrive, a population-level test becomes possible: a systematic offset of future objects from the disk-instability mass–luminosity relation across the full metallicity range would start to disfavor one formation channel.","The entropy-conserving collapse assumption could be checked with 3D radiation-hydrodynamic simulations of collapsing clumps; substantial entropy loss during collapse would shift the inferred masses systematically lower.","Because metallicity shifts masses most at ages of tens of megayears, atmospheric or spectral constraints on the composition of young directly imaged planets could break the degeneracy and sharpen mass estimates.","The result suggests that apparent discrepancies between hot-start models and observed planets should be interpreted as composition and age effects before being attributed to formation pathway."],"forward_implications":["The masses of directly imaged planets can be inferred from luminosity and age using disk-instability tracks, and the resulting estimates agree with independent dynamical masses for HR 8799 e, AF Lep b, Beta Pic b, and Beta Pic c.","Planetary metallicity must be treated as a source of uncertainty in mass estimates; at ages around 30–60 Myr, unknown composition changes the inferred mass by up to $1.5\\,M_{\\rm J}$.","Luminosity alone cannot identify the formation pathway: disk-instability tracks converge with hot-accretion core-accretion models, and with cold-accretion models when the core is massive.","The pre-collapse phase is brief but mass-dependent, lasting about $2.6\\times10^5$ yr for a $1\\,M_{\\rm J}$ clump versus $5.6\\times10^3$ yr for a $10\\,M_{\\rm J}$ clump, and higher metallicity roughly doubles that timescale by raising opacity.","Formation models with different initial entropies can still be distinguished at young ages, so evolutionary models remain useful for diagnosing formation physics even though luminosity is degenerate at later times."],"supporting_citations":[{"why":"Supplies the opacity scaling with metallicity and the pre-collapse timescale proportionality used to construct the clump models.","marker":"Helled & Bodenheimer (2011)"},{"why":"Defines the hot-, warm-, and cold-start entropy regimes used to classify the initial post-collapse entropies of the tracks.","marker":"Spiegel & Burrows (2012)"},{"why":"Provides the core-accretion evolutionary tracks used to test whether luminosity can distinguish formation pathways.","marker":"Mordasini (2013)"},{"why":"Gives the dynamical masses for HR 8799 e, Beta Pic b, and Beta Pic c used as the observational test.","marker":"Brandt et al. (2021b)"},{"why":"Provides the dynamical mass of AF Lep b, the lowest-mass planet with both luminosity and dynamical mass.","marker":"Balmer et al. (2025)"},{"why":"Supplies the dynamical age estimate for the Beta Pic moving group used for AF Lep b and the Beta Pic planets.","marker":"Miret-Roig et al. (2020)"},{"why":"Provides the bolometric luminosity of HR 8799 e used to infer its mass.","marker":"Ruffio et al. (2026)"},{"why":"Provides the bolometric luminosity of Beta Pic c and its direct detection.","marker":"Nowak et al. (2020)"},{"why":"Provides the bolometric luminosity of Beta Pic b used to infer its mass.","marker":"Chilcote et al. (2017)"},{"why":"Provides the bolometric luminosity of AF Lep b used to infer its mass.","marker":"Gratton et al. (2024)"}],"fun_headline_variants":["Disk instability tracks fit imaged planet masses","Clump evolution matches masses of four imaged planets","Disk-instability planets match dynamical mass constraints","Formation history shapes giant planet cooling tracks","Metallicity alters mass inferred from young planet light"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"That the dynamical collapse is adiabatic—the clump's total entropy just before collapse equals its entropy just after, so the newborn planet's radius and luminosity come from an entropy-conserving interpolation table rather than from simulating the collapse—is the load-bearing assumption; if entropy is lost or gained during collapse, the initial radii and luminosities, and with them the masses inferred in Section 6, would shift.","fun_headline_variants_meta":{"raw":{"variants":["Disk instability tracks fit imaged planet masses","Clump evolution matches masses of four imaged planets","Disk-instability planets match dynamical mass constraints","Formation history shapes giant planet cooling tracks","Metallicity alters mass inferred from young planet light"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00028,"raw_usage":{"total_tokens":1783,"prompt_tokens":1192,"completion_tokens":591,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":808,"completion_tokens_details":{"reasoning_tokens":521}},"tokens_in":808,"tokens_out":591,"duration_ms":6592,"temperature":1.0,"reasoning_tokens":521,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:19:13.724730+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A directly imaged planet in the $1$–$12\\,M_{\\rm J}$ range whose dynamical mass lies outside the mass range implied by its measured age and luminosity for every metallicity between $0.5$ and $2$ times protosolar would contradict the tracks; a concrete version is a benchmark planet whose dynamical mass disagrees with the inferred mass by more than the model's $1.5\\,M_{\\rm J}$ metallicity spread. A direct calculation that would also settle the matter is a 3D radiation-hydrodynamic collapse simulation showing that the total entropy before and after collapse differs by more than a few percent.","supporting_citations":[{"cited_title":"and Burrows, Adam , year = 2012, month = feb, journal =","cited_arxiv_id":null,"evidence_quote":"Defines the hot-, warm-, and cold-start entropy regimes used to classify the initial post-collapse entropies of the tracks."},{"cited_title":", year = 2013, month = oct, journal =","cited_arxiv_id":null,"evidence_quote":"Provides the core-accretion evolutionary tracks used to test whether luminosity can distinguish formation pathways."}],"review_version":1}