{"id":"4da80bf7-17bf-487a-8787-82ffdf55c816","arxiv_id":"2505.00071","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"For stars above about 50 solar masses, detailed MESA models expand far less than fast SeBa tracks, shrinking the minimum orbital period for avoiding mass transfer in triples by roughly three orders of magnitude and widening the parameter space for triple compact object formation.","lead":"This paper couples the TRES triple-system evolution code to the detailed stellar code MESA, the first on-the-fly coupling for triple systems. It shows that MESA and the fast code SeBa predict very different maximum stellar radii for stars above 50 solar masses, which changes which triple systems interact and could boost predicted gravitational-wave merger rates.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The three-orders-of-magnitude Pmin reduction is anchored to one extreme case (85 Msun, Dutch scaling=1); under the paper's own default Dutch/3 winds the implied reduction is closer to one to two orders, so the headline overstates the robustness.","rationale":"The reader's CONDITIONAL verdict already captures the main weakness: the quantitative magnitude is fragile because it depends on wind prescriptions and the absence of rotation. My stress-test sharpens this into an internal scoping problem: even without questioning whether the Dutch/1 winds are physically correct, the paper's own default physics (Dutch/3) does not produce the advertised three-order reduction. The abstract states the three-order reduction as a general result, while Sect. 4.5 obtains it only for a single 85 Msun track with the strongest wind scaling. The paper's Fig. 3 and Sect. 3.1 show that with Dutch/3 the radius gap is about one order of magnitude, which by the paper's own Kepler scaling corresponds to roughly a 30x period reduction, not 1000x. This does not undermine the qualitative claim that H00/SeBa tracks overestimate RLOF at high masses because of their inconsistent reaction to mass loss; the examples in Sect. 4.2-4.4 remain illustrative. But the headline number, which is the most citable result, needs to be re-scoped. The independent support in the paper is real: the TRES-MESA coupling is described concretely and made public, the alpha_ov calibration is documented, and the eta Carinae validation is a useful sanity check. None of that, however, fixes the mismatch between the stated default physics and the headline claim. I therefore agree with the reader's CONDITIONAL verdict and would not change it; the concern is addressable by re-presenting the Pmin scaling as a grid rather than a single number.","tokens_in":32829,"tokens_out":5590,"duration_ms":60601,"concrete_test":"Produce a Pmin table from the existing Rmax grid (M = 50, 60, 70, 85, 100, 120 Msun; Dutch_scaling_factor = 0.333 and 1): compute Pmin,MESA/Pmin,SeBa = (Rmax,MESA/Rmax,SeBa)^{3/2} using the same Roche-lobe and Kepler scalings as Sect. 4.5. If the three-order reduction appears only for M>=85 Msun with scaling=1, while scaling=0.333 gives roughly one to two orders, then the abstract and Sect. 5 should be reworded to say the reduction is mass- and wind-dependent, up to three orders for the strongest winds.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is that using MESA instead of SeBa lowers the minimum inner period for avoiding RLOF by three orders of magnitude, Pmin,SeBa~6e3 d to Pmin,MESA~6 d (abstract and Sect. 5). In Sect. 4.5 this is derived by Kepler-scaled extrapolation from a single M=85 Msun track with Dutch_scaling_factor=1, whose MESA Rmax is only ~35 Rsun. The paper's own default wind setting is Dutch/3 (Sect. 2.2.4), and under that prescription the MESA/SeBa maximum-radius discrepancy is about one order of magnitude, not two (Sect. 3.1, Fig. 1b and Fig. 3). Because the RLOF condition has RL proportional to a and P scales as a^{3/2}, a tenfold radius gap implies only ~10^{1.5}~30x period reduction, i.e. Pmin,MESA~200 d rather than 6 d. Thus the 'three orders' statement is an extreme-case upper limit, valid only for the strongest winds and highest masses, not the general code-to-code result advertised. The qualitative divergence is likely robust, but the headline magnitude is conditioned on the most favorable corner of the wind/mass grid; with weaker winds or lower masses the gap shrinks substantially. This is an internal-consistency/scope problem: the abstract generalizes a corner of Fig. 3.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a new coupling of the MESA detailed stellar evolution code to the TRES secular triple-star evolution code through AMUSE, and uses it to compare the evolutionary pathways of massive hierarchical triples with those obtained using the rapid SeBa code. The authors report that MESA and SeBa single-star tracks diverge increasingly with initial mass and wind mass-loss efficiency, that the maximum radii can differ by up to two orders of magnitude, and that the minimum inner period for avoiding Roche-lobe overflow is reduced by three orders of magnitude when MESA replaces SeBa. Several illustrative systems are shown in which the two codes predict different pathways: inner versus tertiary mass transfer, mass transfer versus dynamical destabilization, mass transfer versus orbital unbinding, interacting versus non-interacting outcomes, and a case where self-consistently computed apsidal-motion constants change the outcome. The paper also explores the impact of a modified dynamical-tides prescription from Sciarini et al. (2024).","tokens_in":33221,"tokens_out":9896,"duration_ms":96927,"significance":"If the central period-reduction claim holds, the results imply that rapid-code population synthesis of massive triples systematically overestimates interaction rates and underestimates the formation of triple compact objects, directly affecting gravitational-wave merger rate predictions. The qualitative divergence between rapid and detailed stellar codes for masses above 50 M_sun is consistent with Bavera et al. (2023) and is an important caution for the field. The methodological advance of coupling MESA on-the-fly to a secular triple code is valuable, and the authors make the code publicly available. The paper also provides a careful single-star comparison and is transparent about wind and rotation prescriptions. The main quantitative claim, however, is derived from an extreme corner of the grid and is not robust across the paper's own default choices, so it needs qualification.","major_comments":[{"comment":"The three-orders-of-magnitude reduction in the minimum inner period (Pmin,MESA∼6 days vs Pmin,SeBa∼6×10^3 days) is derived in Sect. 4.5 from a single 85 M_sun MESA track computed with Dutch_scaling_factor=1 (the 'TCO' system). This is not representative of the paper's default wind setting: in Sect. 2.2.4 the authors adopt Dutch_scaling_factor=0.333 as the default, and under that prescription the MESA/SeBa maximum-radius discrepancy in the considered mass range is about one order of magnitude, not two (Sect. 3.1, Fig. 1b; lower panel of Fig. 3). Since the limiting period scales as R_max^{3/2}, a factor-of-ten radius gap implies only a ~30-fold reduction in Pmin (i.e., ~200 days), not a 1000-fold reduction. The abstract and conclusion present the 6-day value as a general result without these qualifications. I recommend stating that the three-orders reduction is an extreme-case upper limit valid for the strongest winds and the highest masses, and giving the estimate under the default wind prescription.","section":"Sect. 4.5, Abstract, Sect. 5"},{"comment":"The MESA tracks are normalized to SeBa at 50 M_sun via the overshoot parameter α_ov, calibrated without winds to reproduce the SeBa maximum MS radius. The paper notes that this calibrated value may be underestimated for higher masses (Sect. 2.2.3, Appendix A). Consequently, the quantitative divergence between MESA and SeBa above 50 M_sun is not fully independent of the chosen calibration; part of the high-mass difference could reflect the one-point normalization rather than solely the self-consistent reaction to mass loss. The authors should state this calibration dependence explicitly when quoting the Pmin estimates and interpreting the order-of-magnitude radius discrepancies.","section":"Sect. 2.2.3 and Appendix A"},{"comment":"The result that the S24 dynamical-tides prescription makes the eccentricity increase for e≳0.7 is a model-dependent property of the low-order Zahn (1977) expansion, as the authors state in Sect. 4.7 and Appendix D. The abstract and the concluding section do not repeat this caveat, so a reader could mistake this for a robust physical finding. Please add an explicit caveat, both in the abstract and in the conclusions, that this eccentricity increase is a prediction of the S24 model and may change if higher-order eccentricity terms are included.","section":"Sect. 4.7 and Appendix D"}],"minor_comments":[{"comment":"In the sentence 'Given Kepler 3rd law (P2∝ a3)', the notation should be typeset as P^2 ∝ a^3, and the derivation should mention explicitly that the Roche-lobe radius is taken as proportional to a at fixed mass ratio, so that the period scales as R_max^{3/2}.","section":"Sect. 4.5"},{"comment":"The system labeled 'η Carinae*' is marked as 'Divergent: No' in Table 1, but Appendix B states that the MESA and SeBa pathways do differ (eccentric versus circular mass transfer). The table footnote explains the nomenclature, but the caption should also note this distinction to avoid apparent inconsistency.","section":"Table 1 and Appendix B"},{"comment":"The abstract should state that the reduction in Pmin is 'up to three orders of magnitude' under the strongest wind prescription, rather than presenting it as a unique value, so that the headline matches the internal-consistency concerns raised in Sect. 4.5.","section":"Abstract and Sect. 5"},{"comment":"There are minor typographical issues, such as the misplaced diacritic in the reference 'Krtiˇcka' and the equation-number formatting in Appendix D. A careful proofread of the final version is recommended.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper makes a useful contribution to the field and is likely to be of interest to A&A readers. The main revision needed is to qualify the three-orders-of-magnitude claim so that it is not overinterpreted as a robust default result. I would ask the authors to provide the Pmin estimate for their default Dutch/3 wind prescription and to explicitly state the dependence of their quantitative conclusions on the wind scaling factor and on the α_ov calibration. Once these qualifications are made, the paper should be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe thing to know: this is the first paper to couple TRES, a triple secular code, to MESA on the fly, and it makes a plausible case that H00-track codes like SeBa badly mispredict the evolution of very massive triples. The qualitative divergence—MESA stars above 50 Msun expand far less than SeBa because winds strip the envelope—is real and lines up with Bavera et al. 2023. But the flashy “three orders of magnitude” reduction in the minimum period for avoiding inner RLOF is built on a single extreme case (85 Msun, Dutch wind scaling 1), and it is not the general result the abstract suggests.\n\nWhat is genuinely new: the code coupling itself, the self-consistent apsidal motion constant, and a handful of worked triple systems showing divergent pathways (inner vs tertiary MT, MT vs destabilization, MT vs non-interacting/TCO). For that, credit is due. The code is public, the comparison is carefully set up, and the authors are explicit about what they do and do not include (no mass-transfer feedback, no rotation).\n\nThe soft spots are in proportion. First, the alpha_ov calibration at 50 Msun to match SeBa means the divergence above 50 Msun is not fully independent—part of it reflects the H00 fit extrapolating outside its calibration grid. The authors mostly frame this correctly, but it is a real limitation. Second, the Pmin claim: under the paper’s own default Dutch/3 winds, the radius gap between MESA and SeBa is about one order of magnitude, which by Kepler scaling gives a period reduction of roughly 30x, not 1000x. The three-orders number only appears for the strongest winds and highest masses. The abstract should either adopt the more modest number or explicitly scope it to the high-wind corner. Third, the S24 tidal section is an interesting aside but depends on their own prior model and a low-order expansion; the e >= 0.7 eccentricity increase is a flagged result, not a demonstrated robust one. On its own, that section does not sink the paper.\n\nBottom line: the qualitative thesis is sound and worth publishing; the quantitative headline needs to be scaled back or re-scoped. Read this if you work on triple evolution, massive binary population synthesis, or GW progenitor pathways. It deserves peer review. I’d cite it.\n\nBest,\n\n[Name]","headline":"First on-the-fly TRES+MESA coupling shows massive triple pathways really do diverge from SeBa, but the headline three-orders-of-magnitude Pmin reduction is an extreme-case artifact.","tokens_in":33725,"tokens_out":3112,"would_cite":true,"duration_ms":31623,"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":"Detailed stellar-structure models shrink the minimum safe orbit for massive triple stars by a thousandfold, changing predicted gravitational-wave progenitor rates.","keywords":["stars: evolution","stars: massive","hierarchical triple systems","stellar winds","rapid vs detailed stellar codes","apsidal motion constant","von Zeipel-Lidov-Kozai oscillations","gravitational wave progenitors"],"falsifier":"Interferometric or eclipsing-binary radius measurements of an ~85$\\,M_\\odot$, solar-metallicity star near the end of main-sequence life would settle which code is right: the detailed model holds the maximum radius to tens of solar radii, while the fast code predicts a red-supergiant expansion to thousands of solar radii, so one such star observed at large radius would overturn the MESA-based period reduction.","tokens_in":32580,"feed_emoji":"🌠","tokens_out":12738,"duration_ms":124985,"temperature":0.7,"pith_summary":"This paper claims that the fast stellar-evolution codes used in triple-star population synthesis substantially mispredict how much very massive stars expand, and that this misprediction changes which triple systems interact. The authors couple a triple secular evolution code to MESA, a detailed one-dimensional stellar-structure code, and compare the same triples evolved with the fast code SeBa. In the 50 to 120 solar-mass range, the maximum stellar radii differ by up to two orders of magnitude, and the minimum inner orbital period that avoids mass transfer drops from about six thousand days to about six days when the detailed code is used. That widening of the non-interacting parameter space matters because triples that avoid mass transfer can become triple compact objects and later merge through gravitational-wave emission. A fair reader should care because the result implies that population-synthesis predictions for massive triples, including merger-rate estimates, depend on the choice of stellar physics as much as on the three-body dynamics.","feed_headline":"Detailed stellar physics shrinks triple-star safe orbits 1000-fold","feed_subtitle":"Fast population-synthesis codes inflate massive-star radii, so predicted compact-object merger rates may be off.","key_machinery":"The load-bearing mechanism is an on-the-fly coupling of the TRES triple secular evolution code to MESA, a detailed one-dimensional stellar-structure code, so that the star's full structure (radius, core mass, apsidal motion constant, gyration radius) is recomputed as the three-body dynamics evolve. In this setup, wind mass loss feeds back into the stellar structure continuously, which is what keeps the most massive models from swelling to red-supergiant dimensions. A second structural ingredient is the apsidal motion constant $k_{\\rm AMC}$, retrieved from the MESA profile at each timestep; it decreases by more than an order of magnitude during the main sequence, reducing precession from tidal and rotational distortion and thereby strengthening the von Zeipel-Lidov-Kozai mechanism. The comparison baseline is the fast code SeBa, whose Hurley fitting formulae extrapolate a grid that ends at 50 solar masses, and Roche-lobe overflow is judged at periastron using the Eggleton formula with an eccentricity correction.","core_discovery":"On the paper's own terms, the central discovery is that the stellar-evolution physics, not the secular dynamics alone, controls many of the divergent fates of massive hierarchical triples. In the fast code, a 70 to 120 solar-mass star loses mass but then shifts onto the track of a lower-mass star, swelling to a red supergiant of thousands of solar radii; in the detailed code, the same star reacts to wind mass loss by contracting, so its maximum radius stays at tens to hundreds of solar radii. Because Roche-lobe overflow is decided by radius against the periastron Roche lobe, this radius gap translates directly into a different classification of the system's evolution. The paper demonstrates divergent outcomes for every category it tracks: inner versus tertiary mass transfer, mass transfer versus dynamical destabilization, mass transfer versus orbit unbinding, and mass transfer versus a non-interacting triple that can become a triple compact object. The same self-consistent stellar structure also lowers the apsidal motion constant along the main sequence, weakening tidal and rotational precession and letting von Zeipel-Lidov-Kozai oscillations persist longer, which further increases the chance of interaction.","pith_inferences":["A consequence the paper leaves implicit: the same fast-code radius bias likely affects massive binary population synthesis, so the correction to interaction rates may extend to binary black-hole merger channels as well as triple ones.","Because the MESA models are non-rotating, the three-orders-of-magnitude period reduction is best read as an upper bound; adding rotation could let stars expand and close part of the gap.","A testable follow-up would be a grid-based population synthesis with the detailed code, converting the per-system pathway flips shown here into a quantitative revision of predicted gravitational-wave merger rates."],"forward_implications":["If MESA's radius evolution is the faithful one, fast-code population synthesis has been overcounting interacting massive triples: systems previously classified as mass-transferring would instead remain detached through the main sequence.","The minimum inner period for avoiding Roche-lobe overflow drops from about 6,000 days to about 6 days, enlarging the parameter space for triple compact objects that can later merge through gravitational-wave emission.","Structure-dependent precession, through a falling apsidal motion constant, keeps von Zeipel-Lidov-Kozai oscillations alive longer, making eccentric mass transfer more likely than constant-coefficient models suggest.","The divergence between codes produces opposite outcomes in every tracked category: inner versus tertiary mass transfer, mass transfer versus dynamical destabilization, mass transfer versus orbit unbinding, and mass transfer versus a non-interacting triple.","The choice of dynamical-tide prescription also changes outcomes for eccentric inner binaries, with the revised prescription producing eccentricity growth instead of circularization for systems above roughly e = 0.7."],"supporting_citations":[{"why":"Supplies the fitting formulae that define the fast SeBa tracks, the baseline whose extrapolation beyond 50 solar masses is under test.","marker":"Hurley et al. 2000"},{"why":"Provides the stellar grid up to 50 solar masses from which the Hurley formulae are fitted; going beyond this grid is where the tracks diverge.","marker":"Pols et al. 1998"},{"why":"The detailed stellar-structure code MESA that replaces the fast tracks, supplying the self-consistent radius and apsidal-motion evolution.","marker":"Paxton et al. 2011"},{"why":"Showed in binaries that fast codes overpredict maximum radii of massive stars because their wind mass loss is not self-consistent; the paper extends this argument to triple systems.","marker":"Bavera et al. 2023"},{"why":"Earlier population synthesis of massive triples with a fast code, the source of the roughly 6,000-day minimum period and the pathway nomenclature the paper compares against.","marker":"Kummer et al. 2023"},{"why":"Defines the TRES triple secular evolution code and its treatment of precession, tides, and stopping conditions that the MESA coupling builds on.","marker":"Toonen et al. 2016"},{"why":"Provides the eta Carinae triple-merger scenario and the earlier example of detailed stellar evolution in triple N-body simulations that this work validates against.","marker":"Portegies Zwart & van den Heuvel 2016"},{"why":"Part of the Dutch wind mass-loss prescription used in the MESA models; the strength of these winds drives the radius suppression.","marker":"Vink et al. 2001"},{"why":"Recent independent coupling of a triple secular code to detailed stellar tracks, used to frame the novelty of on-the-fly MESA coupling.","marker":"Shariat et al. 2025a"}],"fun_headline_variants":["Detailed stellar physics shrinks triple-safe orbits 1000-fold","Fast code inflates massive star radii, altering triple fates","MESA vs SEBA: triple evolution diverges for massive stars","Self-consistent stellar physics changes massive triple outcomes","Detailed stellar code reveals smaller triple merge radii"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result rests on assuming that the detailed code's non-rotating models, with their chosen wind mass-loss rates, describe how very massive stars really expand; if real winds are weaker or rotation makes the stars swell, the claimed thousand-fold period reduction shrinks.","fun_headline_variants_meta":{"raw":{"variants":["Detailed stellar physics shrinks triple-safe orbits 1000-fold","Fast code inflates massive star radii, altering triple fates","MESA vs SEBA: triple evolution diverges for massive stars","Self-consistent stellar physics changes massive triple outcomes","Detailed stellar code reveals smaller triple merge radii"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000634,"raw_usage":{"total_tokens":2993,"prompt_tokens":1078,"completion_tokens":1915,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":694,"completion_tokens_details":{"reasoning_tokens":1835}},"tokens_in":694,"tokens_out":1915,"duration_ms":13908,"temperature":1.0,"reasoning_tokens":1835,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:51:26.534672+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Interferometric or eclipsing-binary radius measurements of an ~85$\\,M_\\odot$, solar-metallicity star near the end of main-sequence life would settle which code is right: the detailed model holds the maximum radius to tens of solar radii, while the fast code predicts a red-supergiant expansion to thousands of solar radii, so one such star observed at large radius would overturn the MESA-based period reduction.","supporting_citations":[{"cited_title":"R., Schr \\\"o der , K.-P., Hurley , J","cited_arxiv_id":null,"evidence_quote":"Provides the stellar grid up to 50 solar masses from which the Hurley formulae are fitted; going beyond this grid is where the tracks diverge."},{"cited_title":"2023, , 678, A60","cited_arxiv_id":null,"evidence_quote":"Earlier population synthesis of massive triples with a fast code, the source of the roughly 6,000-day minimum period and the pathway nomenclature the paper compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the eta Carinae triple-merger scenario and the earlier example of detailed stellar evolution in triple N-body simulations that this work validates against."}],"review_version":1}