{"id":"973d4915-cd63-4c68-bfae-e784b33f22c7","arxiv_id":"2412.10691","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper reviews a two-stage common-envelope model and replaces an earlier fit for the convective-envelope onset temperature with a metallicity-dependent formula tied to Tmin.","lead":"This short proceedings paper from a retirement-meeting talk summarizes recent work on common-envelope evolution in binary stars. It also reports a small correction to the fit for the onset temperature of convective envelopes, intended to make a two-stage common-envelope recipe usable in rapid population synthesis codes.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The two-stage common-envelope claim rests on an untested thermal-timescale response of the radiative intershell; the new Eq. (6) fit is secondary and does not shore up that premise.","rationale":"This is a conference proceedings paper that mostly summarizes the authors' prior work, with the new element being the corrected Tonset formula in Eq. (6). The proceedings format means that full derivations and simulations are not expected, so the absence of a new simulation is not itself a flaw. However, the central scientific claim—that the standard energy-conserving common-envelope formalism is inappropriate for full common-envelope events and should be replaced by a two-stage treatment—depends on a specific microphysical premise: the radiative intershell expands on a thermal timescale, making deposited orbital energy unavailable for envelope ejection. That premise is borrowed from Vigna-Gómez et al. (2022) and is not re-derived or tested here. Because the two-stage formalism predicts final separations and merger rates that differ from the alpha-formalism by orders of magnitude, the premise is genuinely load-bearing. The Eq. (6) fit is simple, physically motivated, and internally consistent, but it addresses track mismatches rather than the thermal-timescale question. I agree with the reader's identification of the weakest assumption. The proposed 1D energy-injection experiment would directly test whether the thermal-timescale premise holds, and would either support or undermine the two-stage formalism. No internal inconsistency or mathematical error is apparent in the paper's order-of-magnitude estimates; the concern is about the strength of external support for a central assumption, which justifies a CONDITIONAL rather than ACCEPT or REJECT verdict.","tokens_in":7011,"tokens_out":6448,"duration_ms":63484,"concrete_test":"Use a 1D stellar-structure code such as MESA to build a 12 solar-mass, solar-metallicity red supergiant with a well-resolved radiative intershell; inject orbital energy locally at the drag rate dE/dt = C_D rho v^3 sigma implied by Eqs. (1)-(3) at radii swept by the inspiraling companion; then measure the local expansion timescale of the intershell and the fraction of injected energy that is radiated away before doing expansion work. If the intershell expands on a dynamical timescale, or if less than a few tens of percent of the injected energy is radiated, the two-stage formalism's premise fails. If the expansion is thermal and most deposited energy is radiated, the premise is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2 moves from Vigna-Gómez et al. (2022) showing that the radiative intershell expands on a thermal timescale to the conclusion that the energy-conserving formalism is inappropriate for the full common-envelope event, and then to the two-stage treatment of Hirai & Mandel (2022). The load-bearing step is that energy deposited in the radiative intershell is radiated away rather than used for envelope ejection, and that the intershell is removed on a thermal, not dynamical, timescale via angular-momentum-conserving mass transfer. This paper presents no simulation or calculation that tests this response. The only support is the citation to Vigna-Gómez et al. (2022), whose analysis is not reproduced. If the intershell instead responds on a dynamical timescale, or if a substantial fraction of deposited orbital energy is converted into P dV work even while the region expands slowly, then the claimed failure of the energy-conserving formalism, and the resulting predictions for final separations and merger rates, would be quantitatively wrong. The new Eq. (6) is a plausible empirical correction to Picker et al. (2024), but it is not the central claim; even a perfect fit to Tonset would not validate the two-stage formalism without the thermal-timescale premise.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings contribution from Mandel, Hirai, and Picker summarizes recent work by their group on common-envelope (CE) evolution. After deriving order-of-magnitude inspiral and ablation timescales, the paper argues that the standard energy-conserving α-formalism is inappropriate for describing full CE events because the radiative intershell of an evolved donor expands on a thermal timescale, so much of the deposited orbital energy is radiated away rather than used for envelope ejection. It advocates instead the two-stage CE formalism of Hirai & Mandel (2022), in which only the outer convective layers are treated adiabatically and the removal of the radiative intershell is modeled as thermal-timescale, angular-momentum-conserving mass transfer. The paper also reports a correction to Picker et al. (2024) that sets the onset temperature Tonset relative to the temperature at maximum convective-envelope extent, Tmin, via the new metallicity-dependent fit in Eq. (6), intended to avoid artifacts from mismatched single stellar evolution tracks. The paper closes with brief remarks on luminous red nova light curves and observational prospects.","tokens_in":7235,"tokens_out":5271,"duration_ms":45571,"significance":"The two-stage common-envelope formalism, if correct, would substantially change predicted post-common-envelope separations and merger rates, potentially relieving the tension between population-synthesis predictions and gravitational-wave observations highlighted by Mandel & Broekgaarden (2022). The paper's strengths are its clear back-of-the-envelope derivations of inspiral timescales and drag regimes, which provide transparent physical intuition, and the practical metallicity-dependent correction in Eq. (6) that can be directly implemented in rapid population-synthesis codes. However, the central physical premise of the two-stage formalism—that the radiative intershell expands on a thermal timescale and radiates away most deposited orbital energy—is not independently tested in this paper; it is inherited from Vigna-Gómez et al. (2022), and the paper presents no new simulation or calculation that checks this response. The new fit in Eq. (6) is presented without uncertainties, residuals, or fitting details, and Figure 4 shows no error bars or scatter, so the claimed mass independence is not quantitatively supported as displayed.","major_comments":[{"comment":"The claim that the energy-conserving formalism is inappropriate for the full common-envelope event rests on the assertion, attributed to Vigna-Gómez et al. (2022), that the radiative intershell between the convective core and convective outer envelope expands on a thermal timescale, so that most energy deposited there is radiated away without doing work to expel the envelope. This premise is load-bearing for the two-stage formalism's predictions of final separations and merger rates, yet the present paper provides no reproduction of that analysis and no new test. If the intershell instead responded on a dynamical timescale, or if a substantial fraction of the deposited energy were converted into expansion work even during slow expansion, the two-stage predictions would be quantitatively wrong. Please either provide a direct calculation or simulation that tests the thermal-timescale response in the parameter space relevant here, or explicitly state that the two-stage formalism inherits this premise from Vigna-Gómez et al. (2022) and summarize the evidence that supports it.","section":"Section 2"},{"comment":"The new correction is presented as an empirical fit, but the fitting procedure, residuals, and uncertainty estimates are not given. Figure 4 shows no error bars or scatter, so the claim that Tmin/Tonset is 'approximately independent of stellar mass' over the range [7, 25] solar masses is not quantitatively supportable as displayed. Please report the number of MESA models used, the scatter around the fit, the metallicity grid, and a measure of goodness of fit (e.g., rms residuals). This information is necessary for readers to judge whether Eq. (6) is reliable enough for use in population-synthesis codes.","section":"Section 2, Eq. (6) and Figure 4"}],"minor_comments":[{"comment":"The phrase 'this seems to be born out' should be 'this seems to be borne out'.","section":"Section 1"},{"comment":"The sentence 'Here, we report a correction to the Picker et al. (2024) that sets Tonset relative to Tmin, rather than via Eq. (6) in that paper' is ambiguous because the new equation is also numbered Eq. (6). Please refer to 'Eq. (6) of Picker et al. (2024)' and 'the present Eq. (6)' to avoid confusion.","section":"Section 2"},{"comment":"The statement that mismatches between MESA tracks and population-synthesis tracks 'can lead to unphysical behaviour' would be more convincing with a brief illustrative example, such as a specific case where Tonset computed from the old fit exceeds the track's surface temperature or produces a non-monotonic convective envelope growth.","section":"Section 2"},{"comment":"The claim that 'the Vera Rubin Observatory may image hundreds of luminous red novae' should be qualified with the underlying population-synthesis assumptions or an explicit reference to the sensitivity of this number to model parameters.","section":"Section 3"},{"comment":"Some references are listed as arXiv e-prints without DOIs (e.g., Lau et al. 2022c, Noughani et al. 2024, Matsumoto & Metzger 2022). Please update to the published versions where available.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings paper summarizing the authors' own published work; the novel contribution is the correction in Eq. (6). The fit needs to be documented with uncertainties and residuals, and the thermal-timescale premise of the two-stage formalism should be presented with a more explicit caveat about the evidence base. The heavy reliance on self-citations is natural for a proceedings contribution, but the present paper should not ask readers to take the central physical premise on faith. Given the venue, a major revision with the requested additions is appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, the actual new content in this paper is one formula: Eq. (6), a fit for Tonset relative to Tmin that avoids mismatches between MESA-calibrated fits and rapid population synthesis tracks. The rest is a conference summary of the group's two-stage common-envelope program. Keep that framing in mind before you referee it: this is a proceedings write-up, not a full research article.\n\nThe order-of-magnitude parts are genuinely clear. The back-of-the-envelope inspiral timescales, the Bondi-Hoyle versus ram-pressure drag distinction, and the ablation estimate are well explained and pedagogical. The two-stage formalism (convective envelope ejected adiabatically, radiative intershell removed on a thermal timescale via angular-momentum-conserving mass transfer) is stated plainly, and the paper is honest that it is summarizing Hirai & Mandel (2022) and Picker et al. (2024).\n\nThe soft spots are in proportion. The new Eq. (6) is introduced with a single figure (Fig. 4) with no error bars, no scatter, no residuals, and no fitting details. The mass-independence claim over 7-25 solar masses is qualified by an unexplained 'small deviation' at high mass and super-solar metallicity, exactly where the formula could matter most for population synthesis. I would want the fit table and residuals before building anything on it.\n\nThe bigger issue is one the stress-test flagged, and I think it is real but not a flaw of this paper per se: the two-stage model rests on the premise that the radiative intershell expands on a thermal, not dynamical, timescale, so orbital energy deposited there is largely radiated away. That premise is cited to Vigna-Gomez et al. (2022), not tested here. For a proceedings summary that is acceptable, as long as you do not mistake the summary for new evidence. The paper's language is careful enough: it says 'showed' about the cited work, and the correction is explicitly an implementation detail.\n\nOverall, this deserves peer review in the sense that the formula and the mass-independence claim should be checked by someone who cares about the details. As a standalone scientific contribution, the evidence for Eq. (6) is thin, but the paper is honest about being a summary. I would send a competent referee to look at the fit, not to re-evaluate the whole two-stage program.","headline":"A clear conference summary with one small but plausible new fitting formula; the evidence for the formula is thin but the paper is honest about being a summary.","tokens_in":7796,"tokens_out":2300,"would_cite":true,"duration_ms":18691,"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 common-envelope events must be modelled in two stages—adiabatic ejection of the convective envelope followed by thermal-timescale removal of the radiative intershell—and reports a correction that lets…","keywords":["common envelopes","binary star evolution","mass transfer stability","two-stage common-envelope formalism","radiative intershell","population synthesis","luminous red novae","gravitational-wave mergers"],"falsifier":"Compare the final separations predicted by the two-stage formalism against a resolved 3D simulation of a common-envelope event with a radiative intershell; if the intershell expands on a dynamical timescale and its deposited orbital energy goes into unbinding, the formalism's predicted separations will be too wide.","tokens_in":6774,"feed_emoji":"💫","tokens_out":6714,"duration_ms":55320,"temperature":0.7,"pith_summary":"This paper argues that the standard energy-conserving 'alpha' formalism for common-envelope events, which assumes all orbital energy lost by the inspiralling companion goes into ejecting the donor's envelope, is the wrong bookkeeping for full common-envelope events. Instead, it advocates a two-stage picture: an adiabatic first stage that removes only the outer convective envelope, followed by a thermal-timescale second stage in which the radiative intershell is lost as non-conservative mass transfer. The paper also reports a corrected formula for when the convective envelope forms, tied to the minimum temperature rather than absolute track values, to avoid artefacts when the model is used in population-synthesis codes. If the two-stage picture is right, predicted merger rates change: many systems that the old formalism would have hardened drastically no longer do, which could relieve tension between population-synthesis models and gravitational-wave observations of black hole mergers.","feed_headline":"Common-envelope mergers follow two stages, not one energy budget","feed_subtitle":"A corrected two-stage formalism predicts fewer black-hole mergers and may explain luminous red novae.","key_machinery":"The central object is the two-stage common-envelope formalism of Hirai & Mandel (2022), which splits the common-envelope event into an adiabatic first stage that ejects the outer convective envelope and a thermal-timescale second stage that removes the radiative intershell as non-conservative mass transfer. The load-bearing physical input is the timescale contrast: convective layers re-expand dynamically and can use deposited orbital energy to unbind, whereas the radiative intershell expands on a much longer thermal timescale, so energy deposited there is lost to radiation. The paper's new technical device is Eq. (6), which expresses the convective-envelope onset temperature $T_{\\rm onset}$ as a metallicity-dependent fraction of $T_{\\rm min}$, the surface temperature at maximum convective-envelope extent, so that the onset condition is pinned to the same stellar track used in the population-synthesis code.","core_discovery":"The central claim is that the energy-conserving common-envelope formalism does not describe a full common-envelope event, because the radiative intershell between a donor's convective core and convective outer envelope responds on a thermal, not dynamical, timescale. Energy deposited there by the inspiralling companion is largely radiated away rather than used to unbind material. The paper therefore endorses a two-stage formalism in which only the outer convective layers are treated adiabatically with energy conservation, while the radiative intershell is removed via angular-momentum-conserving, thermal-timescale mass transfer. A corollary of this model is that extreme orbital hardening by two to three orders of magnitude occurs only for donors with a significant radiative intershell and a core appreciably more massive than the accretor. The paper also presents a corrected calibration, $T_{\\rm onset} = T_{\\rm min} / \\min(0.695 - 0.057 \\log_{10} Z, 0.95)$, that sets the onset temperature for convective-envelope formation relative to the temperature at maximum envelope extent, eliminating artefacts caused by mismatched single-star evolutionary tracks in population-synthesis codes.","pith_inferences":["If the two-stage picture holds, the same timescale argument would apply to any energy injection below a radiative zone in an evolved star, implying that adiabatic, order-unity efficiency assumptions tend to overestimate the unbinding power of deposited orbital energy.","The near-mass-independence of $T_{\\rm min}/T_{\\rm onset}$ over $7\\!-\\!25\\,M_\\odot$ suggests a simple convective-envelope formation criterion tied to surface temperature may hold across metallicity; this could be tested against observed surface temperatures of low-luminosity red giants and supergiants.","Because the two-stage formalism ties final separations to the core-to-accretor mass ratio, population-synthesis predictions for gravitational-wave rates become sensitive to the mapping between core mass and final remnant mass; testing this mapping against observed post-common-envelope binaries could sharpen the predictions.","If the radiative intershell is removed on a thermal timescale, luminous red nova light curves may show a two-component structure—a fast recombination-powered rise from the convective envelope followed by a slower, longer-lived contribution from the intershell—which semi-analytical light-curve models could be built to discriminate."],"forward_implications":["Population-synthesis codes should switch from the energy-conserving $\\alpha$-formalism to the two-stage treatment for full common-envelope events.","Only systems with a significant radiative intershell and a donor core much more massive than the accretor will harden by orders of magnitude.","The two-stage treatment significantly lowers predicted merger rates for binary black holes without a comparable reduction for binary neutron stars.","Some progenitors of low-mass X-ray binaries may survive the common-envelope phase under the two-stage treatment.","With the corrected $T_{\\rm onset}$ formula, the formalism no longer produces artefacts when combined with mismatched single-star evolution tracks in rapid population synthesis."],"supporting_citations":[{"why":"Proposes the two-stage common-envelope formalism that the paper advocates and whose consequences are explored.","marker":"Hirai & Mandel (2022)"},{"why":"Supplies the premise that the radiative intershell expands on a thermal timescale, motivating the split into two stages.","marker":"Vigna-Gómez et al. (2022)"},{"why":"Provides the original calibration of convective-envelope masses and binding energies that the paper corrects with its new Eq. (6).","marker":"Picker et al. (2024)"},{"why":"Three-dimensional hydrodynamical simulations showing inspiral over a few orbits in the Bondi-Hoyle regime, supporting the timescale estimates.","marker":"Lau et al. (2022b)"},{"why":"Wind-tunnel simulations establishing that the drag coefficient is near unity while accretion is suppressed, used in the inspiral and accretion discussion.","marker":"MacLeod & Ramirez-Ruiz (2015)"},{"why":"Introduced the standard energy-conserving alpha formalism that the paper argues is inappropriate for full common-envelope events.","marker":"Webbink (1984)"}],"fun_headline_variants":["Thermal timescale splits common-envelope model","Radiative intershell dictates envelope ejection stages","Corrected onset temperature alters merger rates","Two-stage common-envelope model cuts black-hole mergers","Two-stage envelopes explain luminous red novae"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole two-stage picture rests on the assumption that the radiation-dominated layer between a star's core and its outer convective envelope expands slowly (on a thermal timescale), so energy dumped there is lost as light instead of helping to blow off the envelope.","fun_headline_variants_meta":{"raw":{"variants":["Thermal timescale splits common-envelope model","Radiative intershell dictates envelope ejection stages","Corrected onset temperature alters merger rates","Two-stage common-envelope model cuts black-hole mergers","Two-stage envelopes explain luminous red novae"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000597,"raw_usage":{"total_tokens":2741,"prompt_tokens":841,"completion_tokens":1900,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":457,"completion_tokens_details":{"reasoning_tokens":1831}},"tokens_in":457,"tokens_out":1900,"duration_ms":11610,"temperature":1.0,"reasoning_tokens":1831,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T15:42:34.693038+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare the final separations predicted by the two-stage formalism against a resolved 3D simulation of a common-envelope event with a radiative intershell; if the intershell expands on a dynamical timescale and its deposited orbital energy goes into unbinding, the formalism's predicted separations will be too wide.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Proposes the two-stage common-envelope formalism that the paper advocates and whose consequences are explored."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the original calibration of convective-envelope masses and binding energies that the paper corrects with its new Eq. (6)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Wind-tunnel simulations establishing that the drag coefficient is near unity while accretion is suppressed, used in the inspiral and accretion discussion."},{"cited_title":"F., ApJ 277, 355 (1984)","cited_arxiv_id":null,"evidence_quote":"Introduced the standard energy-conserving alpha formalism that the paper argues is inappropriate for full common-envelope events."}],"review_version":1}