Common envelopes at StanFest

Ilya Mandel; Lewis Picker; Ryosuke Hirai

REVIEW 2 major objections 5 minor 1 cited by

Common envelopes at StanFest

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2412.10691 v1 pith:QTGMB7O4 submitted 2024-12-14 astro-ph.SR astro-ph.HE

Ilya Mandel , Ryosuke Hirai , Lewis Picker This is my paper · ORCID

classification astro-ph.SRastro-ph.HE

keywords commonenvelopesbinarystarevolutionmasstransferstabilitytwo-stagecommon-envelopeformalismradiativeintershellpopulationsynthesisluminousrednovaegravitational-wavemergers

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

The 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).

The 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.

The 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.

Overall, 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.

Referee Report

2 major / 5 minor

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.

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 (2)

[Section 2] 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 2, Eq. (6) and Figure 4] 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.

minor comments (5)

[Section 1] The phrase 'this seems to be born out' should be 'this seems to be borne out'.
[Section 2] 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 2] 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 3] 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.
[References] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (6) is an empirical calibration and the two-stage premise rests on external simulation evidence.

full rationale

This paper is a proceedings summary, not a derivation-heavy original claim. The central two-stage common-envelope formalism is adopted from Hirai & Mandel (2022), and its key physical premise—that the radiative intershell expands on a thermal, not dynamical, timescale—is attributed to Vigna-Gómez et al. (2022). That cited work is a hydrodynamical simulation study, not an input of the present derivation; it is externally falsifiable and does not reduce to the present paper's equations. The only new quantitative element is Eq. (6), a metallicity-dependent mapping Tonset = Tmin / min(0.695 − 0.057 log10 Z, 0.95). This is explicitly an empirical correction to Picker et al. (2024), calibrated to the MESA-based Tmin/Tonset ratio shown in Figure 4; it is not presented as a first-principles prediction, and no later result in the paper is forced by this fit by construction. The paper also openly flags the limitation of the earlier Picker et al. (2024) Tonset parametrization ('this can lead to unphysical behaviour due to mismatches between MESA tracks ... and stellar evolution tracks used in the population synthesis code') and proposes the correction to avoid that artifact. The consequence claims (e.g., reduced binary black hole merger rates) are framed as expectations from the two-stage treatment, not as outputs of Eq. (6). Self-citations appear throughout because the proceedings summarizes the authors' own program, but the load-bearing physical evidence cited (Vigna-Gómez et al. 2022) is an independent published simulation; therefore no step reduces to its input by definition.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central discussion rests on thermal-timescale behavior of radiative intershells, on the fidelity of MESA models for convective envelope boundaries, and on standard drag cross-sections. No new physical entities are introduced. The new temperature formula contributes three fitted constants, and none of those constants is later used as the target prediction the paper claims to explain.

free parameters (3)

0.695 intercept in Eq. (6) denominator = 0.695
Fitted so that Tonset = Tmin / min(0.695 - 0.057 log10 Z, 0.95) matches MESA-derived Tmin/Tonset ratios; no uncertainty or fitting procedure is reported.
0.057 log-metallicity slope = 0.057
Fitted against the Tmin/Tonset ratios in Figure 4 for four metallicities; no residuals are shown.
0.95 cap in Eq. (6) denominator = 0.95
Chosen to prevent Tonset from deviating too far from Tmin at very low metallicity; no physical motivation is stated.

assumptions (3)

domain assumption The radiative intershell between the convective core and convective outer envelope expands on a thermal timescale, so deposited orbital energy is radiated away rather than doing mechanical work.
Invoked in Section 2 through Vigna-Gómez et al. (2022) to justify the two-stage common-envelope formalism.
domain assumption MESA stellar models reliably predict the convective-envelope temperatures Tonset and Tmin for evolved stars.
Eq. (6) is fit entirely to these models; the paper gives no independent observational calibration.
domain assumption The standard drag cross-sections, Bondi-Hoyle for compact companions and ram-pressure for extended companions, describe inspiral energy loss.
Used in Section 1 for the order-of-magnitude timescale estimates, following MacLeod and Ramirez-Ruiz (2015) and De et al. (2020).

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Cite this review

Pith. "Pith review of Common envelopes at StanFest." pith.science (2026). https://pith.science/paper/QTGMB7O4

@misc{pith2026241210691,
  author       = {Pith},
  title        = {Pith review of: Common envelopes at StanFest},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QTGMB7O4}},
  note         = {Machine review of arXiv:2412.10691}
}

read the original abstract

We describe some of our group's recent work on common envelopes. Our goal is to understand the onset and outcomes of dynamically unstable mass transfer, including the properties of the binaries left behind and the outflows during the common envelope stage. We have also started thinking about light curves of common envelope events. During a talk at StanFest, a meeting in honour of Stan Owocki's retirement held in Leuven in July, 2024, the first author reported on some of the results we recently obtained and briefly outlined future prospects.

Figures

Figures reproduced from arXiv: 2412.10691 by the authors.

**Figure 2.** The fraction of interacting binaries that experience exclusive stable (as opposed [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Left: a schematic of the energy conserving and two-stage common-envelope [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: The ratio Tmin/Tonset between the surface temperature at the maximum extent of the convective envelope and the surface temperature at the onset of convective envelope formation as a function of stellar mass for four choices of metallicity. approximately independent of …

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Rapid stellar and binary population synthesis with COMPAS: methods paper II
astro-ph.SR 2025-06 conditional novelty 5.0 of 10

COMPAS v03.22.01 adds new prescriptions for stellar winds, rotation, supernovae, mass transfer, common envelopes, tides, and gravitational-wave radiation to the rapid binary population synthesis code.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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