One's loss is (not) another's gain: Isotropic re-emission destabilizes mass transfer from radiative donor stars

K. D. Temmink; O. R. Pols; S. Justham

REVIEW

One's loss is (not) another's gain: Isotropic re-emission destabilizes mass transfer from radiative donor stars

K. D. Temmink, S. Justham, O. R. Pols

Solar and Stellar Astrophysics · Submitted 23 Apr 2026 · 2 references

Pith's verdict: The paper shows isotropic re-emission can push DDI instability to lower mass ratios than the zeta criterion predicts, but the offset may trace to static versus time-dependent application of zeta.

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arXiv ID2604.21459 (version 1)

CitationK. D. Temmink, O. R. Pols, S. Justham. "One's loss is (not) another's gain: Isotropic re-emission destabilizes mass transfer from radiative donor stars." arXiv:2604.21459 (2026). https://pith.science/paper/2604.21459

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The main point is that detailed stellar evolution runs find lower mass-transfer efficiency beta destabilizes delayed dynamical instability in radiative-donor binaries, moving the critical mass ratio lower by up to a factor of two, while the zeta method predicts the opposite stabilization effect. The authors trace the difference to pre-instability changes in mass ratio and separation that the analytic criterion does not track when applied at initial conditions. This is the first quantified report of that specific mismatch for DDI systems. The calculations themselves are straightforward: they vary beta across representative binaries, follow the tracks, and record when runaway sets in. That direct numerical test against the standard zeta expressions is the useful part, and it flags a real practical issue for anyone using fixed critical mass ratios in population synthesis. The soft spot is the comparison method. Zeta_RL and zeta_star are defined at instantaneous q, so nothing stops evaluating the inequality along the same evolutionary sequence the code follows. If the first violation of the running zeta condition lines up with the numerical instability, the reported factor-of-two offset is just an artifact of the static initial-q benchmark rather than proof that the zeta framework itself is inadequate. The abstract gives no indication they performed that check, nor does it detail the exact instability trigger used in the code or any resolution tests. Readers working on binary population synthesis or compact-object rates will want to see the numbers. The work is clear enough on its own terms to merit a serious referee, mainly to settle whether the discrepancy survives a properly time-dependent zeta test. I would send it for review with that question front and center.

Referee report

Major objections (2)

[Section 4] Section 4 (comparison of numerical critical q with zeta-method): the zeta prediction is evaluated only at the initial mass ratio. To support the claim that the zeta-method inherently fails to capture full evolution, the time-dependent inequality ζ_star(t) > ζ_RL(q(t), β) must be evaluated along the same MESA tracks and shown to either coincide or diverge from the numerically detected runaway. Without this check, the reported factor-of-two offset could be an artifact of static initial-condition application rather than evidence that the zeta framework itself is insufficient.
[Methods] Methods (MESA setup and DDI identification): no explicit criterion is given for declaring the onset of DDI, no error bars or uncertainty ranges are reported on the critical mass ratios, and no robustness tests against numerical parameters (timestep controls, spatial resolution, or initial-condition perturbations) are presented. These omissions are load-bearing because the central claim rests on the precise location of the instability boundary.

Simulated authors' rebuttal

read the rebuttal and 2 point-by-point responses

We thank the referee for the detailed and constructive report. The comments highlight important areas for strengthening the presentation and robustness of our results. We address each major comment below and have revised the manuscript accordingly.

Referee: [Section 4] Section 4 (comparison of numerical critical q with zeta-method): the zeta prediction is evaluated only at the initial mass ratio. To support the claim that the zeta-method inherently fails to capture full evolution, the time-dependent inequality ζ_star(t) > ζ_RL(q(t), β) must be evaluated along the same MESA tracks and shown to either coincide or diverge from the numerically detected runaway. Without this check, the reported factor-of-two offset could be an artifact of static initial-condition application rather than evidence that the zeta framework itself is insufficient.

Authors: We agree that an explicit time-dependent comparison would strengthen the argument that the discrepancy originates from the zeta-method's inability to follow the coupled evolution of q and orbital separation. In the revised manuscript we add a new panel (or subsection) in Section 4 that evaluates ζ_star(t) and ζ_RL(q(t), β) along representative MESA tracks for different β values. This shows that the inequality is satisfied only after significant pre-instability mass transfer has already altered q and a, confirming that the static initial-q evaluation underestimates the true instability boundary. The factor-of-two offset is thereby demonstrated to be a genuine consequence of the time-dependent evolution rather than an artifact. revision: yes
Referee: [Methods] Methods (MESA setup and DDI identification): no explicit criterion is given for declaring the onset of DDI, no error bars or uncertainty ranges are reported on the critical mass ratios, and no robustness tests against numerical parameters (timestep controls, spatial resolution, or initial-condition perturbations) are presented. These omissions are load-bearing because the central claim rests on the precise location of the instability boundary.

Authors: We accept that the methods section requires greater transparency. The revised manuscript now includes: (i) an explicit operational definition of DDI onset based on the point at which the mass-transfer rate exceeds a threshold (e.g., 10^{-4} M_⊙ yr^{-1}) while the donor radius response remains positive; (ii) uncertainty ranges on critical q values derived from small variations in initial conditions and numerical tolerances; and (iii) a dedicated robustness subsection reporting convergence tests with halved timesteps, increased spatial resolution, and perturbed initial separations. These additions confirm that the reported boundaries are stable to within ~5 %. revision: yes

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The paper

The paper claims

Isotropic re-emission destabilizes mass transfer from radiative donor stars

The reading

This paper uses detailed stellar evolution models to examine how isotropic re-emission affects mass transfer stability in close binaries where the donor has a radiative envelope and experiences delayed dynamical instability. It finds that lowering the mass transfer efficiency makes these systems more unstable, the opposite of what the commonly used zeta-method predicts. The mismatch occurs because the zeta-method ignores the ongoing changes in orbital separation and mass ratio that build up before instability begins, sometimes underestimating the critical mass ratio by nearly a factor of two. Accurate stability assessment therefore requires following the full time-dependent binary evolution rather than applying static criteria.

What carries the argument

Detailed stellar evolution calculations that follow the time-dependent orbital separation and mass ratio for varying mass-transfer efficiencies beta, compared against the static zeta-method based on mass-radius exponents

Extended reading notes

Core claim

Through detailed stellar evolution calculations of binaries undergoing delayed dynamical instability with radiative-envelope donors, reducing the mass-transfer efficiency beta via isotropic re-emission causes the transfer to become unstable at higher mass ratios than expected. This directly contradicts the zeta-method, which is based on mass-radius response exponents and predicts greater stability for non-conservative transfer. The zeta-method underestimates the critical mass ratio because it does not track the continuous evolution of the orbit and mass ratio during the preceding phase of stable mass transfer.

Load-bearing premise

The zeta-method based on mass-radius exponents can accurately predict stability boundaries without following the full time-dependent orbital evolution and mass-ratio changes during pre-instability mass transfer.

Original abstract

Non-conservative mass transfer plays a central role in close-binary evolution, yet its effects on mass-transfer stability are uncertain. One widely adopted prescription, isotropic re-emission, is often assumed to promote stability compared to conservative mass transfer. We investigate the impact of isotropic re-emission on the stability of mass transfer in binaries with radiative envelopes that undergo delayed dynamical instability (DDI). We assess whether simplified criteria used in binary population synthesis codes accurately capture stability boundaries under varying mass-transfer efficiencies. We perform detailed stellar evolution calculations for a set of representative binaries undergoing DDI. Varying the mass-transfer efficiency beta, we track the onset of instability and quantify the corresponding critical mass ratio. We compare our results with predictions from the commonly used zeta-method, which is based on mass-radius exponents. We find that a lower mass-transfer efficiency destabilizes mass transfer in DDI systems, whereas the zeta-method predicts that isotropic re-emission should stabilize it. The discrepancy arises because the zeta-method fails to capture the full evolution of the orbit and mass ratio during pre-instability mass transfer. In some cases, the critical mass ratio is underestimated by nearly a factor of two. Our findings show that isotropic re-emission can reduce, rather than enhance, DDI stability, underscoring the limitations of using fixed critical mass ratios and zeta-based criteria. This highlights the need for calibrated prescriptions that capture the time-dependent evolution of mass ratio and orbital separation, with direct implications for modelling X-ray binaries, symbiotic stars, and double white dwarfs, including their transient rates and delay-time distributions.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 8,865 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.47 · randomized assignment 0.01 · states quantitative result 0.93 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Non-conservative mass transfer plays a central role in close-binary evolution, yet its effects on mass-transfer stability are uncertain. One widely adopted prescription, isotropic re-emission, is often assumed to promote stability compared to conservative mass transfer. We investigate the impact of isotropic re-emission on the stability of mass transfer in binaries with radiative envelopes that undergo delayed dynamical instability (DDI). We assess whether simplified criteria used in binary population synthesis codes accurately capture stability boundaries under varying mass-transfer efficiencies. We perform detailed stellar evolution calculations for a set of representative binaries undergoing DDI. Varying the mass-transfer efficiency beta, we track the onset of instability and quantify the corresponding critical mass ratio. We compare our results with predictions from the commonly used zeta-method, which is based on mass-radius exponents. We find that a lower mass-transfer efficiency destabilizes mass transfer in DDI systems, whereas the zeta-method predicts that isotropic re-emission should stabilize it. The discrepancy arises because the zeta-method fails to capture the full evolution of the orbit and mass ratio during pre-instability mass transfer. In some cases, the critical mass ratio is underestimated by nearly a factor of two. Our findings show that isotropic re-emission can reduce, rather than enhance, DDI stability, underscoring the limitations of using fixed critical mass ratios and zeta-based criteria. This highlights the need for calibrated prescriptions that capture the time-dependent evolution of mass ratio and orbital separation, with direct implications for modelling X-ray binaries, symbiotic stars, and double white dwarfs, including their transient rates and delay-time distributions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Non-conservative mass transfer plays a central role in close-binary evolution, yet its effects on mass-transfer stability are uncertain.	background 0.70	0.04	0.02	asserted 0.97
s1	One widely adopted prescription, isotropic re-emission, is often assumed to promote stability compared to conservative mass transfer.	background 0.99	0.04	0.03	asserted 0.66
s2	We investigate the impact of isotropic re-emission on the stability of mass transfer in binaries with radiative envelopes that undergo delayed dynamical instability (DDI).	contribution 0.98	0.58	0.03	asserted 0.50
s3	We assess whether simplified criteria used in binary population synthesis codes accurately capture stability boundaries under varying mass-transfer efficiencies.	contribution 0.85	0.51	0.02	unclear 0.58
s4	We perform detailed stellar evolution calculations for a set of representative binaries undergoing DDI.	method 0.95	0.96	0.02	asserted 0.84
s5	Varying the mass-transfer efficiency beta, we track the onset of instability and quantify the corresponding critical mass ratio.	method 0.98	0.97	0.02	asserted 0.80
s6	We compare our results with predictions from the commonly used zeta-method, which is based on mass-radius exponents.	method 0.95	0.80	0.02	asserted 0.78
s7	We find that a lower mass-transfer efficiency destabilizes mass transfer in DDI systems, whereas the zeta-method predicts that isotropic re-emission should stabilize it.	result 1.00	0.94	0.58	asserted 1.00
s8	The discrepancy arises because the zeta-method fails to capture the full evolution of the orbit and mass ratio during pre-instability mass transfer.	interpretation 0.99	0.52	0.10	asserted 1.00
s9	In some cases, the critical mass ratio is underestimated by nearly a factor of two.	result 1.00	0.89	0.05	asserted 0.92
s10	Our findings show that isotropic re-emission can reduce, rather than enhance, DDI stability, underscoring the limitations of using fixed critical mass ratios and zeta-based criteria.	interpretation 0.51	0.95	0.90	asserted 0.71
s11	This highlights the need for calibrated prescriptions that capture the time-dependent evolution of mass ratio and orbital separation, with direct implications for modelling X-ray binaries, symbiotic stars, and double white dwarfs, including their transient rates and delay-time distributions.	interpretation 0.81	0.45	0.21	asserted 0.89

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Evolution of the mass ratio, semi-major axis and ζL computed using an analytical orbital-evolution prescription (Eqs. 1 and 2), for an initial mass ratio Ma/Ma = 0.275. The colours and styles of the curves correspond to different mass-transfer efficiencies, as indicated in the legend. Vertical lines indicate when the quasi-adiabatic instability criterion (see Temmink et al. 2023) is reached in our MESA simulations of a binary with the same values of β and initial mass ratio, an initial donor mass of 5 M⊙ and an initial period of about 7 days (see Appendix B). Mass transfer is…

**Figure 2.** Comparison of values for the critical mass ratio for stable mass transfer. The four systems correspond to initial periods of approximately Pi ≃ 1.8, 7.1, 10.5, and 72.6 days (for a representative q = 0.25). Panel a shows values for qcrit obtained using the ζ-method (qcrit,ζ ; sphere hashing) and using MESA calculations (qcrit,calc; diagonal hashing). For β = 1 the two methods coincide by construction, since we calibrate ζd from the conservative borderline and then solve ζL(q, β) = ζd to obtain qcrit,ζ . Panel b shows the ratio of these critical mass ratios qcrit,calc/qcrit,ζ . In…

Figures reproduced from arXiv:2604.21459 by the authors.

References

Works cited (2)

[1]

Claeys, J. S. W., Pols, O. R., Izzard, R. G., Vink, J., & Verbunt, F. W. M. 2014, A&A, 563, A83 Eggleton, P. P. 1983, ApJ, 268, 368 Ge, H., Tout, C. A., Chen, X., et al. 2024, ApJ, 975, 254 Han, Z., Podsiadlowski, P., Maxted, P. F. L., Marsh, T. R., & Ivanova, N. 2002, MNRAS, 336, 449 Heber, U. 2016, PASP, 128, 082001 Hjellming, M. S. & Webbink, R. F. 198...

View on Pith 2014
[2]

mark the donor-mass coordinate at which the quasi-adiabatic instabil- ity criterion of Temmink et al. (2023) is met. For this system, reaching the criterion coincides with the mass-transfer rate ris- ing to ˙M∼10 −3 M⊙ yr−1 and with rapidly increasing overfill of the Roche lobe. While the fully conservative sequence remains stable, decreasing the mass-tra...

View on Pith 2023

How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 4 sentences without a confident label

Uses the method or tool of 3 papers

Assuming mass loss occurs exclusively through the isotropic re-emission mode with a constant $β$, the evolution of the binary semi-major axis $a$ may be calculated analytically as [ref] : [equation] Here, the subscript $i$ denotes initial values.

Formation of Low-Mass X-ray Binaries. I. Constraints on Hydrogen-Rich Donors at the Onset of the X-ray Phase · Isotropic re-emission in delayed dynamical instability binaries · 0.82
Assuming mass loss occurs exclusively through the isotropic re-emission mode with a constant $β$, the evolution of the binary semi-major axis $a$ may be calculated analytically as [ref] : [equation] Here, the subscript $i$ denotes initial values.

Stability Criteria for Mass Transfer in Binary Stellar Evolution · Isotropic re-emission in delayed dynamical instability binaries · 0.82
Assuming mass loss occurs exclusively through the isotropic re-emission mode with a constant $β$, the evolution of the binary semi-major axis $a$ may be calculated analytically as [ref] : [equation] Here, the subscript $i$ denotes initial values.

Formation of millisecond pulsars. I. Evolution of low-mass X-ray binaries with P > 2 days · Isotropic re-emission in delayed dynamical instability binaries · 0.82

Cites as background 6 papers

This response is influenced by both the efficiency of mass transfer (the fraction of the mass lost by the donor that is gained by the companion star) and the amount of angular momentum carried away by any material lost from the system [ref] .

Stability Criteria for Mass Transfer in Binary Stellar Evolution · Introduction · 0.97
This response is influenced by both the efficiency of mass transfer (the fraction of the mass lost by the donor that is gained by the companion star) and the amount of angular momentum carried away by any material lost from the system [ref] .

Formation of Low-Mass X-ray Binaries. I. Constraints on Hydrogen-Rich Donors at the Onset of the X-ray Phase · Introduction · 0.97
Unstable mass transfer is thought to lead to a common-envelope (CE) phase [ref] , which can result in either a merger or the formation of a short-period binary [ref] .

Hot subluminous stars · Introduction · 0.99

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

Claeys, J. S. W., Pols, O. R., Izzard, R. G., Vink, J., & Verbunt, F. W. M. 2014, A&A, 563, A83 Eggleton, P. P. 1983, ApJ, 268, 368 Ge, H., Tout, C. A., Chen, X., et al. 2024, ApJ, 975, 254 Han, Z., Podsiadlowski, P., Maxted, P. F. L., Marsh, T. R., & Ivanova, N. 2002, MNRAS, 336, 449 Heber, U. 2016, PASP, 128, 082001 Hjellming, M. S. & Webbink, R. F. 198...

View on Pith 2014

[2] [2]

mark the donor-mass coordinate at which the quasi-adiabatic instabil- ity criterion of Temmink et al. (2023) is met. For this system, reaching the criterion coincides with the mass-transfer rate ris- ing to ˙M∼10 −3 M⊙ yr−1 and with rapidly increasing overfill of the Roche lobe. While the fully conservative sequence remains stable, decreasing the mass-tra...

View on Pith 2023