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The role of mass transfer efficiency in stability criteria: Implementation in SEVN and a test on blue stragglers and binary compact objects

This paper presents a new mass transfer stability criterion implemented in the SEVN population synthesis code that accounts for mass and angular momentum loss, demonstrating that this refined approach significantly increases the predicted formation rates of blue stragglers and binary compact objects (particularly those involving neutron stars) by allowing stable mass transfer in systems with higher donor-to-accretor mass ratios.

Original authors: M. Echeveste, G. J. Escobar, G. Iorio, E. Pancino, M. Mapelli, D. Alvarez Garay, A. Avdeeva, E. Leitinger, S. Nedhath, S. Rani, E. Reggiani, N. Sanna, S. Saracino, L. Steinbauer, A. Turchi

Published 2026-06-30

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CC BY 4.0

Original authors: M. Echeveste, G. J. Escobar, G. Iorio, E. Pancino, M. Mapelli, D. Alvarez Garay, A. Avdeeva, E. Leitinger, S. Nedhath, S. Rani, E. Reggiani, N. Sanna, S. Saracino, L. Steinbauer, A. Turchi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine two stars dancing in a cosmic waltz, locked together by gravity. Sometimes, one star gets so big that it spills its outer layers onto its partner. This is called mass transfer.

The big question astronomers have been wrestling with is: Will this dance stay graceful, or will it turn into a chaotic crash?

If the transfer is stable, the stars adjust, the donor star shrinks a bit, and they continue their dance, potentially creating strange, bright stars called "blue stragglers" or eventually becoming compact objects like black holes. If the transfer is unstable, the donor star gets overwhelmed, the whole system collapses into a "common envelope" (a giant cloud of gas swallowing both stars), and they might merge into a single object or fly apart.

For a long time, computer models used to predict these outcomes (like the code SEVN) had a simplified rule for deciding if the dance would stay stable. They assumed the stars were very conservative, keeping all their mass and spin perfectly.

The New Discovery: A More Realistic Rulebook
The authors of this paper, Echeveste and Escobar, realized that in real life, stars aren't perfect hoarders. When a star spills mass, some of it flies away, taking some of the system's "spin" (angular momentum) with it.

They wrote a new, more accurate mathematical rule (the BD criterion) to replace the old one (the HW criterion). Think of it like this:

The Old Rule (HW): "If you spill too much, you crash." It assumed a strict limit based on how heavy the donor is compared to the receiver.
The New Rule (BD): "If you spill mass, but some of it flies away carrying spin, the orbit changes differently. You might be able to spill more mass without crashing."

The Results: What Happens When We Use the New Rule?

The team ran massive computer simulations (like running a cosmic weather forecast 100,000 times) to see how this new rule changed the universe's population.

1. The "Blue Stragglers" (The Rejuvenated Stars)
Blue stragglers are stars that look younger and bluer than they should be. They are thought to be "vampires" that stole mass from a partner to stay young.

The Finding: Under the old rules, many of these thefts were predicted to fail (causing a crash). Under the new rules, more of these thefts succeed.
The Analogy: Imagine a tightrope walker (the donor) passing a heavy box (mass) to a partner. The old rule said, "If the box is too heavy, the tightrope snaps." The new rule says, "If the box is heavy, but the walker drops a few bricks along the way to lighten the load, the tightrope holds!"
The Outcome: The new model predicts more blue stragglers, and they are found in wider orbits (further apart). This helps fix a long-standing problem where computer models couldn't find enough of these stars to match what telescopes actually see.

2. The "Compact Objects" (Black Holes and Neutron Stars)
These are the heavyweights left behind after massive stars die. They are the parents of gravitational waves (ripples in space-time).

The Finding: The new rule changes the recipe for how these pairs form. It allows more systems to survive the "mass transfer" phase without merging.
The Outcome: Specifically for systems involving neutron stars, the new rule suggests there are more potential gravitational wave sources than previously thought. It opens up new "channels" (pathways) for these pairs to form stably, rather than crashing and burning early.

The Bottom Line
By updating the math to account for the fact that stars lose mass and spin in a messy, non-conservative way, the authors showed that the universe is a bit more stable than we thought.

More stable dances mean more blue stragglers and more binary black holes/neutron stars.
This simple tweak in the code helps astronomers' predictions line up much better with what we actually see in the sky.

In short, the paper says: "We fixed the calculator, and now the universe makes more sense."

Technical Summary: The Role of Mass Transfer Efficiency in Stability Criteria

Problem Statement
The stability of mass transfer (MT) via Roche-lobe overflow is a critical determinant in the evolutionary pathways of interacting binary systems. Current population synthesis codes, including SEVN, rely on stability criteria that often assume conservative mass transfer (where total mass and angular momentum are conserved) to define the transition between stable and unstable MT. However, the actual MT process is frequently non-conservative, involving mass loss and angular momentum loss (AML) from the system. The standard formalism, often referred to as the Hurley-Webbink (HW) criterion, utilizes a critical mass ratio ( $q_c$ ) derived under conservative assumptions. This approach may inaccurately predict the onset of unstable MT and subsequent common envelope (CE) phases or mergers, particularly when mass transfer efficiency is low. This discrepancy contributes to tensions between theoretical predictions and observations, notably regarding the formation rates of blue straggler stars (BSSs) and binary compact objects (BCOs).

Methodology
The authors developed a new mass transfer stability criterion that explicitly accounts for non-conservative mass and angular momentum loss.

Theoretical Derivation: Building on the formalism of Echeveste & Escobar (2026) and Escobar & Echeveste (2026), the authors derived a generalized expression for the Roche-lobe radius response ( $\zeta_L$ ) to mass loss. This expression incorporates the mass transfer efficiency parameter ( $\beta$ , where $\beta=1$ is conservative) and the specific angular momentum loss parameter ( $\gamma$ ). Two distinct AML modes were considered: loss from the vicinity of the accretor (isotropic re-emission, $\gamma=q$ ) and loss from the vicinity of the donor (Jeans mode, $\gamma=q^{-1}$ ).
Implementation: The new criterion, termed the "BD" (beta-dependent) criterion, was implemented in the SEVN population synthesis code. Unlike the HW criterion, which uses a pre-calculated $q_c$ based on conservative assumptions, the BD criterion dynamically compares the donor's adiabatic mass-radius exponent ( $\zeta_{ad}$ ) with the calculated $\zeta_L(q, \beta, \gamma)$ at every time step.
Simulations: Two distinct test cases were simulated using SEVN version 2.16.0:
- Blue Straggler Stars (BSSs): Simulations of $10^5$ binaries with masses $0.7-10 M_\odot$ and metallicity $Z=0.014$ , using MIST stellar tracks.
- Binary Compact Objects (BCOs): Simulations of $10^7$ binaries with masses $5-150 M_\odot$ and $Z=0.014$ , using PARSEC tracks.
- The simulations varied the mass transfer efficiency ( $\beta$ from 0.1 to 0.9) and the AML mode, comparing the BD results against the standard HW prescription.

Key Results

Stability Thresholds: The BD criterion yields higher critical mass ratios ( $q_c$ ) for lower mass transfer efficiencies ( $\beta < 1$ ). This implies that systems with higher donor-to-accretor mass ratios, which would be deemed unstable under the HW criterion, can remain stable under the BD prescription.
Blue Straggler Stars:
- The BD prescription increases the predicted formation efficiency of BSSs, particularly at low $\beta$ values and when AML occurs from the donor.
- The new criterion favors the formation of BSSs in wider orbits, addressing a known discrepancy where standard models struggle to produce long-period BSSs.
- Specific evolutionary tracks show that the BD criterion prevents premature CE phases or mergers in systems where the donor is on the giant branch, allowing them to evolve into stable BSS binaries rather than merging.
Binary Compact Objects:
- The impact on BCOs varies by system type. The strongest effects are observed in binaries containing at least one neutron star.
- For low mass transfer efficiency, the BD prescription enhances the contribution of channels involving stable mass transfer (specifically Channel II), leading to a larger number of BCOs, including gravitational wave (GW) progenitors.
- In the specific metallicity regime tested ( $Z=0.014$ ), where standard models rely heavily on unstable MT channels (I, III, IV) for GW progenitor formation, the BD criterion shifts the balance toward stable MT channels.

Significance and Claims
The paper claims that refining the mass transfer stability criterion to include mass transfer efficiency and angular momentum loss modes is essential for improving the accuracy of binary population synthesis. The authors demonstrate that the standard HW formalism effectively provides a lower bound on the critical mass ratio, potentially leading to an overestimation of unstable MT episodes and mergers.

By implementing the BD criterion, the study suggests that:

The discrepancy between theoretical BSS counts and observations (specifically regarding formation in wider orbits) can be partially mitigated.
The formation channels for GW progenitors are more diverse than previously thought, with stable mass transfer playing a more significant role in low-efficiency scenarios than standard models predict.
The new prescription offers a more self-consistent framework that can be easily adapted to future improvements in stellar structure calculations ( $\zeta_{ad}$ ), providing a flexible tool for understanding the formation channels of specific stellar populations.

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