Populations of evolved massive binary stars in the Small Magellanic Cloud II: Predictions from rapid binary evolution

Massive star evolution plays a crucial role in astrophysics but bares large uncertainties. This problem becomes more severe by the majority of massive stars being born in close binary systems, whose evolution is affected by the interaction of their components. We want to constrain major uncertainties in massive binary star evolution, in particular the efficiency and the stability of the first mass transfer phase. We use the rapid population synthesis code ComBinE to generate synthetic populations of post-interaction binaries, assuming constant mass-transfer efficiency. We employ a new merger criterion that adjusts self-consistently to any prescribed mass-transfer efficiency. We tailor our synthetic populations to be comparable to the expected binary populations in the Small Magellanic Cloud (SMC). We find that the observed populations of evolved massive binaries can not be reproduced with a single mass-transfer efficiency. Instead, a rather high efficiency (>50%) is needed to reproduce the number of Be stars and Be/X-ray binaries in the SMC, while a low efficiency (~10%) leads to a better agreement with the observed number of Wolf-Rayet stars. We construct a corresponding mass-dependent mass-transfer efficiency recipe to produce our fiducial synthetic SMC post-interaction binary population. It reproduces the observed number and properties of the Be/X-ray and WR-binaries rather well, and is not in stark disagreement with the observed OBe star population. It further predicts two large, yet unobserved populations of OB+BH binaries, that is ~100 OB+BH systems with rather small orbital periods (<20 days) and ~40 longer period OBe+BH systems.

💡 Research Summary

This paper investigates the population of evolved massive binary systems in the Small Magellanic Cloud (SMC) by employing the rapid binary population synthesis code ComBinE. The authors focus on the first Roche‑lobe overflow (RLO) episode, whose physics—particularly the fraction of transferred mass that is actually accreted (the mass‑transfer efficiency, β) and the stability of the transfer—remains highly uncertain. They generate synthetic post‑interaction binaries (OB stars with neutron‑star, black‑hole, or Wolf‑Rayet companions) and compare them with observed numbers of Be/X‑ray binaries, Wolf‑Rayet (WR) binaries, and OBe stars in the SMC.

Key methodological points:

1. Initial distributions – Primary masses are drawn from a Kroupa‑like IMF (α = 2.3) between 3–100 M⊙, secondary masses from a power‑law mass‑ratio distribution (q^κ), and orbital periods from a log‑normal distribution (log P^π). Four sets of κ and π values are explored, based on Galactic, LMC, and Cygnus OB2 studies.
2. Stellar models – The code uses a dense grid of detailed single‑star models (computed with BEC, based on Brott et al. 2011 physics) for SMC metallicity (≈0.2 Z⊙). Both hydrogen‑rich and helium‑star tracks are included, with wind mass‑loss rates scaled appropriately.
3. Mass‑transfer treatment – The mass‑transfer efficiency β is initially assumed constant for each simulation, but the authors introduce a new merger criterion that self‑adjusts to the chosen β. They later adopt a mass‑dependent β(M₁) to reconcile observations.
4. Stability and outcomes – Unstable RLO is assumed to lead to a merger (no common‑envelope ejection). Stable RLO follows the analytic formalism of Soberman et al. (1997) with the ejected material carrying the specific orbital angular momentum of the accretor. Post‑transfer rejuvenation of the accretor and stripping of the donor to a helium star are handled by interpolating the model grid.
5. Supernova kicks and compact‑object formation – Different kick velocity distributions are assigned to electron‑capture SNe, core‑collapse SNe of hydrogen‑rich, helium‑star, and post‑Case‑BB/BC progenitors. Black‑hole formation is assumed when the carbon‑core mass exceeds 6.6 M⊙ (based on Sukhbold et al. 2018).

Results:

• A single, constant β cannot reproduce both the observed Be/X‑ray binary population (≈70 systems) and the WR binary population (≈15 systems). High efficiencies (β ≳ 0.5) are required to generate enough Be/X‑ray binaries, whereas low efficiencies (β ≈ 0.1) better match the WR binary counts.
• By introducing a mass‑dependent efficiency, β≈0.6 for massive primaries (>30 M⊙) and β≈0.1 for lower‑mass primaries (~10 M⊙), the fiducial model simultaneously reproduces the observed numbers and orbital‑period distributions of Be/X‑ray binaries, WR binaries, and the overall OBe star fraction.
• The model predicts two substantial, yet unobserved, populations: (i) ~100 OB+BH binaries with short orbital periods (<20 days) and (ii) ~40 OBe+BH binaries with longer periods (≈30–200 days). These arise because low metallicity reduces wind‑driven angular‑momentum loss, allowing the accretor to retain rapid rotation and form a decretion disk (the Be phenomenon) while the companion collapses into a black hole.
• The predicted OB+BH systems are expected to be X‑ray faint (due to low accretion rates) but could be detectable via radial‑velocity surveys, astrometric wobble (e.g., Gaia), or future gravitational‑wave observations of their eventual mergers.

Conclusions: The study demonstrates that the efficiency of the first mass‑transfer episode must be a strong function of the donor’s mass to reconcile the diverse observed massive binary populations in the SMC. This mass‑dependent prescription provides a physically motivated framework for future binary‑population synthesis work. Moreover, the predicted hidden OB+BH and OBe+BH binaries offer concrete targets for upcoming observational campaigns (e.g., eROSITA, SKA, LIGO‑Virgo‑KAGRA), and their detection would significantly tighten constraints on massive binary evolution, common‑envelope physics, and black‑hole formation channels at low metallicity.