A case for Case A: detailed look at binary black hole formation through stable mass transfer

In isolated binary evolution, binary black hole (BBH) mergers are generally formed through stable mass transfer (SMT) or common envelope evolution. In recent years, the SMT channel has received significant attention due to detailed binary models showing increased mass transfer stability compared to previous studies. In this work, we perform a full zero-age-main-sequence to compact object merger analysis using detailed binary models at eight metallicities between $10^{-4}Z_\odot$ and $2Z_\odot$ to self-consistently model the population properties of BBH mergers in the SMT channel, determined their progenitor initial conditional, and investigate the binary physics governing their formation and metallicity dependence. We use the population synthesis code POSYDON to determine the population of BBH mergers from SMT. Using its extended grids of MESA binary models, we determine the essential physics in the formation of BBH mergers. SMT produces BBH mergers predominantly from systems with $P_{ZAMS}\leq10$ days. In these systems, both the initial mass transfer between two stars and the subsequent interaction between the remaining star and the first-born BH take place while the respective donor star is on the main-sequence (Case A). We find a limited contribution from wider Case B/C systems. Without a natal kick, the SMT channel does not produce BBH mergers above $Z>0.2Z_\odot$ due to orbital widening from stellar wind mass loss. The primary BH mass distribution shows a strong dependence on metallicity, while the mass ratio prefers unity independent of metallicity due to mass ratio reversal. Additionally, the $χ_{eff}$ distributions contain peaks at $χ_{eff}=0$ and ~0.15 of which the former disappears at high metallicities. A mass-scaled natal kick leave this sub-population unchanged but introduce a low-mass, unequal mass ratio sub-population that merges due to their high eccentricity.

💡 Research Summary

This paper presents a comprehensive, zero‑age‑main‑sequence (ZAMS) to binary‑black‑hole (BBH) merger study of the stable mass‑transfer (SMT) channel using detailed MESA binary models incorporated into the POSYDON population‑synthesis framework. Eight metallicities ranging from 10⁻⁴ Z⊙ to 2 Z⊙ are explored, allowing the authors to self‑consistently trace the evolution of binaries through the star‑star, star‑BH, and BH‑star phases. The key finding is that BBH mergers produced via SMT overwhelmingly originate from short‑period (P_ZAMS ≤ 10 days) systems in which both mass‑transfer episodes occur while the donor star is still on the main sequence – classic Case A mass transfer. This “double‑Case A” pathway leads to mass‑ratio reversal, driving the final BH mass ratio toward unity regardless of metallicity.

The study shows that post‑main‑sequence (Case B/C) mass transfer contributes only marginally because it either becomes dynamically unstable or widens the orbit so much that the resulting binary cannot merge within a Hubble time. Metallicity plays a decisive role: at low Z (≲ 0.2 Z⊙) weak stellar winds keep the orbit compact, enabling the double‑Case A channel to produce BBH mergers across a wide range of primary BH masses (up to ≈ 40 M⊙). At higher metallicities, wind‑driven orbital expansion prevents the formation of merging BBHs when natal kicks are omitted.

The primary BH mass distribution therefore shifts strongly with metallicity, while the mass‑ratio distribution remains sharply peaked at q ≈ 1. The effective spin (χ_eff) distribution exhibits two distinct peaks: one at χ_eff ≈ 0 (essentially non‑spinning) and another at χ_eff ≈ 0.15, the former disappearing at high metallicity. Introducing a mass‑scaled natal kick (Maxwellian with σ = 265 km s⁻¹) does not alter the χ_eff ≈ 0 peak but creates an additional sub‑population of low‑mass, unequal‑mass BBHs that merge quickly because the kick induces high eccentricities.

Methodologically, the authors define mass‑transfer stability using physically motivated thresholds (mass‑transfer rate > 0.1 M⊙ yr⁻¹ or exceeding the photon‑trapping radius, and L₂‑point mass loss). They limit BH accretion to the Eddington rate and treat angular‑momentum transport during stellar accretion with a rotationally limited scheme, allowing tides to spin down the accretor when appropriate. The remnant‑mass prescription follows Fryer et al. (2012), and pair‑instability supernovae are modeled with updated limits. Sensitivity tests in the appendix (different remnant prescriptions, semi‑convection parameters) confirm that the dominance of Case A, the metallicity ceiling at Z ≈ 0.2 Z⊙, and the near‑unity mass‑ratio are robust.

In summary, the paper demonstrates that detailed binary evolution modeling reveals a dominant, previously under‑appreciated formation pathway for BBH mergers: double Case A stable mass transfer in short‑period binaries at low metallicity. This pathway naturally explains observed features of the BBH population—such as the primary‑mass metallicity dependence, the prevalence of near‑equal mass ratios, and the bimodal χ_eff distribution—while highlighting the limited role of natal kicks in shaping these bulk properties. The work underscores the importance of incorporating detailed stellar physics into population synthesis to accurately predict gravitational‑wave source demographics.