Stable mass transfer in massive binaries leading to merging black holes

TL;DR

This work demonstrates that a full, self-consistent evolution of close, massive binary systems with stable mass transfer can form merging binary black holes. By evolving both stars from the ZAMS to the second BH without simplifying prescriptions, and by accounting for differential rotation, mass/ angular momentum transfer, and rejuvenation, the authors identify two dominant pathways (Case A-Case B and Case A-Case A) that produce BBHs with distinct mass ratios and spin signatures. Case A-Case B systems yield modest spins ($\chi_{ m eff}\approx0.1$–$0.25$) and mass ratios around $q_{\rm BBH}\approx0.7$, aligning with many GWTC-4 observations, while Case A-Case A systems can yield high second-born BH spins ($a_{ m spin,2nd}\sim0.5$–$1.0$) and higher $\chi_{ m eff}$, though they may occupy regions less densely populated by current data. The study argues that the stable mass transfer channel is a robust contributor to the observed BBH population and highlights the necessity of full evolutionary modeling to capture the resulting spin and mass-ratio distributions, complementing other channels such as CHE and CEE."

Abstract

The vast majority of massive binary systems in the universe is evidently unsuited to produce merging binary black holes. However, several narrow evolutionary paths of isolated massive binaries towards this goal have recently been identified. Due to the high degree of simplification and assumptions applied in previous modelling of these paths, conclusions remained vague so far. For one of these paths, the stable mass transfer channel, we now construct detailed binary evolution models which include internal differential rotation as well as mass and angular momentum transfer between the stars, all the way from the zero-age main sequence to the formation of the black holes, only skipping the rapid late burning stages. This allows us to follow the mass and chemical structure evolution of the mass accreting component, which turns out to have a key influence on the phase of reverse mass transfer, that allows the obtained black hole spins and mass ratios to naturally fall into the regime observed for the gravitational-wave source in the 10--25$M_\odot$ primary black hole mass range. As for this channel, also a large number of progenitor binaries are known, we conclude that it likely contributes to the observed population of gravitational wave sources.

Figures (19)

• Figure 1: Evolution of stellar structure (Kippenhahn diagrams) in the example model. In each panel, the X-axis shows the time until the first or second BH formation event, and Y-axis represent the internal mass coordinate of the depicted star, from centre (0) to surface (black solid line). Top left: evolution of the initially more massive star from zero age until it forms a BH. Bottom left: evolution of the initially less massive star over the same time period as in the top panel, showing the rich history of internal chemical mixing induced by mass accretion. Bottom right: evolution of the initially less massive star from the time of the first BH formation until the second BH formation. In all panels, the top black line indicates the stellar mass, the nuclear energy generation rate is colour-coded, while different hatching patterns correspond to different mixing processes: convection (green), overshooting (purple), red (semiconvection), thermohaline (yellow). The pink and red dotted lines indicate the mass of the helium and carbon core, respectively.
• Figure 2: Initial binary parameter space leading to merging BBH. In the depicted initial mass ratio-initial orbital period ($q_{\rm ZAMS}$-log$_{\rm 10}\,P_{\rm orb,ZAMS}$) plane, each dot represents one detailed binary evolution models, with the initially more massive star starting with 31.6$\,M_\odot$. Red and purple dots correspond to mergers during the first and second mass transfer respectively (bottom hatching). Black dots represent BBHs with merger timescales ($\tau_{\rm M}$) above 14 Gyr (top hatching). The colourbar indicates the merger timescale in units of $14\,$Gyr for the obtained merging BBHs (unhatched background). Our example model is marked by a red star. The blue curve approximately separates Case A-Case A and Case A-Case B systems.
• Figure 3: Predicted BH-MS binaries and comparison with BH-ZAMS models. Location of the models from our grid in the companion mass-orbital period plane at the time of the formation of the first BH (filled circles, where the colour reflects the merger time, as in Fig. \ref{['grid_outcomes']}). The hatching patterns represent the parameter space of merging-BBH progenitors of our models (left-leaning diagonal and red borderlines), and of the BH-ZAMS models from refKlencki2025arXiv250508860K (right-leaning diagonal and black borderlines) computed with a BH mass of $13\,M_\odot$ (the first-born BHs in our models have masses 13--14$\,M_\odot$; cf., Supplementary Section \ref{['app:BH-mass']}). The solid grey line connects our models with $q_\mathrm{ZAMS}=0.99$, which limits the allowed parameter space. The solid blue line separates models in our grid with Case A and with Case B mass transfer towards the BH companion. The blue dashed line is the corresponding line for the BH-ZAMS models. Our example model is plotted as a red star.
• Figure 4: Effective spins $\chi_{\rm eff}$ and mass ratios $q_{\rm BBH}$ of merging binary black holes. The BBHs predicted by our models are indicated by coloured dots, with the colour representing the merger time as in Fig. \ref{['grid_outcomes']}. All our Case A-Case A models fall into the top right rectangle. We plot the effective spins and mass ratios obtained for the observed merging BBHs from the Gravitational-Wave Transient Catalogue 4 (GWTC-4; LVK2025arXiv250818082T) as gray dots with error bars, where black circles mark the observed BBHs with BH masses close to those of our merging BBH models (see legend). The red star corresponds to our example model. Purple arrows at the bottom indicate the effect of the ejection of the outer 10% of the mass of the stripped stars upon collapse to a black hole on the predicted $\chi_{\rm eff}$ (Supplementary Section \ref{['app:Xeff-mass-ejection']}).
• Figure 5: Core carbon mass fraction $X_{\rm c12,core}$ and carbon core mass $M_{\rm C,core}$ at core helium depletion of the progenitors of the merging BBHs presented in the main text Fig. \ref{['BH-BH']}. The blue and orange dots correspond to initial primary and secondary stars respectively. The black solid line $X_{\rm c12,single}$ is the result of the non-rotating single star models in ref.Xu2025arXiv250323876X computed with the same input physics as our full-evolution models. The black dotted and dashed lines are $X_{\rm c12,single}+0.01$ and $X_{\rm c12,single}+0.02$, plotted for comparison purpose.