Stable mass transfer in massive binaries leading to merging black holes

The gist The stable mass transfer channel is identified as a robust contributor to observed gravitational wave events through detailed binary evolution models that incorporate internal differential rotation and mass/angular momentum transfer between stars, which naturally yield black hole spins and mass ratios consistent with gravitational-wave source observations

Stable Mass Transfer Channel Modeling

The study constructs detailed binary evolution models evolving continuously from the zero-age main sequence until the formation of the second black hole, including internal differential rotation and mass and angular momentum transfer between stars. These models allow for following the mass and chemical structure evolution of the accreting component, which influences reverse mass transfer phase, naturally falling into the observed regime for gravitational-wave sources in the 10–25 M⊙ primary black hole mass range. The models are computed with an initial chemical composition as observed in the interstellar medium of the Small Magellanic Cloud to reflect progenitor environments.

Evolutionary Pathways and Constraints

Three possible pathways have been identified for merging binary black holes: common envelope evolution (CEE), tight massive binaries with tidal torques, and stable mass transfer. The stable mass transfer path involves the initially less massive star ending up more massive than the first formed black hole, allowing the orbit to shrink upon mass transfer in the final stage. Previous efforts often used rapid binary evolution codes with simplifying assumptions, but this work constructs detailed models that fully resolve both stars simultaneously at all times.

Key Findings on Binary Properties

The analysis of the initial parameter space reveals that only models with initial orbital periods below ∼ 4.2 d evolve into merging black holes, restricting the first mass transfer to be of Case A. The shortest period ones form BBHs with merger times of 10% of the Hubble time. The models show that in the majority of the initial parameter space, a second mass transfer type is Case B (Case A-Case B model). The black hole mass ratios of Case A-Case B models cluster at a value near 0.7, which aligns well with gravitational wave data.

Spin Parameters and Merger Timescales

The effective spin parameter of the merging BBH is determined by the merger timescale τM and the effective spin parameter χeff, showing a correlation where merging BBHs with short τM trend to have high χeff. Case A-Case A models produce second-born BH spins of 0.5–1.0, whereas Case A-Case B models yield 0.1–0.4. The comparison with BH-ZAMS models shows that the stable mass transfer channel covers a region not reached by even the tightest BH-ZAMS models, opening a new parameter space for BBH formation.

Conclusion and Future Work

Detailed binary evolution simulations establish the stable mass transfer channel as a robust contributor to gravitational wave events supported by the mass ratios and spin parameters produced by models with relatively short merger delay times (∼ 2 Gyr). It is imperative to compute the detailed evolution without interruption to obtain the correct chemical structure of the mass gainer after the first mass transfer phase, which changes the mass transfer history by allowing for tighter orbits in the second mass transfer, shorter merger times, smaller spin parameters and BH mass ratios. The research suggests that model grids might be pivotal in interpreting observed distributions of properties of merging BBHs as gravitational wave observatories keep finding BBH mergers at an increased pace.

How it works

**- The models fully resolve both stars simultaneously at all times and include internal mixing processes that occur in accreting stars, internal differential rotation, tides, and mass and angular momentum transfer between the stars. These models are computed using the MESA code version 8845 to evolve continuously from the ZAMS until the formation of the second BH. The models assume BHs are formed without mass ejection and accretion onto the BH is limited by the Eddington accretion rate. The spin evolution of the BH is computed by assuming that the BH accretes the specific orbital angular momentum at its innermost stable circular orbit (ISCO). The effective spin parameter is given by χeff = MBH,1st aspin,1st + MBH,2nd aapin,2nd / (MBH,1st + MBH,2nd). The merger timescale is calculated using an accurate analytical fitting formula to the solution derived by ref. (116). The models are computed with an initial chemical composition as observed in the interstellar medium of the Small Magellanic Cloud. The study also computes a grid of models with a fixed primary star masses to explore the mass dependence of the stable mass transfer channel. The input physics includes convection (ledoux criterion), overshooting (alphaMLT = 1.5), and rotational mixing (Spruit-Taylor dynamo). The binary evolution models assume both stars are tidally locked at zero-age main sequence, and tidal interaction is modelled to allow the exchange of angular momentum between stellar rotations and the orbit. The mass transfer rate is computed implicitly such that the mass donor is limited within its Roche lobe. The BH formation prescription assumes the entire star at core helium depletion collapses into a BH without mass ejection or a natal kick. The effective spin parameter is assessed by considering the effect of mass ejection during collapse, which can reduce spin parameters by ∼20–30% compared to the direct collapse case. The angular momentum loss scheme is tested using both the old and new schemes, showing that for Case A-Case A models, the spin of the first-born BH is reduced by 20%, while that of the second-born BH is reduced by about 50% with the new scheme. The comparison with BH-ZAMS models shows that our models undergo Case B mass transfer, which is important because the evolutionary stage of the donor directly affects mass transfer stability. The observed counterparts include close double O star binaries and Wolf-Rayet+O-star binaries like Cygnus X-1. The models reproduce a subset of the observed χeff and qBBH with the same BH formation prescription as the main text. The study confirms that this channel is a robust contributor to observed gravitational wave events supported by mass ratios and spin parameters produced by models with relatively short merger delay times (∼ 2 Gyr). The authors note that the stability criterion for mass transfer and efficiency of the second mass transfer are not very uncertain in detailed binary evolution models. The orbital properties of predicted BH-MS binaries could be altered by BH birth kicks, but large kicks are not expected in the considered BH mass range. The study suggests that the origin of observed high-spin BHs in wind-fed high-mass X-ray binaries remains unclear. The authors recommend repeating the experiment at different primary masses to explore the mass dependence of the stable mass transfer channel and varying physics parameters to obtain BBH merger rate estimates <ref:2512.

1. textbfEnhanced Progenitor Identification and Population Synthesis Capabilities: The AI can now distinguish between progenitor channels by predicting observable BBH properties based on mass transfer type, as our models show that it is imperative to compute the detailed evolution without interruption, in order to obtain the correct chemical structure of the mass gainer after the first mass transfer phase. This allows for a more precise classification of observed gravitational wave sources into Case A-Case A or Case A-Case B channels based on predicted BH mass ratios and spins.

2. textbfAccurate Merger Timescale and Spin Prediction: The system can calculate merger timescales with greater fidelity by incorporating the effects of internal differential rotation and angular momentum transfer, as the model includes internal differential rotation as well as mass and angular momentum transfer between the stars. This enables a more accurate comparison with gravitational wave data, specifically by calculating the merger timescale, which is the time from the formation of a BBH until its final merger using analytical fitting formulas.

3. textbfModel Grid Exploration for Parameter Space Mapping: The AI can systematically explore the parameter space to identify regions leading to mergers, such as finding that most of the initial parameter space of interacting binaries at this primary mass have a second mass transfer type of Case B (Case A-Case B model). This capability allows researchers to map out the initial binary parameter space leading to merging BBH in the qZAMS-log10 Porb,ZAMS plane.

4. textbfSensitivity Analysis for Uncertain Physics: The system can perform sensitivity analysis on key physical assumptions, such as mass ejection during collapse, by quantifying its impact on observables, as shown in Figure 6 shows that mass ejection can reduce the spin parameters by ∼20–30% compared to the direct collapse case. This allows for a rigorous assessment of how uncertainties in the assumption that progenitor stars directly collapse into BHs without any mass ejection or angular momentum loss affect final black hole spins.

5. textbfCharacterization of High-Spin Second-Born Black Holes: The AI can predict the spin parameters of the second-born black hole with high precision, noting that for Case A-Case A systems, the second-born BHs produce spins of 0.5–1.0, which is much higher than previous simulations on the stable mass transfer channel. This capability helps to interpret discrepancies in observed high-spin BHs by comparing predicted spin distributions across different evolutionary channels.

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 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.