Context. Various binary black hole formation channels have been proposed since the first gravitational event GW150914 was discovered by the Advanced Laser Interferometer Gravitational-Wave Observatory (AdLIGO). For all evolutionary channels based on the evolution of isolated binaries, the immediate progenitor of the binary black hole is a close binary system composed of a black hole and a helium star. Aims. We study the spin angular momentum evolution of the helium star in order to constrain the spin of the second-born black hole. Methods. We perform detailed stellar structure and binary evolution calculations that take into account, mass-loss, internal differential rotation, and tidal interactions between the helium star and the black hole companion, where we also calculate the strength of the tidal interactions from first principles based on the structure of the helium stars. We systematically explore the parameter space of initial binary properties, including initial black hole and helium star masses, initial rotation of the helium star as well as metallicity.Results. We argue that the spin of the first-born black hole at its birth is negligible ( 0.1), hence the second-born black hole's spin dominates the measured effective spin, χ eff , from gravitational wave events of double black hole mergers. We find that tides can be important only when orbital periods are shorter than 2 days. Upon core collapse, the helium star produces a black hole (the secondborn black hole in the system) with a spin that can span the entire range from zero to maximally spinning. We show that the bimodal distribution of the spin of the second-born black hole obtained in recent papers is mainly due to oversimplifying assumptions. We find an anti-correlation between the merging timescale of the two black holes, T merger , and the effective spin χ eff . Finally, we provide new prescriptions for the tidal coefficient E 2 for both H-rich and the helium-rich stars. Conclusions. To understand the spin of the second-born black hole, careful treatments of both tides and stellar winds are needed. We predict that, with future improvements to AdLIGO's sensitivity, the sample of merging binary black hole systems will show an overdensity of sources with positive but small χ eff originating from lower mass black hole mergers born at low redshift.

The formation and evolution of binary stars are critical components of several fields in astronomy. The most numerous sources for gravitational wave observatories are inspiraling or merging compact binaries, while binary stars are present in nearly every electromagnetic survey regardless of the target population. Simulations of large binary populations serve to both predict and inform observations of electromagnetic and gravitational wave sources. Binary population synthesis is a tool that balances physical modeling with simulation speed to produce large binary populations on timescales of days. We present a community-developed binary population synthesis suite, COSMIC, which is designed to simulate compact-object binary populations and their progenitors. As a proof of concept, we simulate the Galactic population of compact binaries and their gravitational wave signals observable by the Laser Interferometer Space Antenna.

We study the impact of mass-transfer physics on the observable properties of binary black hole populations that formed through isolated binary evolution. We used the POSYDON framework to combine detailed MESA binary simulations with the COSMIC population synthesis tool to obtain an accurate estimate of merging binary black hole observables with a specific focus on the spins of the black holes. We investigate the impact of mass-accretion efficiency onto compact objects and common-envelope efficiency on the observed distributions of the effective inspiral spin parameter χeff, chirp mass Mchirp, and binary mass ratio q. We find that low common envelope efficiency translates to tighter orbits following the common envelope and therefore more tidally spun up second-born black holes. However, these systems have short merger timescales and are only marginally detectable by current gravitational-wave detectors as they form and merge at high redshifts (z ∼ 2), outside current detector horizons. Assuming Eddington-limited accretion efficiency and that the first-born black hole is formed with a negligible spin, we find that all non-zero χeff systems in the detectable population can come only from the common envelope channel as the stable mass-transfer channel cannot shrink the orbits enough for efficient tidal spin-up to take place. We find that the local rate density (z ≃ 0.01) for the common envelope channel is in the range of ∼17–113 Gpc−3 yr−1, considering a range of αCE ∈ [0.2, 5.0], while for the stable mass transfer channel the rate density is ∼25 Gpc−3 yr−1. The latter drops by two orders of magnitude if the mass accretion onto the black hole is not Eddington limited because conservative mass transfer does not shrink the orbit as efficiently as non-conservative mass transfer does. Finally, using GWTC-2 events, we constrained the lower bound of branching fraction from other formation channels in the detected population to be ∼0.2. Assuming all remaining events to be formed through either stable mass transfer or common envelope channels, we find moderate to strong evidence in favour of models with inefficient common envelopes.