Progenitors of low-mass binary black-hole mergers in the isolated binary evolution scenario

Context. The formation history, progenitor properties, and expected rates of the binary black holes discovered by the LIGO-Virgo collaboration via the gravitational-wave emission during their coalescence are a topic of active research.Aims. We aim to study the progenitor properties and expected rates of the two lowest-mass binary black hole mergers, GW151226 and GW170608, detected within the first two Advanced LIGO-Virgo observing runs, in the context of the classical isolated binary-evolution scenario.Methods. We used the publicly available 1D-hydrodynamic stellar-evolution code MESA, which we adapted to include the black-hole formation and the unstable mass transfer developed during the so-called common-envelope phase. Using more than 60 000 binary simulations, we explored a wide parameter space for initial stellar masses, separations, metallicities, and mass-transfer efficiencies. We obtained the expected distributions for the chirp mass, mass ratio, and merger time delay by accounting for the initial stellar binary distributions. We predicted the expected merger rates and compared them with those of the detected gravitational-wave events. We studied the dependence of our predictions with respect to the (as yet) unconstrained parameters inherent to binary stellar evolution.Results. Our simulations for both events show that while the progenitors we obtained are compatible over the entire range of explored metallicities, they show a strong dependence on the initial masses of the stars, according to stellar winds. All the progenitors we found follow a similar evolutionary path, starting from binaries with initial separations in the 30-200 R-circle dot range experiencing a stable mass transfer interaction before the formation of the first black hole, followed by a second unstable mass-transfer episode leading to a common-envelope ejection that occurs either when the secondary star crosses the Hertzsprung gap or when it is burning He in its core. The common-envelope phase plays a fundamental role in the considered low-mass range: only progenitors experiencing such an unstable mass-transfer phase are able to merge in less than a Hubble time.Conclusions. We find integrated merger-rate densities in the range 0.2-5.0 yr(-1) Gpc(-3) in the Local Universe for the highest mass-transfer efficiencies explored here. The highest rate densities lead to detection rates of 1.2-3.3 yr(-1), which are compatible with the observed rates. The common-envelope efficiency alpha (CE) has a strong impact on the progenitor populations. A high-efficiency scenario with alpha (CE)=2.0 is favoured when comparing the expected rates with the observations.