  The possible formation mechanisms of massive close binary black holes (BHs)
that can merge in the Hubble time to produce powerful gravitational wave bursts
detected during advanced LIGO O1 and O2 science runs include the evolution from
field low-metallicity massive binaries, the dynamical formation in dense
stellar clusters and primordial BHs. Different formation channels produce
different source distributions of total masses ${M_\mathrm{tot}}$ and effective
spins $\chi_\mathrm{eff}$ of coalescing binary BHs. Using a modified
\textsc{bse} code, we carry out extensive population synthesis calculations of
the expected effective spin and total mass distributions from the standard
field massive binary formation channel for different metallicities of BH
progenitors (from zero-metal Population III stars up to solar metal abundance),
different initial rotations of the binary components, stellar wind mass loss
prescription, different BH formation models and a range of common envelope
efficiencies. The stellar rotation is treated in two-zone (core-envelope)
approximation using the effective core-envelope coupling time and with an
account of the tidal synchronization of stellar envelope rotation during the
binary system evolution. The results of our simulations, convolved with the
metallicity-dependent star-formation history, show that the total masses and
effective spins of the merging binary black holes detected during LIGO O1-O2
runs but the heaviest one (GW170729) can be simultaneously reproduced by the
adopted BH formation models. Noticeable effective spin of GW170729 requires
additional fallback from the rotating stellar envelope.
