Common-envelope ejection in massive binary stars: Implications for the progenitors of GW150914 and GW151226

Context. The recently detected gravitational wave signals (GW150914 and GW151226) of the merger event of a pair of relatively massive stellar-mass black holes (BHs) calls for an investigation of the formation of such progenitor systems in general. Aims. We analyse the common-envelope (CE) stage of the traditional formation channel in binaries where the first-formed compact object undergoes an in-spiral inside the envelope of its evolved companion star and ejects the envelope in this process. Methods. We calculated envelope binding energies of donor stars with initial masses between 4 and 115M sub([middot in circle]) for metallicities of Z= Z sub(Milky Way) = Z sub([middot in circle])/ 2 and Z= Z sub([middot in circle])/ 50, and derived minimum masses of in-spiralling objects needed to eject these envelopes. Results. In addition to producing double white dwarf and double neutron star binaries, CE evolution may also produce massive BH-BH systems with individual BH component masses of up to ~50 - 60M sub([middot in circle]), in particular for donor stars evolved to giants beyond the Hertzsprung gap. However, the physics of envelope ejection of massive stars remains uncertain. We discuss the applicability of the energy-budget formalism, the location of the bifurcation point, the recombination energy, and the accretion energy during in-spiral as possible energy sources, and also comment on the effect of inflated helium cores. Conclusions. Massive stars in a wide range of metallicities and with initial masses of up to at least 115M sub([middot in circle]) may shed their envelopes and survive CE evolution, depending on their initial orbital parameters, similarly to the situation for intermediate- and low-mass stars with degenerate cores. In addition to being dependent on stellar radius, the envelope binding energies and [lambda]-values also depend on the applied convective core-overshooting parameter, whereas these structure parameters are basically independent of metallicity for stars with initial masses below 60M sub([middot in circle]). Metal-rich stars > or = 60M sub([middot in circle]) become luminous blue variables and do not evolve to reach the red giant stage. We conclude that based on stellar structure calculations, and in the view of the usual simple energy budget analysis, events like GW150914 and GW151226 might be produced by the CE channel. Calculations of post-CE orbital separations, however, and thus the estimated LIGO detection rates, remain highl