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 115 M _ { \odot } for metallicities of Z = Z _ { Milky Way } \simeq Z _ { \odot } / 2 and Z = Z _ { \odot } / 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 \sim 50 - 60 M _ { \odot } , 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 115 M _ { \odot } 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 60 M _ { \odot } .
Metal-rich stars \ga 60 M _ { \odot } 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 highly uncertain .