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

Abstract: 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. 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 that process. We calculate envelope binding energies of donor stars with initial masses between 4 and 115 Msun for metallicities of Z=Zsun/2 and Z=Zsun/50, and derive minimum masses of in-spiralling objects needed to eject these envelopes. We find that CE evolution, besides from producing WD-WD and NS-NS binaries, may, in principle, also produce massive BH-BH systems with individual BH component masses up to ~50-60 Msun, in particular for donor stars evolved to giants. 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. Massive stars in a wide range of metallicities and with initial masses up to at least 115 Msun may possibly shed their envelopes and survive CE evolution, depending on their initial orbital parameters, similarly to the situation for intermediate mass and low-mass stars with degenerate cores. We conclude that based on stellar structure calculations, and in the view of the usual simple energy budget analysis, events like GW150914 and GW151226 could possibly be produced from the CE channel. Calculations of post-CE orbital separations, however, and thus the estimated LIGO detection rates, remain highly uncertain. [Abridged]