On the formation and evolution of black-hole binaries

We present the results of a systematic study of the formation and evolution of binaries containing black holes and normal-star companions with a wide range of masses. We first reexamine the standard formation scenario for close black-hole binaries, where the progenitor system, a binary with at least one massive component, experienced a common-envelope phase and where the spiral-in of the companion in the envelope of the massive star caused the ejection of the envelope. We estimate the formation rates for different companion masses and different assumptions about the commonenvelope structure and other model parameters. We find that black-hole binaries with intermediateand high-mass secondaries can form for a wide range of assumptions, while black-hole binaries with low-mass secondaries can only form with apparently unrealistic assumptions (in agreement with previous studies). We then present detailed binary evolution sequences for black-hole binaries with secondaries of 2 to 17 M and demonstrate that in these systems the black hole can accrete appreciably even if accretion is Eddington limited (up to 7 M for an initial black-hole mass of 10 M ) and that the black holes can be spun up significantly in the process. We discuss the implications of these calculations for well-studied black-hole binaries (in particular GRS 1915+105) and ultra-luminous X-ray sources of which GRS 1915+105 appears to represent a typical Galactic counterpart. We also present a detailed evolutionary model for Cygnus X-1, a massive black-hole binary, which suggests that at present the system is most likely in a wind mass-transfer phase following an earlier Roche-lobe overflow phase. Finally, we discuss how some of the assumptions in the standard model could be relaxed to allow the formation of low-mass, short-period black-hole binaries which appear to be very abundant in Nature.