On the formation and evolution of black hole binaries

Abstract

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 common-envelope structure and other model parameters. We find that black hole binaries with intermediate-and 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 ultraluminous 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.

On the formation of galactic black hole low-mass X-ray binaries

“…However, for stars less massive than 30 M ⊙ , λs increase again when they have ascended the asymptotic giant branch and developed a deep envelope (see also Podsiadlowski et al 2003). As an illustration, Fig.…”

“…In this case the progenitor stars are usually more massive than 28 M ⊙ in binaries. For such massive stars the binding energy of the envelope is so large that with λ = λg a low-mass secondary inevitably merges with the He core of the primary, and no successful BH LMXBs can form (see also Podsiadlowski et al 2003). So in models A1 and A2 we set αCE = 1 with λ = λ b and λ h , respectively.…”

Accretion, ablation and propeller evolution in close millisecond pulsar binary systems

“…or the entire donor mass is used in the initial orbital equation (Webbink 1984;de Kool 1990;Podsiadlowski et al 2003;Belczynski et al 2008),…”

“…Although the value is known to vary with stellar type and age, many previous models have assumed a constant value, typically λ = 0.5 (Portegies Zwart & Yungelson 1998;Hurley, Tout & Pols 2002;Belczynski et al 2002;Podsiadlowski, Rappaport & Han 2003). The variation with stellar age has also been examined in detailed stellar evolution codes (Dewi & Tauris 2001;Ivanova & Taam 2003;Podsiadlowski et al 2003), where λ is shown to vary between 0.02 − 0.7. Population synthesis calculations that use a non constant value of λ are Voss & Tauris 2003;Podsiadlowski et al 2003;Kiel & Hurley 2006;Kiel et al 2008Kiel et al , 2010Hurley et al 2010).…”

“…The variation with stellar age has also been examined in detailed stellar evolution codes (Dewi & Tauris 2001;Ivanova & Taam 2003;Podsiadlowski et al 2003), where λ is shown to vary between 0.02 − 0.7. Population synthesis calculations that use a non constant value of λ are Voss & Tauris 2003;Podsiadlowski et al 2003;Kiel & Hurley 2006;Kiel et al 2008Kiel et al , 2010Hurley et al 2010). Since its inception bse has been updated to include an algorithm that calculates a value of λ based on comparison to the detailed models of Pols et al (1998), see Kiel & Hurley (2006) and Hurley et al (2010).…”