Formation of high mass X-ray black hole binaries

Abstract The discrepancy in the past years of many more black-hole soft X-ray transients (SXTs), of which a dozen have now been identified, had challenged accepted wisdom in black hole evolution. Reconstruction in the literature of high-mass X-ray binaries has required stars of up to ∼40 M ⊙ to evolve into low-mass compact objects, setting this mass as the limit often used for black hole formation in population syntheses. On the other hand, the sheer number of inferred SXTs requires that many, if not most, stars of ZAMS masses 20–35 M ⊙ end up as black holes ( Portegies Zwart et al., 1997 , Ergma and van den Heuvel, 1998 ). In this paper we show that this can be understood by challenging the accepted wisdom that the result of helium core burning in a massive star is independent of whether the core is covered by a hydrogen envelope, or ‘naked’ while it burns. The latter case occurs in binaries when the envelope of the more massive star is transferred to the companion by Roche Lobe overflow while in either main sequence or red giant stage. For solar metallicity, whereas the helium cores which burn while naked essentially never go into high-mass black holes, those that burn while clothed do so, beginning at ZAMS mass ∼20 M ⊙ , the precise mass depending on the 12C(α,γ)16O rate as we outline. In this way the SXTs can be evolved, provided that the H envelope of the massive star is removed only following the He core burning. Whereas this scenario was already outlined in 1998 by Brown et al. [NewA 4 (1999) 313], their work was based on evolutionary calculations of Woosley et al. [ApJ 448 (1995) 315] which employed wind loss rates which were too high. In this article we collect results for lower, more correct wind loss rates, finding that these change the results only little. We go into the details of carbon burning in order to reconstruct why the low Fe core masses from naked He stars are relatively insensitive to wind loss rate. The main reason is that without the helium produced by burning the hydrogen envelope, which is convected to the carbon in a clothed star, a central 12C abundance of ∼1/3 remains unburned in a naked star following He core burning. The later convective burning through 12C+12C reactions occurs at a temperature T∼80 keV. Finally, we show that in order to evolve a black hole of mass ≳10 M ⊙ such as observed in Cyg X-1 , even employing extremely massive progenitors of ZAMS mass ≳60 M ⊙ for the black hole, the core must be covered by hydrogen during a substantial fraction of the core burning. In other words, the progenitor must be a WNL star. We evolve Cyg X-1 in an analogous way to which the SXTs are evolved, the difference being that the companion in Cyg X-1 is more massive than those in the SXTs, so that Cyg X-1 shines continuously.