1999ApJ...517..318B

We consider the merging of compact binaries consisting of a high-mass black hole and a neutron star. From stellar evolutionary calculations that include mass loss, we estimate that a zero-age main sequence (ZAMS) mass of ≳80 M_☉ is necessary before a high-mass black hole can result from a massive O star progenitor. We first consider how Cyg X-1, with its measured orbital radius of ∼17 R_☉, might evolve. Although this radius is substantially less than the initial distance of two O stars, it is still so large that the resulting compact objects will merge only if an eccentricity close to unity results from a high kick velocity of the neutron star in the final supernova explosion. We estimate the probability of the necessary eccentricity to be ∼1%; i.e., 99% of the time the explosion of a Cyg X-1-type object will end as a binary of compact stars, which will not merge in Hubble time (unless the orbit is tightened in common envelope evolution, which we discuss later). Although we predict ∼7 massive binaries of Cyg X-1 type, we argue that only Cyg X-1 is narrow enough to be observed, and that only Cyg X-1 has an appreciable chance of merging in Hubble time. This gives us a merging rate of ∼3x10^–8 yr^–1 in the galaxy, the order of magnitude of the merging rate found by computer-driven population syntheses, if extrapolated to our mass limit of 80 M_☉ ZAMS mass for high-mass black hole formation. Furthermore, in both our calculation and in those of population syntheses, almost all of the mergings involve an eccentricity close to unity in the final explosion of the O star. From this first part of our development we obtain only a negligible contribution to our final results for mergers, and it turns out to be irrelevant for our final results. In our main development, instead of relying on observed binaries, we consider the general evolution of binaries of massive stars. The critical stage is when the more massive star A has become a black hole and the less massive star B is a giant reaching out to A. We then have a common envelope, and we expect hypercritical accretion to star A. Star A will accept a small fraction of the mass of the envelope of star B, but it will plunge deep into star B while expelling the envelope of star B. We expect that star B can at least be in the mass range 15∼35 M_☉, while the black hole A has a mass of 10 M_☉. About 20% of the binaries of this type are found to end up in a range of orbital radii favorable for merging; i.e., outside of the relevant Roche lobes, but close enough so that these final binaries of compact objects will merge in Hubble time. The narrow black hole O star orbits do not seem to be found in population syntheses, because in them mergers happen almost completely as a result of kick velocities. In the exception (case H of Portegies Zwart & Yungelson, which includes hypercritical accretion), common envelope evolution is more effective and we are in agreement with their results. We find that the high-mass black hole neutron star systems contribute substantially to the predicted observational frequency of gravitational waves. We discuss how our high-mass black hole formation can be reconciled with the requirements of nucleosynthesis, and we indicate that a bimodal distribution of masses of black holes in single stars can account, at least qualitatively, for the many transient sources that contain high-mass black holes.