Contribution of high-mass black holes to mergers of compact binaries

We consider the merging of compact binaries consisting of a high-mass black hole and a neutron star. From stellar evolutionary calculations that inclu de mass loss, we estimate that a zero-age main sequence (ZAMS) mass of grea ter than or similar to 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, wi th its measured orbital radius of similar to 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 ne utron star in the final supernova explosion. We estimate the probability of the necessary eccentricity to be similar to 1%; i.e., 99% of the time the explosion of a Cyg X-1-type object will end as a binary of compact stars, w hich will not merge in Hubble time (unless the orbit is tightened in common envelope evolution, which we discuss later). Although we predict similar t o 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 m erging in Hubble time. This gives us a merging rate of similar to 3 x 10(-8 ) yr-l in the galaxy, the order of magnitude of the merging rate found by c omputer-driven population syntheses, if extrapolated to our mass limit of 8 0 M, ZAMS mass for high-mass black hole formation. Furthermore, in both our calculation and in those of population syntheses, almost all of the mergin gs involve an eccentricity close to unity in the final explosion of the O s tar. From this first part of our development we obtain only a negligible co ntribution to our final results for mergers, and it turns out to be irrelev ant for our final results. In our main development, instead of relying on o bserved binaries, we consider the general evolution of binaries of massive stars. The critical stage is when the more massive star A has become a blac k hole and the less massive star B is a giant reaching out to A. We then ha ve 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 similar to 35 M., w hile the black hole A has a mass of 10 M.. About 20% of the binaries of thi s type are found to end up in a range of orbital radii favorable for mergin g; i.e., outside of the relevant Roche lobes, but close enough so that thes e final binaries of compact objects will merge in Hubble time. The narrow b lack hole O star orbits do not seem to be found in population syntheses, be cause in them mergers happen almost completely as a result of kick velociti es. 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 ho le neutron star systems contribute substantially to the predicted observati onal frequency of gravitational waves. We discuss how our high-mass black h ole formation can be reconciled with the requirements of nucleosynthesis, a nd we indicate that a bimodal distribution of masses of black holes in sing le stars can account, at least qualitatively, for the many transient source s that contain high-mass black holes.