We consider the merging of compact binaries consisting of a high-mass black-hole and a neutron star .
From stellar evolutionary calculations which include mass loss we estimate that a ZAMS mass of \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ > $ } } 80 ~ { } % { M } _ { \odot } 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 \sim 17 R _ { \odot } 
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 \sim 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 a Hubble time ( unless the orbit is tightened in common envelope evolution which we discuss later ) .

Although we predict \sim 7 massive binaries of Cyg X-1 type , we argue that only Cyg X-1 is narrow enough to be observed and that only it has an appreciable chance of merging in a Hubble time .
This gives us a merging rate of \sim 3 \times 10 ^ { -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 } _ { \odot } 
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 A .
A will accept a small fraction of the mass of the envelope of B but will plunge deep into B while expelling B ’ s envelope .

We expect that star B can at least be in the mass range 15 \sim 35 ~ { } { M } _ { \odot } 
while the black hole A has a mass of 10 ~ { } { M } _ { \odot } .
About 20 percent 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 a 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 ( 1998 ) 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 for high-mass black hole formation can be reconciled with the requirements of nucleosynthesis and indicate that a bimodal distribution of masses of black holes in single stars can account , at least qualitatively , for the many transient sources which contain high-mass black holes .