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For massive binaries, we assumed an initial mass ratio exponent , and obtained the total amount of both types of binary PSR with BH per Galaxy of 2 , which is in agreement with independent estimates of Narayan et al. (1991). As we have shown in the previous section, roughly half of all binary BH+PSR systems in their evolutionary history must pass through the stage BH+II which can be observationally identified with Cyg X-1-like binaries. Using this correlation N(BH+II)-N(BH+PSR) we can obtain another independent estimate, which is free of selection effects, of the expected number of BH+PSR. In Figure 34 we plot the ratio of total calculated N(PSR+BH)+N(BH+PSR) to that of PSR, against calculated N(BH+II) for different combinations of parameters , , , and both isotropic and anisotropic BH collapse. The above estimate of number of bright BH+II binaries (similar to Cyg X-1), about 10 per Galaxy, yields a lower limit for the expected N(PSR+BH) 0.3 per 700 single pulsars (Figure 34).
Figure 34: Scenario machine calculation of galactic number
of BH+PSR binaries against BH+II (Cyg X-1-like binaries), for different
combinations of parameters of the evolutionary scenario. Crosses and pluses
correspond to isotropic and anisotropic collapse to BH, respectively (Lipunov
et al., 1994b).
We note that when estimating the number of bright BHC binaries one misses dim X-ray BH+II systems with long orbital periods. From the parsity of PSR+BH binaries detected so far (an upper limit 1 per 700 known pulsars) we can infer an upper limit to the total galactic number of BH in pairs with blue supergiants 100 per Galaxy (upper dashed line in Figure 34). These estimates mean that PSR+BH systems may be discovered in the near future.