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The discovery of binary radiopulsars with massive unseen companions (>3- ) would be of great importance to fundamental physics and modern theory of stellar evolution, providing a compelling evidence for the existence of BH in nature. The formation of binaries consisting of a BH in a pair with a radiopulsar (PSR) has been discussed previously by Narayan et al. (1991). Their estimates of the total number of NS+NS and BH+NS binaries in the Galaxy ( - ) were derived from the statistics of binary pulsars and current pulsar surveys. As is well known, observations of a radiopulsar in a binary system (Hulse and Taylor, 1975; Brumberg et al., 1975; Blandford and Teukolsky, 1975) provide the most accurate information about the physical parameters of the binary companion. This does not just concern the mass of the companion, which until now has been the main signature of a BH. The pulsar radioemission can be used as a probe of the plasma emitted by the secondary star (Lipunov and Prokhorov 1984, Lipunov et al., 1994a) and, consequently, by giving a picture of the physical properties of the adjacent medium, can prove the BH nature of the companion. Some relativistic effects specific to BH can be observed in these systems, such as propagation of the radiation through the BH ergosphere.
We have found that PSR+BH binaries are final evolutionary products of two different types of original binary. In Tables 9 and 10 we show representative evolutionary tracks for both types.
úÄÅÓØ ÄÏÌÖÎÁ ÂÙÔØ Table 9
úÄÅÓØ ÄÏÌÖÎÁ ÂÙÔØ Table 10
The first type (Table 9) originates from very massive binaries with high initial mass difference ( , ), so a CE stage is inevitable at the first mass transfer episode. The remaining massive helium WR-star collapses further directly to a BH provided its mass . We note that Cyg X-1-like binaries (BH+OB-supergiant) can be formed in this way (see the next section for further discussion). The secondary component (now seen possibly as a Be-star) passes through the stage of violent mass transfer to the BH (SS 433-like stage) with supereddington accretion (``SBH'') and finally collapses to form a NS (as its mass prior to collapse). Thus a young pulsar (ejecting NS) in elliptical orbit around a massive BH is formed.
The second type of binary BH+PSRs (Table 10) is a descendant of binaries with lower initial masses ( -) and moderate mass ratios ( 1), so the first mass transfer proceeds more or less conservatively and the initial secondary becomes more massive. After the first supernova explosion a young PSR with a Be-star (like PSR B1259-63) is formed, and then silent collapse of the massive supergiant to a BH gives rise to a PSR+BH binary in a wide eccentric orbit. We note that in all calculation runs the contribution of each type of track to the overall number of PSR+BH varied from 30 to 70 percent, depending on parameters.
úÄÅÓØ ÄÏÌÖÎÁ ÂÙÔØ Table 11 (Note Ë Table 11)
In Table 11 we show the number of calculated binary pulsars with a NS, BH or WD companion, normalized to all PSR formed from single and binary systems in a 500 000 run. For comparison we estimated the galactic numbers of the same binary types (taken from van den Heuvel, 1991), normalized to the number of known pulsars (taken as 700). This permits us (partially, of course) to get rid off selection effects. The numbers are shown in dependence on two principal parameters of binary NS formation, and . We have assumed that if a star collapses to form a NS (in other terms, if the presupernova mass ), the remnant acquires an additional (kick) velocity of 75 km s . The need for such a kick velocity follows from a statistical analysis of radiopulsars with OB-companions (Kornilov and Lipunov, 1984; Dewey and Cordes, 1987; see, however, Lipunov et al., 1995d). In the case of collapse into a BH () we considered both isotropic and anisotropic collapse. The first set of models (upper rows in Table 11) was calculated under the assumption that the BH remnant acquires no recoil velocity, whereas in the second set we introduced the kick velocity proportional to the mass lost during the collapse, . These models are shown in the bottom rows of Table 11 and are marked by a letter with an asterisk. As a separate independent criterion we included the calculated galactic number of BH candidates (BHC) with evolved OB-companions. The observational estimation 10 per Galaxy is given by a fraction ( 1/4) of the BHC among the observed number of bright massive X-ray binaries (MXRB), scaled to the total galactic number of MXRB ( 40, see van Paradijs and McClintock, 1993).
Figure 33: The calculated distributions of BH+PSR binaries on
orbital periods (left-hand panel) and on eccenticities (right-hand panel).
Solid line marks the case without anisotropy of the collapse to BH, dashed
line corresponds to the anisotropy of the BH formation (see the text) (Lipunov
et al., 1994b).
The observational data from Table 11 (second column) impose some restrictions on the parameters and . It is seen from this table that lower values of are less likely. Too low values of would give too ``light'' BH with masses in the range 3- , and the large mass loss during the collapse would make binaries with high mass ratio unbound, so it would be difficult to understand how low-mass binary BH candidates with high mass ratios observed now as X-ray novae had been formed. Higher values of require higher values of , giving more massive BH. Here, again, uppermost values for -0.7 are less likely according to the most probable estimation of BH mass in Cyg X-1 . These considerations make us favor the values , . This mass corresponds to the initial mass of the star of 60-70 .
By adopting these parameters, we calculated binaries to find expected distributions of binary BH+PSR on orbital periods and eccentricities (Figure 33)
Solid lines in the histograms in Figure 33 correspond to calculations without anisotropy, dashed lines, with the anisotropy of BH formation as described above.
The statistics obtained do not account for the BH binaries that could be formed in dense globular stellar clusters and then expelled from there due to possible stellar encounters (Kulkarni et al., 1993). However, at present there are no reliable estimates of such events in the Galaxy.