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Binary Radiopulsars with Black Holes

The discovery of binary radiopulsars with massive unseen companions (>3-tex2html_wrap_inline11498 ) 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)[144]. Their estimates of the total number of NS+NS and BH+NS binaries in the Galaxy ( tex2html_wrap_inline8945 tex2html_wrap_inline11502 - tex2html_wrap_inline9939 ) 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[69]; Brumberg et al., 1975[26]; Blandford and Teukolsky, 1975[18]) 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[110], Lipunov et al., 1994a[123]) 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 Tables9 and 10 we show representative evolutionary tracks for both types.

Table 9

Table 10

The first type (Table9) originates from very massive binaries with high initial mass difference ( table3968, table3991), 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 tex2html_wrap_inline11548 . 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 (SS433-like stage) with supereddington accretion (``SBH'') and finally collapses to form a NS (as its mass tex2html_wrap_inline11550prior to collapse). Thus a young pulsar (ejecting NS) in elliptical orbit around a massive BH is formed.

The second type of binary BH+PSRs (Table10) is a descendant of binaries with lower initial masses ( tex2html_wrap_inline11552-tex2html_wrap_inline11554) and moderate mass ratios ( tex2html_wrap_inline11475 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.

Table 11 (Note Table 11)


In Table11 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[204]), 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, tex2html_wrap_inline11439 and tex2html_wrap_inline11558. We have assumed that if a star collapses to form a NS (in other terms, if the presupernova mass table4022), the remnant acquires an additional (kick) velocity of 75km stex2html_wrap_inline8853 . The need for such a kick velocity follows from a statistical analysis of radiopulsars with OB-companions (Kornilov and Lipunov, 1984[87]; Dewey and Cordes, 1987[45]; see, however, Lipunov et al., 1995d[128]). In the case of collapse into a BH (tex2html_wrap_inline11626) we considered both isotropic and anisotropic collapse. The first set of models (upper rows in Table11) 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, tex2html_wrap_inline11628. These models are shown in the bottom rows of Table11 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 tex2html_wrap_inline8945 10 per Galaxy is given by a fraction ( tex2html_wrap_inline8945 1/4) of the BHC among the observed number of bright massive X-ray binaries (MXRB), scaled to the total galactic number of MXRB ( tex2html_wrap_inline8945 40, see van Paradijs and McClintock, 1993[208]).


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 Table11 (second column) impose some restrictions on the parameters tex2html_wrap_inline11439 and tex2html_wrap_inline11558. It is seen from this table that lower values of tex2html_wrap_inline11634are less likely. Too low values of figure4083would give too ``light'' BH with masses in the range 3-tex2html_wrap_inline11498 , 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 tex2html_wrap_inline11439 require higher values of tex2html_wrap_inline11558, giving more massive BH. Here, again, uppermost values for tex2html_wrap_inline11646-0.7 are less likely according to the most probable estimation of BH mass in Cyg X-1 tex2html_wrap_inline8945 tex2html_wrap_inline9178 . These considerations make us favor the values tex2html_wrap_inline11648, tex2html_wrap_inline10334 . This mass corresponds to the initial mass of the star of tex2html_wrap_inline8945 60-70 tex2html_wrap_inline11656.


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 Figure33 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[91]). However, at present there are no reliable estimates of such events in the Galaxy.

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Mike E. Prokhorov
Sat Feb 22 18:38:13 MSK 1997