Formation and coalescence of relativistic binary stars: the effect of kick velocity

Using Monte Carlo calculations of the modern scenario for binary stellar evolution, and taking account of the spin evolution of magnetized compact stars (the ‘scenario machine’), we compute for the first time the number of galactic binary pulsars with different companion types OB star, white dwarf (WD), neutron star (NS), black hole (BH), or planet assuming various phenomenological distributions for kick velocities of newborn NSs. We demonstrate a strong dependence of the binary pulsar population fractions relative to single pulsars on the mean kick velocity, and find an optimal kick velocity of 150–200 km s−1. We also investigate the way in which the merging rates of relativistic binary stars (NS + NS, NS + BH, BH + BH) depend on the kick velocity. We show that the BH + BH merging may occur, depending on the parameters of BH formation, at a rate of one per 200000–500000 yr in a Milky Way-type galaxy. The NS + NS merging rate Rns is found to be 1 per ∼ 3000 yr for zero recoil, and decreases to one per 10 000 yr even for the highest kick velocities of 400 km s−1. That the merging rates derived from evolutionary calculations are higher, by two orders of magnitude, than those based on binary pulsar statistics only, is suggested to be the result of the fact that the observable binary pulsars in pairs with NSs form only a fraction of the total number of binary NS systems. The merging rates obtained imply an expected detection rate of binary BHs (by a gravitational wave detector) comparable with and even higher than the binary NS merging rate for a wide range of parameters. Detecting the final frequency of a merging event at about 100 Hz and the shaping of the waveforms would bring firm evidence of the existence of BHs in nature.