The evolution of the spin and tilt of black holes in compact black hole-neutron star and black hole-black hole binary systems is investigated within the framework of the coalescing compact star binary model for short gamma ray bursts via the population synthesis method. Based on recent results on accretion at super critical rates in slim disk models, estimates of natal kicks, and the results regarding fallback in supernova models, we obtain the black hole spin and misalignment. It is found that the spin parameter, aspin, is less than 0.5 for initially nonrotating black holes and the tilt angle, itilt, is less than 45° for 50% of the systems in black hole-neutron star binaries. On comparison with the results of black hole-neutron star merger calculations we estimate that only a small fraction (~0.01) of these systems can lead to the formation of a torus surrounding the coalesced binary potentially producing a short-hard gamma ray burst. On the other hand, for high initial black hole spin parameters (aspin 0.6) this fraction can be significant (~0.4). It is found that the predicted gravitational radiation signal for our simulated population does not significantly differ from that for nonrotating black holes. Due to the (1) insensitivity of signal detection techniques to the black hole spin and the (2) predicted overall low contribution of black hole binaries to the signal we find that the detection of gravitational waves are not greatly inhibited by current searches with nonspinning templates. It is pointed out that the detection of a black hole-black hole binary inspiral system with LIGO or VIRGO may provide a direct measurement of the initial spin of a black hole.
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