Bounds on Expected Black Hole Spins in Inspiraling Binaries

As a first step towards understanding the angular momentum evolutionary history of black holes in merging black-hole/neutron-star binaries, we perform population synthesis calculations to track the distribution of accretion histories of compact objects in such binaries. We find that there are three distinct processes can possibly contribute to the black-hole spin magnitude: a birth spin for the black hole, imparted at either (i) the collapse of a massive progenitor star to a black hole or (ii) the accretion-induced collapse of a neutron star to a black hole; and (iii) an accretion spin-up when the already formed black hole [via (i) or (ii)] goes through an accretion episode (through an accretion disk or a common-envelope phase). Our results show that of these three mechanisms, only accretion episodes associated with common-envelope phases and hypercritical accretion rates can significantly affect the black hole spin in merging binaries of interest. Furthermore, from the observed sample of NS binaries we infer that the birth spins of black holes [through either channel (i) or (ii)] are probably small. Given an astrophysically consistent bound on the BH birth spin, and using a conservative upper bound on the specific angular momentum of accreted matter, we discuss the expected range of black hole spins. We conclude with comments on the significance of these results for ground-based gravitational-wave searches of inspiral signals from black hole binaries.