Bounds on Expected Black Hole Spins in Inspiraling Binaries

As a first step toward understanding the angular momentum evolution 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 that can possibly contribute to the black hole spin magnitude: a birth spin for the black hole, imparted at either (1) the collapse of a massive progenitor star to a black hole or (2) the accretion-induced collapse of a neutron star to a black hole, and (3) an accretion spin-up when the already formed black hole (via processes 1 or 2) goes through an accretion episode (through an accretion disk or a common-envelope phase). Our results show that, with regard to accretion-induced spin-up in merging BH-NS binaries (method 3 above), only accretion episodes associated with common-envelope phases and hypercritical accretion rates occur in the formation history of merging black hole/neutron star binaries. Lacking unambiguous experimental information about BH birth spins (i.e., regarding the results of processes 1 and 2), we choose two fiducial values for the BH birth angular momentum parameter a = J/M², consistent with observations of (1) NS birth spins (a ≃ 0) and (2) X-ray binaries (a = 0.5). Using these two fiducial values and a conservative upper bound on the specific angular momentum of accreted matter, we discuss the expected range of black hole spins in the binaries of interest. We conclude with comments on the significance of these results for ground-based gravitational wave searches of inspiral signals from black hole binaries.