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, a spin , is less than 0.5 for initially non rotating black holes and the tilt angle, i tilt , is less than 45 • for 50% of the systems in black hole -neutron star binaries. Upon 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 (a spin > 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 non rotating black holes. Due to the (i) insensitivity of signal detection techniques to the black hole spin and the (ii) 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 non spinning 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.

We use a 3D relativistic SPH (smoothed particle hydrodynamics) code to study mergers of black hole-neutron star (BH-NS) binary systems with low mass ratios, adopting q M NS /M BH ' 0:1 as a representative case. The outcome of such mergers depends sensitively on both the magnitude of the BH spin and its obliquity (i.e., the inclination of the binary orbit with respect to the equatorial plane of the BH ). In particular, only systems with sufficiently high BH spin parameter a and sufficiently low orbital inclinations allow any NS matter to escape or to form a long-lived disk outside the BH horizon after disruption. Mergers of binaries with orbital inclinations above $60 lead to complete prompt accretion of the entire NS by the BH, even for the case of an extreme Kerr BH. We find that the formation of a significant disk or torus of NS material around the BH always requires a near-maximal BH spin and a low initial inclination of the NS orbit just prior to merger.

In black hole X-ray binaries, a misalignment between the spin axis of the black hole and the orbital angular momentum can occur during the supernova explosion that forms the compact object. In this letter we present population synthesis models of Galactic black hole X-ray binaries, and study the probability density function of the misalignment angle, and its dependence on our model parameters.In our modeling, we also take into account the evolution of misalignment angle due to accretion of material onto the black hole during the X-ray binary phase.The major factor that sets the misalignment angle for X-ray binaries is the natal kick that the black hole may receive at its formation. However, large kicks tend to disrupt binaries, while small kicks allow the formation of XRBs and naturally select systems with small misalignment angles. Our calculations predict that the majority (> 67%) of Galactic field BH XRBs have rather small ( 10 o ) misalignment angles, while some systems may reach misalignment angles as high as ∼ 90 o and even higher. This results is robust among all population synthesis models. The assumption of small small misalignment angles is extensively used to observationally estimate black hole spin magnitudes, and for the first time we are able to confirm this assumption using detailed population synthesis calculations.

It has been suggested that the observed rotation periods of radio pulsars might be induced by a non-axisymmetric spiral-mode instability in the turbulent region behind the stalled supernova bounce shock, even if the progenitor core was not initially rotating. In this paper, using the three-dimensional AMR code CASTRO with a realistic progenitor and equation of state and a simple neutrino heating and cooling scheme, we present a numerical study of the evolution in 3D of the rotational profile of a supernova core from collapse, through bounce and shock stagnation, to delayed explosion. By the end of our simulation (∼420 ms after core bounce), we do not witness significant spin up of the proto-neutron star core left behind. However, we do see the development before explosion of strong differential rotation in the turbulent gain region between the core and stalled shock. Shells in this region acquire high spin rates that reach ∼150 Hz, but this region contains too little mass and angular momentum to translate, even if left behind, into rapid rotation for the full neutron star. We find also that much of the induced angular momentum is likely to be ejected in the explosion, and moreover that even if the optimal amount of induced angular momentum is retained in the core, the resulting spin period is likely to be quite modest. Nevertheless, induced periods of seconds are possible.

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