Gravitational recoil from accretion-aligned black-hole binaries

Abstract

We explore the newly discovered "hangup-kick" effect, which greatly amplifies the recoil for configurations with partial spin-/ orbital-angular momentum alignment, by studying a set of 48 new simulations of equal-mass, spinning black-hole binaries. We propose a phenomenological model for the recoil that takes this new effect into account and then use this model, in conjunction with statistical distributions for the spin magnitude and orientations, based on accretion simulations, to find the probabilities for observing recoils of several thousand km s −1 . In addition, we provide initial parameters, eccentricities, radiated linear and angular momentum, precession rates and remnant mass, spin, and recoils for all 48 configurations. Our results indicate that surveys exploring peculiar (redshifted or blueshifted) differential line-of-sight velocities should observe at least one case above 2000 km s −1 out of four thousand merged galaxies. On the other hand, the probability that a remnant BH recoils in any direction at a velocity exceeding the ∼ 2000 km s −1 escape velocity of large elliptical galaxies is 0.03%. Probabilities of recoils exceeding the escape velocity quickly rise to 5% for galaxies with escape velocities of 1000 km s −1 and nearly 20% for galaxies with escape velocities of 500 km s −1 . In addition the direction of these large recoils is strongly peaked toward the angular momentum axis, with very low probabilities of recoils exceeding 350 km s −1 for angles larger than 45• with respect to the orbital angular momentum axis.

Effects of post-Newtonian spin alignment on the distribution of black-hole recoils

“…The recent LZ simulations [25,26] have two potentially important consequences from an astrophysical point of view. First of all, the maximum possible "hang-up" kick magnitude is about 25% larger than predicted by the ordinary, "no hang-up" superkick formula: 4,900 km/s rather than 3,750 km/s.…”

“…Furthermore, the LZ kick formula is most reliable for mass ratios close to unity, since all 48 of the new NR simulations were carried out for q = 1 [26]. We therefore begin our study of the likelihood of very large kicks by considering comparable-mass binaries.…”

“…We calculate the component v || of the recoil velocity parallel to L using both the new LZ "hang-up" formula [25,26] and the older kick formula from Campanelli et al [11]. We calculate the components v m , v ⊥ perpendicular to L from the fitting formula of [11]: cf.…”

“…The initial value of θ1 (the alignment angle of the larger SBH) is indicated by the different symbols, while the spin χ 2 of the smaller SBH is initially isotropically distributed. Left panels: prediction according to the LZ papers [25,26]; right panels: prediction without this newly discovered hang-up effect. In all plots the dashed lines correspond to the initial distributions at ri = 1000M , while the solid lines give the distributions at r f = 10M , after PN spin alignment has occurred.…”

“…Recent equal-mass NR simulations by Lousto and Zlochower ( [25,26]; henceforth LZ) have qualitatively and quantitatively changed the predicted dependence of gravitational recoils on the SBH spins χ i . The maximum possible kick, extrapolated to maximal initial spins, is now ∼ 4, 900 km/s, and this kick occurs not in the previously described "superkick" configuration but for spins with θ i ≃ 50 • .…”