Can binary mergers produce maximally spinning black holes?

Abstract

Gravitational waves carry away both energy and angular momentum as binary black holes inspiral and merge. The relative efficiency with which they are radiated determines whether the final black hole of mass M f and spin S f saturates the Kerr limit (χ f ≡ S f /M 2 f ≤ 1). Extrapolating from the test-particle limit, we propose expressions for S f and M f for mergers with initial spins aligned or anti-aligned with the orbital angular momentum. We predict the the final spin at plunge for equalmass non-spinning binaries to better than 1%, and that equal-mass maximally spinning aligned mergers lead to nearly maximally spinning final black holes (χ f ≃ 0.9988). We also find black holes can always be spun up by aligned mergers provided the mass ratio is small enough.Recent breakthroughs in numerical relativity have led to successful simulations of the inspiral, merger, and ringdown of binary black holes (BBHs) [1,2,3]. Despite this progress, approximations underlying these simulations limit them to mergers with large but submaximal initial spins (χ i 0.9) and order-unity mass ratios (q ≡ m 2 /m 1 ≥ 1/6). Yet the maximally spinning regime is of considerable theoretical and observational interest. Maximally spinning black holes barely manage to hide their singularities within their event horizons, and observable, "naked" singularities are expected for spins χ > 1. While infinitesimal processes like steady accretion cannot produce naked singularities [4], Penrose's cosmic-censorship conjecture [5] that such singularities can never be created has not been proven for comparable-mass BBH mergers. Black-hole spins are not a purely theoretical concern; they can be measured by reverberation mapping of iron Kα fluorescence in the spectra of active galactic nuclei (AGN) [6]. This technique has been applied to XMM-Newton observations of the Seyfert 1.2 galaxy MCG-06-30-15, leading to a measured spin χ = 0.989 +0.009 −0.002 very near the maximal limit [7]. The spins of supermassive black holes (SBHs) also offer important insights into their formation. Some expect that highly spinning SBHs will only be found in gas-rich systems like spirals [8]. Others suggest that gas accretion occurs through a series of chaotically oriented episodes, leading to moderate spins (χ ∼ 0.1−0.3) lower than those expected from comparable-mass mergers in gas-poor ellipticals [9]. Comparing measured spins in spirals and ellipticals will distinguish between these two scenarios.In the absence of reliable simulations of maximally spinning BBH mergers, we must rely on various approximations in this important regime. Hughes and Blandford (hereafter HB) [10] assumed that the energy and angular momentum radiated during the inspiral stage dominates that radiated during the comparatively brief merger and ringdown. They then used conservation of energy and angular momentum to equate these quantities when the BBHs reach their innermost stable circular orbit (ISCO) to the mass and spin of the final black hole,Here E(χ) is the energy per unit mass of a test particle...

Maximum black-hole spin from quasicircular binary mergers

“…The value of χ i for which a given curve crosses the horizontal dotted line ∂χ f /∂q = 0 determines the maximum spin χ lim to which a black hole can be spun up by test-particle mergers. We see that the superradiant scattering of gravitational waves produced during the inspiral reduces χ lim from the Kerr limit as predicted by Bardeen [4], HB [23], and K [25] and shown by the blue (short-dashed) curve to χ i = 0.9979 shown by the black (solid) curve. The red (long-dashed) curve shows the predictions of the BKL [24] model described in Sec.…”

“…In this model black holes can only be spun up by test particles to the fictitious limit χ lim = 0.948 at which ∂χ f /∂q = 0. Kesden [25] (hereafter K) sought to remedy this by replacing Eq. (3a) with…”

Predicting the Direction of the Final Spin From the Coalescence of Two Black Holes

“…The mass M rad radiated to gravitational waves can be neglected, i.e., M fin = M ≡ M 1 + M 2 . The radiated mass could be accounted for by using the NR data for M fin (Tichy & Marronetti 2008) or extrapolating the test-particle behavior (Kesden 2008). The reason why assumption (I) is reasonable is that M rad is largest for aligned binaries, but these are also the ones employed to fit the free coefficients in Equation (3).…”

“…Despite the mathematical complexity of the problem, many results of the NR simulations can be reproduced accurately using semianalytical prescriptions (Damour & Nagar 2009;Buonanno et al 2009) based on post-Newtonian (PN) and BH perturbation theory. It is therefore not entirely surprising that the dimensionless spin of the remnant from a BH-binary merger, a fin = S fin /M 2 fin , can be described, with increasing accuracy, via simple prescriptions based on point particles (Hughes & Blandford 2003;Buonanno et al 2008;Kesden 2008), on fits to the NR data (Rezzolla et al 2008b(Rezzolla et al , 2008cTichy & Marronetti 2008;, or on a combination of the two approaches (Rezzolla et al 2008a;see Rezzolla 2009 for a review). These formulas are useful because they provide information over the entire seven-dimensional parameter space for BH binaries in quasi-circular orbits, namely, the mass ratio q ≡ M 2 /M 1 and the six components of the initial dimensionless spin vectors a 1,2 = S 1,2 /M 2 1,2 .…”

Modeling the Black Hole Merger of QSO 3C 186

“…Full numerical simulations of the merger of binary black holes have produced detailed predictions for the remnant final black hole mass, spin, and recoil velocity (Rezzolla et al 2008a(Rezzolla et al , 2008bKesden 2008;Tichy & Marronetti 2008;Lousto et al 2010a;Lousto & Zlochower 2013Zlochower & Lousto 2015) and the probability of a given recoil velocity to be observed (Schnittman & Buonanno 2007;Lousto et al 2010bLousto et al , 2012. Those "phenomenological" formulas relate the binary parameters of the progenitor, i.e., individual masses and spins, to the final mass, spin, and (recoil) velocity of the merged hole with high accuracy.…”