The final spin from binary black holes in quasi-circular orbits

Abstract

We revisit the problem of predicting the spin magnitude and direction of the black hole resulting from the merger of two black holes with arbitrary masses and spins inspiralling in quasi-circular orbits. We do this by analyzing a catalog of 619 recent numerical-relativity simulations collected from the literature and spanning a large variety of initial conditions. By combining information from the post-Newtonian approximation, the extreme mass-ratio limit and perturbative calculations, we improve our previously proposed phenomenological formulae for the final remnant spin. In contrast with alternative suggestions in the literature, and in analogy with our previous expressions, the new formula is a simple algebraic function of the initial system parameters and is not restricted to binaries with spins aligned/anti-aligned with the orbital angular momentum, but can be employed for fully generic binaries. The accuracy of the new expression is significantly improved, especially for almost extremal progenitor spins and for small mass ratios, yielding a root-mean-square error $\sigma \approx 0.002$ for aligned/anti-aligned binaries and $\sigma \approx 0.006$ for generic binaries. Our new formula is suitable for cosmological applications and can be employed robustly in the analysis of the gravitational waveforms from advanced interferometric detectors.

arXiv comment6 pages, 3 figures. Matches ApJL accepted version. Coefficients ${\epsilon }_{\alpha }$, ${\epsilon }_{\beta }$ and ${\epsilon }_{\gamma }$ slightly changed to reflect dataset filtered of imprecise NR data; contains comparison with newly published NR catalog

References in corpus (53)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Effective one-body approach to general relativistic two-body dynamics
• Frequency-domain gravitational waves from non-precessing black-hole binaries. I. New numerical waveforms and anatomy of the signal
• Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
• Science with the space-based interferometer eLISA. I: Supermassive black hole binaries
• A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
• Accretion during the merger of supermassive black holes
• Cosmological black hole spin evolution by mergers and accretion
• Analysis of spin precession in binary black hole systems including quadrupole-monopole interaction
• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• The evolution of massive black holes and their spins in their galactic hosts
• Grand unification of AGN activity in the LambdaCDM cosmology
• The International Pulsar Timing Array
• Measuring the Spins of Accreting Black Holes
• Compact Binary Merger Rates: Comparison with LIGO/Virgo Upper Limits
• On the final spin from the coalescence of two black holes
• An improved effective-one-body Hamiltonian for spinning black-hole binaries
• Estimating the final spin of a binary black hole coalescence
• Predicting the direction of the final spin from the coalescence of two black holes
• The Transition from Inspiral to Plunge for a Compact Body in a Circular Equatorial Orbit Around a Massive, Spinning Black Hole
• Linking the spin evolution of massive black holes to galaxy kinematics
• The final mass and spin of black hole mergers
• Black hole evolution: III. Statistical properties of mass growth and spin evolution using large-scale hydrodynamical cosmological simulations
• Remnant mass, spin, and recoil from spin aligned black-hole binaries
• The evolution of active galactic nuclei and their spins
• The final spin from the coalescence of aligned-spin black-hole binaries
• Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
• On the mass radiated by coalescing black-hole binaries
• Multi-timescale analysis of phase transitions in precessing black-hole binaries
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• The Formation and Gravitational-Wave Detection of Massive Stellar Black-Hole Binaries
• Effective potentials and morphological transitions for binary black-hole spin precession
• Simulations of non-equal mass black hole binaries with spectral methods
• Improved methods for simulating nearly extremal binary black holes
• Spin Diagrams for Equal-Mass Black-Hole Binaries with Aligned Spins
• Numerical relativity reaching into post-Newtonian territory: a compact-object binary simulation spanning 350 gravitational-wave cycles
• Accurate gravitational waveforms for binary-black-hole mergers with nearly extremal spins
• Final spin and radiated energy in numerical simulations of binary black holes with equal masses and equal, aligned or anti-aligned spins
• Gravitational memory in binary black hole mergers
• High accuracy simulations of black hole binaries:spins anti-aligned with the orbital angular momentum
• Comparing gravitational waves from nonprecessing and precessing black hole binaries in the corotating frame
• Final spins from the merger of precessing binary black holes
• Final spin of a coalescing black-hole binary: an Effective-One-Body approach
• Simulations of black-hole binaries with unequal masses or non-precessing spins: accuracy, physical properties, and comparison with post-Newtonian results
• Modeling the remnant mass, spin, and recoil from unequal-mass, precessing black-hole binaries: The Intermediate Mass Ratio Regime
• Decoding mode-mixing in black-hole merger ringdown
• Can binary mergers produce maximally spinning black holes?
• Nearly extremal apparent horizons in simulations of merging black holes
• Black hole binary remnant mass and spin: A new phenomenological formula
• Intermediate-mass-ratio black hole binaries II: Modeling Trajectories and Gravitational Waveforms
• Mergers of black-hole binaries with aligned spins: Waveform characteristics
• Where angular momentum goes in a precessing black hole binary
• The importance of precession in modelling the direction of the final spin from a black-hole merger

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