Maximum black-hole spin from quasicircular binary mergers

Black holes of mass M must have a spin angular momentum S below the Kerr limit (χ ≡ S/M^2 ≤ 1), but whether astrophysical black holes can attain this limiting spin depends on their accretion history. Gas accretion from a thin disk limits the black-hole spin to χ_(gas) ≲ 0.9980 ± 0.0002, as electromagnetic radiation from this disk with retrograde angular momentum is preferentially absorbed by the black hole. Extrapolation of numerical-relativity simulations of equal-mass binary black-hole mergers to maximum initial spins suggests these mergers yield a maximum spin χ_(eq) ≲ 0.95. Here we show that for smaller mass ratios q ≡ m/M ≪ 1, the superradiant extraction of angular momentum from the larger black hole imposes a fundamental limit χ_(lim) ≲ 0.9979 ± 0.0001 on the final black-hole spin even in the test-particle limit (q→0) of binary black-hole mergers. The nearly equal values of χ_(gas) and χ_(lim) imply that measurement of supermassive black-hole spins cannot distinguish a black hole built by gas accretion from one assembled by the gravitational inspiral of a disk of compact stellar remnants. We also show how superradiant scattering alters the mass and spin predicted by models derived from extrapolating test-particle mergers to finite mass ratios.