Maximum black-hole spin from quasi-circular binary mergers

TL;DR

This paper establishes a fundamental upper limit on the spin of black holes resulting from binary mergers, considering superradiant effects, which is close to the maximum spin achievable through gas accretion.

Contribution

It demonstrates that superradiant scattering imposes a universal spin limit on black holes from binary mergers, refining previous estimates and linking spin measurements to black hole formation history.

Findings

Superradiant effects limit black hole spins to below 0.998.

Maximum spin from mergers is less than 0.95 for equal-mass cases.

The spin limit from superradiance (~0.998) is close to the gas accretion limit (~0.998).

Abstract

Black holes of mass M must have a spin angular momentum S below the Kerr limit chi = 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 chi_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 chi_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 chi_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 chi_gas and chi_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.