Signatures of spin precession and nutation in isolated black-hole binaries

Abstract

The spin precession of binary black holes (BBHs) that originate from isolated high-mass binary stars is determined by the interplay of phenomena such as tides, winds, accretion, common-envelope evolution, natal kicks, and stellar core-envelope coupling. In previous work, we identified regions of the parameter space that may produce BBHs with large misalignments from natal kicks and high spin magnitudes from three mechanisms - tides, accretion, or inheritance via minimal core-envelope coupling. Here, we explore the spin precession of such BBHs using five parameters that describe the amplitude and frequency with which the orbital angular momentum precesses and nutates about the total angular momentum, modulating the gravitational-wave emission. Precession is generally possible for sufficiently strong natal kicks provided at least one of the black holes is spinning. Nutation is a consequence of spin-spin coupling and depends on the three spin-up mechanisms. Tidal synchronization can leave a distinct correlation between the aligned effective spin and the nutation frequency, but does not produce large nutations. When a black hole accretes $\gtrsim 20\%$ of its companion's envelope, the precession frequency and amplitude are large. A much smaller amount of accretion, e.g., $\approx 2\%$, is needed to provide a large precession frequency and amplitude when the accretor is a Wolf-Rayet (WR) star. The inheritance of high natal WR spins ($\gtrsim 5\%$ of their maximum breakup value) via minimal core-envelope coupling is the most promising mechanism for producing nutating BBHs, implying that a measurement of nutation from gravitational-wave observations may suggest isolated-binary origin with minimal core-envelope coupling.