[Paper Review] Signatures of spin precession and nutation in isolated black-hole binaries

Nathan Steinle, Michael Kesden|arXiv (Cornell University)|Jun 1, 2022

Pulsars and Gravitational Waves ResearchPhysics and Astronomy59 references9 citations

TL;DR

This paper quantifies spin precession and nutation in isolated binary black holes (BBHs) using five geometric precession parameters, linking them to astrophysical formation pathways. It finds that nutation—driven by spin-spin coupling—is most prominent when black holes inherit high spins from Wolf-Rayet stars via minimal core-envelope coupling, making nutation a potential 'smoking gun' for isolated binary formation with such coupling.

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.

Motivation & Objective

• To identify astrophysical pathways in isolated binary evolution that produce significant spin precession and nutation in binary black holes.
• To quantify how precession and nutation amplitudes and frequencies depend on initial binary parameters such as natal kick strength, accretion fraction, and initial spin.
• To determine whether gravitational-wave observations of nutation can distinguish isolated binary formation from dynamical origins.
• To establish that nutation is a robust signature of minimal core-envelope coupling in isolated BBHs, offering a new diagnostic for formation channels.

Proposed method

• Uses five geometric precession parameters—precession amplitude ⟨θL⟩, precession frequency ⟨ΩL⟩, nutation amplitude ∆θL, nutation frequency ω, and precession-frequency variation ∆ΩL—derived from the effective potential formalism.
• Applies these parameters to model BBHs formed via four evolutionary pathways: stable mass transfer (SMT), common-envelope evolution (CEE), and supernova natal kicks, with varying initial conditions.
• Models spin evolution using three mechanisms: tidal synchronization, accretion of up to 20% of companion’s envelope, and inheritance of Wolf-Rayet star spins (fraction fB of breakup limit).
• Simulates isolated binary evolution with ZAMS masses, separations, metallicity, and natal kick velocity dispersion σ, tracking spin and orbital angular momentum evolution.
• Analyzes the dependence of precession and nutation parameters on fB, fa (accreted fraction), σ, and aZAMS (initial separation), using post-Newtonian approximations.
• Compares outcomes across pathways to identify which mechanisms produce large precession and nutation, especially under minimal core-envelope coupling.

Experimental results

Research questions

• RQ1 Which isolated binary formation pathways produce significant spin precession and nutation in binary black holes?
• RQ2 How do natal kick strength and accretion fraction influence precession and nutation amplitudes and frequencies?
• RQ3 Can nutation serve as a unique diagnostic for minimal core-envelope coupling in isolated BBHs?
• RQ4 What is the role of tidal synchronization versus accretion in producing precessing systems?
• RQ5 How do the five precession parameters correlate with astrophysical formation mechanisms like WR spin inheritance or accretion?

Key findings

• Nutation is generally possible only when stellar angular momentum transport is inefficient, making it a strong indicator of minimal core-envelope coupling.
• Accretion of ≳20% of the companion’s envelope leads to large precession frequency and amplitude, while ≈2% accretion from a Wolf-Rayet star can produce large precession frequency and amplitude.
• Tidal synchronization produces a distinct correlation between effective spin and nutation frequency but does not generate large nutations.
• Inheritance of high natal WR spins (≳5% of breakup value) via minimal core-envelope coupling is the most promising mechanism for producing detectable nutating BBHs.
• Precession is possible for sufficiently strong natal kicks provided at least one black hole is spinning, with precession amplitude and frequency scaling with kick strength and spin magnitude.
• Nutation amplitude and frequency are strongly correlated with the time-varying total spin magnitude, confirming that nutation arises from spin-spin coupling when S is not conserved.