Connecting Stellar-Binary Evolution with Binary Black-Hole Spin Precession

Stellar-mass binary black-holes (BBHs) can form in one of two main ways: either the black holes (BHs) form first from single stars and then form a binary through dynamical interactions in a dense cluster, or the BHs form together from the kindred evolution of isolated binary stars. Distinguishing between these two formation channels with BBH sources observed via gravitational-wave (GW) detection is a new and promising field of research. Although the masses of the BBH are easier parameters to constrain, the spin orientations are more useful for determining the BBH’s origin: isotropically distributed spin directions are expected in the dynamical channel, whereas spin directions depend on the particular astrophysical evolution in the isolated channel. This has consequences for the resultant spin precession of the BBHs, since it implies that BBHs from the dynamical channel are expected to exhibit generic spin precession features, while those from the isolated channel are expected to have mostly aligned spins and hence suppressed spin precession. However, if BHs receive natal kicks when their stellar progenitors undergo core collapse, or if binary stars generally form with misalignments, then BBH spins may not be aligned in the isolated channel, and spin precession would be present. Motivated by this, we present a simplified model of binary stellar evolution to identify regions of the parameter space that produce BBHs with large spins misaligned with their orbital angular momentum. The masses and spins of these BBHs are determined by the complicated interplay of phenomena such as tides, winds, accretion, common-envelope evolution (CEE), supernova (SN) natal kicks, and stellar core-envelope spin coupling. In Scenario A [B] of our model, stable mass transfer (SMT) occurs after Roche-lobe overflow (RLOF) of the more [less] massive star, while CEE follows RLOF of the less [more] massive star. Each scenario is further divided into Pathways 1 and 2 depending on whether the core of the more massive star collapses before or after RLOF of the less massive star. We parameterize the boundary in the parameter space between these two pathways with the transition mass ratio, qtrans, which depends on the initial separation, masses, and metallicity. If the stellar cores are weakly coupled to their envelopes, highly spinning BBHs can be produced if natal spins greater than 10% of the breakup value are preserved during the Wolf-Rayet (WR) stage. BBHs can alternatively acquire high spins by tidal synchronization during the WR stage in Scenario A or accretion onto the initially more massive star in Scenario B. BBH spins can become highly misaligned if the SN kicks are comparable to the orbital velocity which is more easily achieved in Pathway A1 where the SN of the more massive star precedes CEE. It was previously unclear whether such highly spinning and misaligned binaries are possible from the isolated channel. Our model of isolated BBH formation motivates our new framework for modeling the spin precession of BBHs. Various studies over previous decades have uncovered a great diversity of spin precession dynamics. We summarize these possibilities into a “taxonomy” using a multitimescale analysis in which the entire dynamics on the precession timescale tpre ∼ r 5/2/M3/2 depends only on the evolution of the total spin magnitude S = |S1 + S2| (Kesden et al., 2015; Gerosa et al., 2015). Precession is “generic” when L nutates (raises and lowers like a draw bridge) at frequency ω, due to the oscillation of S, while L precesses in a cone about the total angular momentum J, which is fixed in direction, at frequency ΩL. In the special case of “regular” precession, nutation vanishes since S is constant implying that ΩL and the angle θL subtending L and J are both constant. We present five parameters that describe the motion of the direction of L as functions of S: the precession amplitude hθLi, the precession frequency hΩLi, the nutation amplitude ∆θL, the nutation frequency ω, and the precessionfrequency variation ∆ΩL. Using BBHs with isotropically distributed spin directions, we explore the behavior of these parameters and we stress that nutation is a generic feature of BBH spin precession. High spin magnitudes allow for the largest nutations at moderate mass ratios (q ≈ 0.6). Maximally nutating systems are correlated with binaries that satisfy the condition J k L sometime during inspiral, one such binary is the “up-down” configuration. In the extreme limits of q, nutation vanishes due to the constancy of S and precession is “regular”. Lastly, we outline future avenues of research. (1) We use our new spin precession framework to study the precession and nutation of the BBHs generated from our model of isolated stellar-binary evolution. BBHs with significant misalignments from natal kicks precess unless alignment mechanisms, such as tides in Scenario A or accretion in Scenario B, realign the WR or BH spins. Although aspects of stellar-binary evolution conspire against the emergence of highly nutating systems, e.g., strong core-envelope coupling produces small BH spins implying BBHs might exhibit “regular” precession, we find that such systems are still plausible. BBHs that evolve from Scenario A can highly nutate if high BH spins are inherited from weak core-envelope coupling of the stellar progenitors, and if the initial separation is sufficiently large to avoid tidal alignment - but not too large in Pathway A1 otherwise too many binaries can be unbound by the first natal kick. High BH spin from tidal synchronization of the WR progenitor is only effective on the initially less massive star in Pathway A1 but is effective on both stars in Pathway A2, while tidal alignment suppresses the precession amplitude hθLi. In Scenario B, the initially more massive star generally evolves into a highly spinning BH, implying that ∆θL can be significant if the BH that forms from the initially less massive star inherits a high spin from weak core-envelope coupling. ∆θL is suppressed in Pathway B1 if accretion is Eddington-limited, or in Pathway B2 if a substantial amount of mass loss accompanies BH formation of the initially more massive star, due to the Kerr spin limit, resulting in a high BBH mass ratio. Stellar binaries with weak core-envelope coupling in Pathway B2 generally allow for systems with significant ∆θL. We compare these behaviors to those of BBHs with isotropic spin misalignments, as would be expected from the dynamical formation channel. (2) We compare the observational signatures of our five parameters to the signatures of other spin precession parameters in the literature, such as the effective precession parameter, χp, and the leading-order post-Newtonian spin-dependent correction to the GW phase, β, to try to elucidate the various nuances that make a genuine detection of nutation difficult.