Gravitational wave observations indicate the existence of merging black holes (BHs) with high spin (a ≳ 0.3), whose formation pathways are still an open question. A possible way to form those binaries is through the tidal spin-up of a Wolf–Rayet (WR) star by its BH companion. In this work, we investigate this scenario by directly calculating the tidal excitation of oscillation modes in WR star models, determining the tidal spin-up rate, and integrating the coupled spin–orbit evolution for WR–BH binaries. We find that, for short-period orbits and massive WR stars, the tidal interaction is mostly contributed by standing gravity modes, in contrast to Zahn's model of traveling waves, which is frequently assumed in the literature. The standing modes are less efficiently damped than traveling waves, meaning that prior estimates of tidal spin-up may be overestimated. We show that tidal synchronization is rarely reached in WR–BH binaries, and the resulting BH spins have a ≲ 0.4 for all but the shortest-period (Porb ≲ 0.5 day) binaries. Tidal spin-up in lower-mass systems is more efficient, providing an anticorrelation between the mass and spin of the BHs, which could be tested in future gravitational wave data. Nonlinear damping processes are poorly understood but may allow for more efficient tidal spin-up. We also discuss a new class of gravito-thermal modes that appear in our calculations.
Tidal Spin-up of Black Hole Progenitor Stars
Abstract
Copyright and License
© 2023. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Acknowledgement
We thank the anonymous referee for a constructive report that helped to improve this work. We also thank Hang Yu, Rich Townsend, and Katie Breivik for helpful discussions. This work is partially supported by NASA through grant 20-XRP20 2-0147. J.F. is thankful for support through an Innovator Grant from The Rose Hills Foundation, and the Sloan Foundation through grant FG-2018-10515.
Software References
MESA (Paxton et al. 2011, 2013, 2015, 2018, 2019), GYRE (Townsend & Teitler 2013; Townsend et al. 2018; Goldstein & Townsend 2020).
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Additional details
- ISSN
- 1538-4357
- 20-XRP20 2-0147
- National Aeronautics and Space Administration
- Rose Hills Foundation
- FG-2018-10515
- Alfred P. Sloan Foundation
- Caltech groups
- Walter Burke Institute for Theoretical Physics, Astronomy Department, TAPIR