Gravitational Wave Astrophysics pp 137-145 | Cite as

# Rival Families: Waveforms from Resonant Black-Hole Binaries as Probes of Their Astrophysical Formation History

- 1.3k Downloads

## Abstract

Astrophysical binary black holes formed following the successive core collapses of sufficiently massive binary stars are likely to be resonant. Post-Newtonian theory predicts the existence of two one-parameter families of equilibrium solutions (“resonances”) in which the angular momentum and both spins share a common plane and precess at the same frequency. The two families are differentiated by either aligned or anti-aligned spin components in the orbital plane but both resonances have the capacity to attract generic non-resonant configurations. We develop astrophysical formation models showing that the fraction of binary black holes in each family is neatly related to the main stages of their formation history. Moreover, the gravitational-wave signals emitted from the two families are qualitatively different. Resonant binaries can be efficiently distinguished in events with signal-to-noise ratios ∼ 10, typical of those expected for the first detections with Advanced LIGO/Virgo. Spin-orbit resonances thus consist in powerful, viable, probes of astrophysical processes in stellar-mass black-hole binary formation and evolution.

## Keywords

Astrophysical Formation Stellar-mass BH Binaries Rival Families Spin-orbit Resonance Astrophysical Processes## Notes

### Acknowledgements

The work contained in the present contribution has been done in collaboration with Emanuele Berti, Michael Kesden, Richard O’Shaughnessy and Ulrich Sperhake. DG is supported by the UK Science and Technology Facility Council and the Isaac Newton Studentship of the University of Cambridge; partial support to attend the Sant Cugat Forum on Astrophysics is also acknowledged from Darwin College, University of Cambridge.

## References

- J. Abadie, B.P. Abbott, R. Abbott, M. Abernathy, T. Accadia, F. Acernese, C. Adams, R. Adhikari, P. Ajith, B. Allen et al., TOPICAL REVIEW: predictions for the rates of compact binary coalescences observable by ground-based gravitational-wave detectors. Class. Quantum Grav.
**27**(17), 173001 (2010)Google Scholar - P. Eggleton,
*Evolutionary Processes in Binary and Multiple Stars*Cambridge University Press, ISBN 0521855578 (July 2006)Google Scholar - D. Gerosa, M. Kesden, E. Berti, R. O’Shaughnessy, U. Sperhake, Resonant-plane locking and spin alignment in stellar-mass black-hole binaries: a diagnostic of compact-binary formation. Phys. Rev. D
**87**(10), 104028 (2013)Google Scholar - D. Gerosa, R. O’Shaughnessy, M. Kesden, E. Berti, U. Sperhake, Distinguishing black-hole spin-orbit resonances by their gravitational wave signature.
**89**, 124025 (2014)Google Scholar - V. Kalogera, Spin-orbit misalignment in close binaries with two compact objects. ApJ
**541**, 319–328 (2000)Google Scholar - M. Kesden, U. Sperhake, E. Berti, Final spins from the merger of precessing binary black holes. Phys. Rev. D
**81**(8), 084054 (2010)Google Scholar - L. Lindblom, B.J. Owen, D.A. Brown, Model waveform accuracy standards for gravitational wave data analysis. Phys. Rev. D
**78**(12), 124020 (2008)Google Scholar - P. C. Peters, J. Mathews, Gravitational radiation from point masses in a keplerian orbit. Phys. Rev.
**131**, 435–440 (1963)Google Scholar - J.D. Schnittman, Spin-orbit resonance and the evolution of compact binary systems. Phys. Rev. D
**70**(12), 124020 (2004)Google Scholar