Interactions between multiple supermassive black holes in galactic nuclei: A solution to the final parsec problem

Taeho Ryu*, Rosalba Perna, Zoltán Haiman, Jeremiah P. Ostriker, Nicholas C. Stone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


Using few-body simulations, we investigate the evolution of supermassive black holes (SMBHs) in galaxies (M* = 1010-1012M at z = 0) at 0 < z < 4. Following galaxy merger trees from the Millennium simulation, we model BH mergers with two extreme binary decay scenarios for the 'hard binary' stage: a full or an empty loss cone. These two models should bracket the true evolution, and allow us to separately explore the role of dynamical friction and that of multibody BH interactions on BH mergers. Using the computed merger rates, we infer the stochastic gravitational wave background (GWB). Our dynamical approach is a first attempt to study the dynamical evolution of multiple SMBHs in the host galaxies undergoing mergers with various mass ratios (10-4 < q* < 1). Our main result demonstrates that SMBH binaries are able to merge in both scenarios. In the empty loss cone case, we find that BHs merge via multibody interactions, avoiding the 'final parsec' problem, and entering the pulsar timing arrays band with substantial orbital eccentricity. Our full loss cone treatment, albeit more approximate, suggests that the eccentricity becomes even higher when GWs become dominant, leading to rapid coalescences (binary lifetime ≲1Gyr). Despite the lower merger rates in the empty loss cone case, due to their higher mass ratios and lower redshifts, the GWB in the full/empty loss cone models are comparable (0.70 × 10-15 and 0.53 × 10-15 at a frequency of 1 yr-1, respectively). Finally, we compute the effects of high eccentricities on the GWB spectrum.

Original languageAmerican English
Pages (from-to)3410-3433
Number of pages24
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
StatePublished - Jan 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 The Authors.


  • Galaxy: evolution
  • Galaxy: kinematics and dynamics
  • Galaxy: nucleus
  • Gravitational waves
  • Quasars: general


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