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Massive Binary Black Holes in Galactic Nuclei and Their Path to Coalescence


Massive binary black holes (105 M–109 M) form at the centre of galaxies that experience a merger episode. They are expected to coalesce into a larger black hole, following the emission of gravitational waves. Coalescing massive binary black holes are among the loudest sources of gravitational waves in the Universe, and the detection of these events is at the frontier of contemporary astrophysics. Understanding the black hole binary formation path and dynamics in galaxy’s mergers is therefore mandatory. A key question poses: during a merger, will the black holes descend over time on closer orbits, form a Keplerian binary and coalesce shortly after? Here we review progress discussing the fate of black holes in different environments: from major mergers of collisionless galaxies to major and minor mergers of gas-rich disc galaxies, from smooth and clumpy circum-nuclear discs to circum-binary discs present on the smallest scales inside galactic nuclei.

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  1. 1.

    See Gerosa and Sesana (2014) for missing black holes in the brightest cluster galaxies following black hole coalescence and ejection by gravitational recoil.

  2. 2.

    This view, however, has been criticised by Vasiliev et al. (2013) who compared the evolution of binary black holes in spherical, axisymmetric and triaxial equilibrium galaxy models. They find that the rate of binary hardening exhibits a significant N-dependence in all the models, in the investigated range of 105N≤106. Their hardening rates are substantially lower than those expected if the binary loss cone remained full, with rates between the spherical and non-spherical models differing in less than a factor of two. This finding seems to cast doubt on claims that triaxiality or axisymmetry alone are capable of solving the final-parsec problem. Vasiliev and co-authors invite caution in extrapolating results to galaxies with high values of N until all discrepancies or intrinsic differences between equilibrium models and merged galaxy models are not understood deeply.

  3. 3.

    This is a possibility that may occur in the case of a minor merger where the incoming black hole in the satellite galaxy enters the main galaxy from a co-planar counter-rotating orbit.

  4. 4.

    In a uniform, isotropic gaseous background, gas-dynamical friction vanishes when the velocity of the perturber falls below the sound speed (Ostriker 1999). Dynamical friction is a non-local process and in a disc there is a residual velocity difference between the black hole and the more distant rotating fluid elements. One can view the migration process described in the text again as a manifestation of the large scale gravitational perturbation excited by the black hole mass, but this time the drag is inside a rotating inhomogeneous background. The net torque results from the sum of positive (inside the black hole orbit) and negative (outside) contributions as the perturbation is highly non axisymmetric due to differential rotation.

  5. 5.

    The coefficient ζ can be inferred from dedicated numerical experiments. In the case explored, the coefficient ζ′∼0.04, to match the sinking time with a simulation. A systematic analysis is necessary to estimate ζ′ in a Mestel disc (paper in preparation). Furthermore, the scaling of \(\tau^{I}_{\mathrm{mig}, \mathrm{Mestel}}\) with the aspect ratio h/a can not be derived from this elementary argument, as discussed in Armitage (2013).

  6. 6.

    As an example, in recent studies of planet migration by Duffell et al. (2014) it has been shown, using highly accurate numerical calculations, that the actual migration rate is dependent on disc and planet parameters, and can be significantly larger or smaller than the viscous drift rate \(\tau^{-1}_{\nu}\). In the case of disc-dominated migration the rate saturates to a constant value which is in excess of the viscous rate while in the opposite regime of a low-mass disc, the migration rate decreases linearly with disc mass.


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I would like to thank my collaborators Simone Callegari, Massimo Dotti, Davide Fiacconi, Lucio Mayer, Constanze Roedig, Alberto Sesana and Marta Volonteri for many useful and illuminating discussions over the years. I would like also to thank the International Space Science Institute for kind hospitality.

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Correspondence to Monica Colpi.

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Colpi, M. Massive Binary Black Holes in Galactic Nuclei and Their Path to Coalescence. Space Sci Rev 183, 189–221 (2014). https://doi.org/10.1007/s11214-014-0067-1

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  • Black hole physics
  • Dynamics
  • Galaxy mergers
  • Black hole binaries