A New Mechanism for Massive Binary Black-Hole Evolution

Abstract

Abstract It is still unknown how a binary black hole (BBH) evolves after its semi-major axis has reached the sub-parsec scale, where dynamical friction with neighboring stars is no longer effective (the so-called final-parsec problem). In this paper, we propose a new mechanism by which a massive BBH can naturally coalesce within a Hubble time. We consider the evolution of a BBH with a triple disk composed of an accretion disk around each black hole and one circumbinary disk surrounding them. While the circumbinary disk removes the orbital angular momentum of the BBH via a binary-disk resonant interaction, the mass transfer from the circumbinary disk to each black hole adds some fraction of its angular momentum to the orbital angular momentum of the BBH. We find that there is a critical value of the mass-transfer rate where extraction of the orbital angular momentum from the BBH is balanced with the addition of orbital angular momentum to the BBH. The semi-major axis of the BBH decays with time, whereas the orbital eccentricity of the BBH grows with time, if the mass-transfer rate is smaller than the critical one, and vice versa. Its evolutionary timescale is characterized by the product of the viscous timescale of the circumbinary disk and the ratio of the total black-hole mass to the mass of the circumbinary disk. Most massive BBHs are able to merge within a Hubble time by the proposed mechanism, which helps to solve the final parsec problem.