The mass ratio distribution of MBH binaries in the hierarchical model**Supported by the National Natural Science Foundation of China.

Abstract

We present different mass ratio distributions of massive black hole (MBH) binaries due to different mechanisms involved in binary evolution. A binary system of MBHs forms after the merger of two galaxies, which has three stages: the dynamical friction stage, the stellar scattering or circumbinary disk stage, and the gravitational radiation stage. The second stage was once believed to be the “final parsec problem” (FPP) as the binary stalled at this stage because of the depletion of stars. Now, the FPP has been shown to no longer be a problem. Here we get two different mass ratio distributions of MBH binaries under two mechanisms, stellar scattering and the circumbinary disk interaction. For the circumbinary disk mechanism, we assume that the binary shrinks by interaction with a circumbinary disk and the two black holes (BHs) have different accretion rates in the simulation. We apply this simple assumption to the hierarchical coevolution model of MBHs and dark matter halos, and we find that there will be more equal-mass MBH binaries in the final coalescence for the case where the circumbinary mechanism operates. This is mainly because the secondary BH in the circumbinary disk system accretes at a higher rate than the primary one.