Orbital Evolution of an IMBH in the Galactic Nucleus with a Massive Central Black Hole

Abstract

Resent observations and theoretical interpretations suggest that intermediate-mass black holes (IMBHs; 100-105 M☉) are formed in the centers of young and compact star clusters born close to the center of their parent galaxy. Such a star cluster would sink toward the center of the galaxy, and at the same time stars are stripped out of the cluster by the tidal field of the parent galaxy. We investigated the orbital evolution of the IMBH, after its parent cluster is completely disrupted by the tidal field of the parent galaxy, by means of large-scale N-body simulations. We constructed a model of the central region of our galaxy, with a supermassive black hole (SMBH; ≥106 M☉) and Bahcall-Wolf stellar cusp, and placed an IMBH in a circular orbit of radius 0.086 pc. The IMBH sinks toward the SMBH through dynamical friction, but dynamical friction becomes ineffective when the IMBH reaches the radius inside which the initial stellar mass is comparable to the IMBH mass. This is because the IMBH kicks out the stars. This behavior is essentially the same as the loss-cone depletion observed in simulations of massive SMBH binaries. After the evolution through dynamical friction stalled, the eccentricity of the orbit of the IMBH goes up, resulting in the strong reduction of the merging timescale through gravitational wave radiation. Our result indicates that the IMBHs formed close to the galactic center can merge with the central SMBH in short time. The number of merging events detectable with DECIGO or BBO is estimated to be around 50 yr-1. The event rate for LISA would be similar or less, depending on the growth mode of IMBHs.