  Resent observations and theoretical interpretations suggest that IMBHs
(intermediate-mass black hole) 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 an SMBH (supermassive black hole) and Bahcall-Wolf stellar
cusp, and placed an IMBH in a circular orbit of radius 0.086pc. The IMBH sinks
toward the SMBH through dynamical friction, but dynamical friction becomes
ineffective when the IMBH reached 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 in 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 is estimated to be around 50
per year. Event rate for LISA would be similar or less, depending on the growth
mode of IMBHs.
