  We investigated the dynamical reaction of the central region of galaxies to a
falling massive black hole by N-body simulations. As the initial galaxy model,
we used an isothermal King model and placed a massive black hole at around the
half-mass radius of the galaxy. We found that the central core of the galaxy is
destroyed by the heating due to the black hole and that a very weak density
cusp ($\rho \propto r^{-\alpha}$, with $\alpha \sim 0.5$) is formed around the
black hole. This result is consistent with recent observations of large
elliptical galaxies with Hubble Space Telescope. The velocity of the stars
becomes tangentially anisotropic in the inner region, while in the outer region
the stars have radially anisotropic velocity dispersion. The radius of the weak
cusp region is larger for larger black hole mass. Our result naturally explains
the formation of the weak cusp found in the previous simulations of galaxy
merging, and implies that the weak cusp observed in large elliptical galaxies
may be formed by the heating process by sinking black holes during merging
events.
