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 .