On the Cusp around Central Black Holes in Luminous Elliptical Galaxies

In this letter, we show that a massive black hole (MBH) which falls into the center of a galaxy in dynamical timescale leaves a weak cusp ($\rho \propto r^{-1/2}$) around it, which is in good agreement with the recent observations of luminous ellipticals by Hubble Space Telescope. Such event is a natural outcome of merging of two galaxies which have central MBHs. This is the only known mechanism to form weak cusps in luminous ellipticals. Therefore, the existence of the weak cusps indicates the central BHs of luminous ellipticals have fallen to the center from outside, most likely during a major merger event.