  In this paper, we investigate the structures of galaxies which either have or
have had three BHs using $N$-body simulations, and compare them with those of
galaxies with binary BHs. We found that the cusp region of a galaxy which have
(or had) triple BHs is significantly larger and less dense than that of a
galaxy with binary BHs of the same mass. Moreover, the size of the cusp region
depends strongly on the evolution history of triple BHs, while in the case of
binary BHs, the size of the cusp is determined by the mass of the BHs. In
galaxies which have (or had) three BHs, there is a region with significant
radial velocity anisotropy, while such a region is not observed in galaxies
with binary BH. These differences come from the fact that with triple BHs the
energy deposit to the central region of the galaxy can be much larger due to
multiple binary-single BH scatterings. Our result suggests that we can
discriminate between galaxies which experienced triple BH interactions with
those which did not, through the observable signatures such as the cusp size
and velocity anisotropy.
