Dynamical friction of radio galaxies in galaxy clusters

The distribution of luminous radio galaxies in galaxy clusters has been observed to be concentrated in the inner region. We consider the role of dynamical friction of massive galaxies ($M\sim 10^{12.5}$ M$_{\odot}$), assuming them to be hosts of luminous radio galaxies, and show that beginning with a Navarro-Frenk-White density profile of a cluster of mass $M_{cl}\sim 10^{15}$ M$_{\odot}$ of concentration $c\sim 5$ and collapsing at $z\sim 1$, the density profile of radio galaxies evolve to a profile of concentration $c \sim 25$, as observed, in a time scale of $t\sim 3\hbox{--}5$ Gyr.