Distribution of Baryonic Matter in Dark Matter Halos: Effect of Dynamical Friction

We studied the evolution of the two mass components system with NFW initial density distribution by direct integration of the Fokker-Planck equations. The low mass component is regarded the dark matter particles while the high mass component is assumed to be conglomerates of baryonic matter in order to depict the 'stars'. While the true mass ratio between these two types of particles should be extremely large, our adopted mass ratio is about 1000 beyond which the dynamical evolution and density distribution tend to converge. Since the dynamical evolution is dominated by the dynamical friction, the high mass component slowly moves toward the central part, and eventually undergoes the core collapse. The system reaches the core-collapse at about $7.1{\times}10^{-3}$ $t_{fh}$ in NFW models, where $t_{fh}$is the dynamical friction time at half-mass radius. The distribution of the high mass component is well fitted by the Sersic profiles or modified Hubble profile when the mass segregation is established. From these results, the surface brightness of elliptical galaxies may be explained by the high mass component experiencing dynamical friction by the dark matter particles. In order for the mass segregation to be effective within Hubble time, the mass of the luminous component should be greater than $10^5M_{\bigodot}$.