The connection between the cusp-to-core transformation and observational universalities of DM halos

Observations have revealed interesting universal properties of dark matter (DM) halos especially around low-mass galaxies. Strigari et al. (2008) showed that DM halos have common enclosed masses within 300pc (Strigari relation). Kormendy & Freeman (2004) reported DM halos having almost identical central surface densities (the $\mu_{\rm 0D}$ relation). In addition, there exists a core-cusp problem, a discrepancy of the central density distribution between simulated halos and observations. We investigate whether a scenario where cuspy halos transform into cores by some dynamical processes can also explain their universal structural properties. It is shown that a cusp-to-core transformation model naturally reproduces the $\mu_{\rm 0D}$ relation and that Strigari relation follows from the $\mu_{\rm 0D}$ relation for dwarf galaxies. We also show that the central densities of cored dark halos provide valuable information about their formation redshifts.