Scaling Relations in the Phase-Space Structure of Dark Matter Haloes

We present new scaling relations for the isotropic phase-space distribution functions (DFs) and energy distributions of simulated dark matter haloes. These relations are inspired by those for the singular isothermal sphere with density profile (r) r^-2, for which the DF satisfies f (E) r_^-2 (E) and the energy distribution satisfies dM/dE r_ (E), with r_ (E) being the radius where the gravitational potential equals energy E. For the simulated haloes, we find f (E) r_^-2. 08 (E) and dM/dE r_ (E) across broad energy ranges. In addition, the proportionality coefficients depend on the gravitational constant and the parameters of the best-fit Navarro-Frenk-White density profile. These scaling relations are satisfied by haloes over a wide mass range and provide an efficient method to approximate their DFs and energy distributions. Understanding the origin of these relations may shed more light on halo formation.