Presentation #206.03 in the session Galaxy Dynamics Posters.
Smalls scale challenges suggest some missing pieces in our current understandings of dark matter. A cascade theory for dark matter is proposed to provide extra insights, similar to the cascade in hydrodynamic turbulence. The kinetic energy is cascaded in dark matter from small to large scales with a constant rate εu~-4.6x10-7m2/s3. Confirmed by N-body simulations, the energy cascade leads to a two-thirds law for kinetic energy vr2 on scale r such that vr2 ~(εur)2/3. Equivalently, a four-thirds law can be established for mean halo density ρs enclosed in the scale radius rs such that ρs~ εu2/3G-1rs-4/3, which can be confirmed by galaxy rotation curves. Critical properties of dark matter might be obtained by identifying key constants on relevant scales. First, the largest halo scale rl can be determined by -u03/εu, where u0 is the velocity dispersion. Second, the smallest scale rη is dependent on the nature of dark matter. For collisionless dark matter, rη~(-Gh/εu)1/3, where h is the Planck constant. For self-interacting dark matter, rη~εu2 G-3(σ/m)3, where σ/m is the cross-section of interaction. On halo scale, the energy cascade leads to an asymptotic density slope γ=-4/3 for fully virialized haloes with a vanishing radial flow, which might explain the nearly universal halo density. Based on the continuity equation, halo density slope is analytically shown to be closely dependent on the radial flow and mass accretion, such that simulated haloes can have different limiting slopes. A modified Einasto density profile is proposed accordingly.