Mass and energy cascade in collisionless dark matter flow and relevant constraints on the dark matter particle mass (2109.09985v3)

Abstract: The cascade phenomenon is fundamental to turbulence, a typical non-equilibrium system. In turbulence, energy is cascaded from large to small scales, where it is dissipated by fluid viscosity. Using Illustris and Virgo simulations, this paper presents the cascade in non-equilibrium collisionless dark matter flow. The cosmic energy of dark matter decreases with time, as if "dissipated" due to the expanding background. This is facilitated by the energy cascade from large to small haloes via halo merging and from large to small scales in individual haloes via particle migration in fluctuating non-uniform potential, such that the cosmic energy is "dissipated" on small scales. Inverse mass cascade across haloes of different sizes leads to a random walk of haloes in halo mass space. The halo mass function is naturally given by the Fokker-Planck equation for halo random walk. Similarly, the random walk of particles in haloes leads to the distribution of particles. The halo density profile can also be analytically derived. Universal scaling laws were identified for the halo density, mass, and velocity dispersion. The different inner density slopes of simulated haloes can be explained by the nonzero net mass and energy flux in individual haloes. The mass and energy cascade establishes a statistically steady state to continuously release energy and maximize entropy. The key feature of this state is scale-independent rates of cascade such that the statistical structures of the haloes are self-similar and scale-free, and there is no net accumulation of mass and energy on any intermediate scales. Since the waiting time and jumping length for particle random walk depends on the particle mass $m_p$, new mass constraints can be identified as $m_p\ge 10^{-15}$kg or $10^{12}$GeV. This constraint excludes standard WIMPs and suggests a heavy dark matter scenario (superheavy right-handed neutrinos, etc.).