http://arxiv.org/abs/2209.03313
Smalls scale challenges suggest some missing pieces in our current understandings of dark matter. A cascade theory for dark matter flow is proposed to provide extra insights, similar to the cascade in hydrodynamic turbulence. The energy cascade from small to large scales with a constant rate $\varepsilon_u$ ($\approx -4.6\times 10^{-7}m^2/s^3$) is a fundamental feature of dark matter flow. Energy cascade leads to a two-thirds law for kinetic energy $v_r^2$ on scale $r$ such that $v_r^2 \propto (\varepsilon_u r)^{2/3}$, as confirmed by N-body simulations. This is equivalent to a four-thirds law for mean halo density $\rho_s$ enclosed in the scale radius $r_s$ such that $\rho_s \propto \varepsilon_u^{2/3}G^{-1}r_s^{-4/3}$, as confirmed by data from galaxy rotation curves. By identifying relevant key constants, critical scales of dark matter might be obtained. The largest halo scale $r_l$ can be determined by $-u_0^3/\varepsilon_u$, where $u_0$ is the velocity dispersion. The smallest scale $r_{\eta}$ is dependent on the nature of dark matter. For collisionless dark matter, $r_{\eta} \propto (-{G\hbar/\varepsilon_{u}}) ^{1/3}\approx 10^{-13}m$, where $\hbar$ is the Planck constant. A uncertainty principle for momentum and acceleration fluctuations is also postulated. For self-interacting dark matter, $r_{\eta} \propto \varepsilon_{u}^2 G^{-3}(\sigma/m)^3$, where $\sigma/m$ is the cross-section. On halo scale, the energy cascade leads to an asymptotic slope $\gamma=-4/3$ for fully virialized halos with a vanishing radial flow, which might explain the nearly universal halo density. Based on the continuity equation, halo density is analytically shown to be closely dependent on the radial flow and mass accretion such that simulated halos can have different limiting slopes. A modified Einasto density profile is proposed accordingly.
Z. Xu
Thu, 8 Sep 22
18/77
Comments: 7 pages, 7 figures