Pacific Northwest National Laboratory, Richland, WA, 99354, USA.
Sci Rep. 2023 Mar 13;13(1):4165. doi: 10.1038/s41598-023-31083-z.
Smalls scale challenges suggest some missing pieces in our current understanding of dark matter. A cascade theory for dark matter is proposed to provide extra insights, similar to the cascade phenomenon in hydrodynamic turbulence. The kinetic energy is cascaded in dark matter from small to large scales involves a constant rate [Formula: see text] ([Formula: see text]). Confirmed by N-body simulations, the energy cascade leads to a two-thirds law for kinetic energy [Formula: see text] on scale r such that [Formula: see text]. Equivalently, a four-thirds law can be established for mean halo density [Formula: see text] enclosed in the scale radius [Formula: see text] such that [Formula: see text], which was 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 [Formula: see text] can be determined by [Formula: see text], where [Formula: see text] is the velocity dispersion. Second, the smallest scale [Formula: see text] is dependent on the nature of dark matter. For collisionless dark matter, [Formula: see text], where [Formula: see text] is the Planck constant. An uncertainty principle for momentum and acceleration fluctuations is also postulated. For self-interacting dark matter, [Formula: see text], where [Formula: see text] is the cross-section of interaction. On halo scale, the energy cascade leads to an asymptotic density slope [Formula: see text] for fully virialized haloes 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 haloes can have different limiting slopes. A modified Einasto density profile is proposed accordingly.
小规模的挑战表明，我们目前对暗物质的理解还存在一些缺失。为了提供额外的见解，提出了一种暗物质级联理论，类似于流体力学湍流中的级联现象。暗物质的动能从小尺度到大尺度的级联涉及到一个恒定的速率[公式：见正文]（[公式：见正文]）。通过 N 体模拟证实，能量级联导致了动能的三分之二定律[公式：见正文]，在尺度 r 上，使得[公式：见正文]。等效地，可以为在尺度半径[公式：见正文]内包含的平均晕密度[公式：见正文]建立四分之三定律，使得[公式：见正文]，这被星系旋转曲线所证实。通过在相关尺度上识别关键常数，可以获得暗物质的临界性质。首先，可以通过[公式：见正文]确定最大晕尺度[公式：见正文]，其中[公式：见正文]是速度弥散度。其次，最小尺度[公式：见正文]取决于暗物质的性质。对于无碰撞暗物质，[公式：见正文]，其中[公式：见正文]是普朗克常数。还假设了动量和加速度涨落的不确定性原理。对于自相互作用的暗物质，[公式：见正文]，其中[公式：见正文]是相互作用的横截面。在晕尺度上，能量级联导致完全处于完全束缚状态且径向流为零的晕的渐近密度斜率[公式：见正文]，这可能解释了几乎普遍的晕密度。基于连续性方程，分析表明晕密度与径向流和质量吸积密切相关，因此模拟晕可以具有不同的限制斜率。因此，提出了一个修正的 Einasto 密度分布。
