论文标题
部分可观测时空混沌系统的无模型预测
Universal scaling laws and density slope for dark matter haloes
论文作者
论文摘要
小规模的挑战表明，我们对暗物质的理解中缺少一些作品。提出了一种针对暗物质的级联理论，可以提供额外的见解，类似于流体动力湍流中的级联现象。从小到大的暗物质中，动能涉及恒定速率$ \ VAREPSILON_U $（$ \ of -4.6 \ times 10^{ - 7} m^2/s^3 $）。通过N体模拟确认，Energy Cascade导致动力学能量$ V_R^2 $在规模上$ r $的三分之二法律，因此$ v_r^2 \ propto（\ varepsilon_u r）^{2/3} $。可以为平均光晕密度$ρ_s$建立四分之二的法律，以尺度半径$ r_s $包含在$ρ_S\ propto \ varepsilon_u^{2/3} g^{ - 1} r_s^{-1} r_s^{ - 4/3} $，由人星层旋转圈子确认。通过在相关尺度上识别关键常数可以获得暗物质的关键特性。最大的光环量表$ r_l $可以由$ -U_0^3/\ varepsilon_u $确定，其中$ u_0 $是速度分散。最小的比例$r_η$取决于暗物质的性质。对于无碰撞暗物质，$r_η\ propto（ - {g \ hbar/\ varepsilon_ {u}}） 10^{12} gev $，其中$ \ hbar $是普朗克常数。还假定了动量和加速波动的不确定性原理。对于自我交织的暗物质，$r_η\ propto \ varepsilon_ {u}^2 g^{ - 3}（σ/m）^3 $，其中$σ/m $是交互的横截面。在光晕尺度上，能量级联导致渐近密度$γ= -4/3 $，用于完全病毒的光环，径向流动消失，这可能解释了几乎通用的光环密度。基于连续性方程，分析表明光环密度密切取决于径向流量和质量积聚，因此模拟的光环可以具有不同的限制斜率。
Small scale challenges suggest some missing pieces in our 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 $\varepsilon_u$ ($\approx -4.6\times 10^{-7}m^2/s^3$). Confirmed by N-body simulations, energy cascade leads to a two-thirds law for kinetic energy $v_r^2$ on scale $r$ such that $v_r^2 \propto (\varepsilon_u r)^{2/3}$. A four-thirds law can be established for mean halo density $ρ_s$ enclosed in the scale radius $r_s$ such that $ρ_s \propto \varepsilon_u^{2/3}G^{-1}r_s^{-4/3}$, which was confirmed by galaxy rotation curves. Critical properties of dark matter might be obtained by identifying key constants on relevant scales. 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 $r_η$ is dependent on the nature of dark matter. For collisionless dark matter, $r_η \propto (-{G\hbar/\varepsilon_{u}}) ^{1/3}\approx 10^{-13}m$ is found along with the mass scale $m_X\propto (-\varepsilon_u\hbar^5G^{-4})^{1/9}\approx 10^{12}GeV$, where $\hbar$ is the Planck constant. An uncertainty principle for momentum and acceleration fluctuations is also postulated. For self-interacting dark matter, $r_η \propto \varepsilon_{u}^2 G^{-3}(σ/m)^3$, 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 is analytically shown to be closely dependent on the radial flow and mass accretion, such that simulated haloes can have different limiting slopes.
