论文标题
在暗物质流和运动的整体常数中的能量，动量和自旋参数的演变
Evolution of energy, momentum, and spin parameter in dark matter flow and integral constants of motion
论文作者
论文摘要
在具有静态背景和固定阻尼的转换系统中重新制定了共同体系统中的N体运动方程。两种系统都严格制定了暗物质流中的能量和动量演化。转化系统中的能量演化具有与阻尼的谐波振荡器相同的简单形式。宇宙能量方程可在两个系统中很容易得出。对于整个N身体系统，1）结合两体崩溃模型（TBCM），随着时间的$ t $ $ t = $ k_p = \ varepsilon_ut $和$ p_y = -7 \ 7 \ varepsilon_ut/5 $，$ \ varepsilon_u $是$ \ varepsilon_u $是casscade comstants Casscade; 2）由于快速生长的光环的表面能，可以确定有效的重力潜在指数$ n_e = -10/7 \ ne-1 $（$ n_e = -1.38 $）。 3）径向动量$ g \ propto a^{3/2} $和角动量$ h \ propto a^{5/2} $，其中$ a $是比例因子。在光晕量表上，1）光环动力和势能可以通过二小无常数$α_s^*$和$β_S^*$建模。这两个常数都独立于时间和光环质量。 2）光晕径向和角动量$ \ propto a^{3/2} $，并且可以通过两个质量依赖的系数进行建模$τ_s^*$和$η_s^*$; 3）光环旋转参数由$α_s^*$和$η_s^*$确定，并以光晕质量减小，小和大晕孔的派生值为0.09和0.031。最后，径向和角动量与运动$ i_m $的积分常数密切相关，即速度相关性的积分或在长波长极限下的能量光谱的$ m $ th导数。在大规模上，角动量可以忽略不计，$ i_2 $ = 0反映了线性动量的保护，而$ i_4 $反映了径向动量$ g $的波动。在光晕量表上，$ i_4 $是由彼此相当的动量决定的。
N-body equations of motion in comoving system and expanding background are reformulated in a transformed system with static background and fixed damping. The energy and momentum evolution in dark matter flow are rigorously formulated for both systems. The energy evolution in transformed system has a simple form that is identical to the damped harmonic oscillator. The cosmic energy equation can be easily derived in both systems. For entire N-body system, 1) combined with the two-body collapse model (TBCM), kinetic and potential energy increase linearly with time $t$ such that $K_p=\varepsilon_ut$ and $P_y=-7\varepsilon_ut/5$, where $\varepsilon_u$ is a constant rate of energy cascade; 2) an effective gravitational potential exponent $n_e=-10/7\ne-1$ ($n_e=-1.38$ from simulation) can be identified due to surface energy of fast growing halos; 3) the radial momentum $G\propto a^{3/2}$ and angular momentum $H\propto a^{5/2}$, where $a$ is the scale factor. On halo scale, 1) halo kinetic and potential energy can be modelled by two dimensionless constants $α_s^*$ and $β_s^*$. Both constants are independent of time and halo mass; 2) both halo radial and angular momentum $\propto a^{3/2}$ and can be modeled by two mass-dependent coefficients $τ_s^*$ and $η_s^*$; 3) halo spin parameter is determined by $α_s^*$ and $η_s^*$ and decreases with halo mass with derived values of 0.09 and 0.031 for small and large halos. Finally, the radial and angular momentum are closely related to the integral constants of motion $I_m$, i.e. the integral of velocity correlation or the $m$th derivative of energy spectrum at long wavelength limit. On large scale, angular momentum is negligible, $I_2$=0 reflects the conservation of linear momentum, while $I_4$ reflects the fluctuation of radial momentum $G$. On halo scale, $I_4$ is determined by both momentum that are comparable with each other.
