论文标题
暗物质光环质量功能和质量和能量级联的密度曲线
Dark matter halo mass functions and density profiles from mass and energy cascade
论文作者
论文摘要
在不依赖球形或椭圆形塌陷模型的情况下，我们根据暗物质流中的质量和能量级联理论得出了分析性得出Halo质量函数和Cuspy Halo密度（-4/3的内斜率）。分层光环结构的形成可导致带有位置依赖的等待时间$τ_g$的光环或粒子随机行走。从小到大尺度的逆质量级联反向级数导致巨大空间中的光环随机步行，$τ_g\ propto m_h^{--λ} $，其中$ m_h $是光晕质量，$λ$是卤代差异参数，预测值为2/3。在质量空间中，用于光晕随机步行的相应福克 - 普兰克解决方案可从小规模上具有幂律行为，并大规模衰减。可以通过考虑两个不同的$λ$的光环$ M_H^*$，即双$ $λ$ halo质量功能，可以进一步改善这一点。双$γ$密度曲线可以根据粒子随机步行在3D空间中的随机步行而得出，其依赖位置的等待时间$τ_g\ proptoφ（r）^{ - 1} \ propto r^{ - γ} $，其中$φ$是重力潜力，$ r $ $ r $是粒子距离halo中心的粒子。理论预测$γ= 2/3 $，导致cuspy密度曲线，内斜率为-4/3，与能量级联的预测缩放定律一致。压力机质量功能和Einasto密度曲线是所提出模型的特殊情况。由于质量和能量级联的比例无关，因此可以识别小规模的持久性，在小尺度上，不同光晕质量和红移的密度曲线会汇聚到$ -4/3 $缩放定律（$ρ_H\ propto r^{ - 4/3} $）上。理论预测用质量为$ \ propto m_h^{ - 1.9} $的光环数密度尺度，而光晕质量密度尺度则为$ \ propto m_h^{4/9} $。将结果与插图模拟进行了比较。
Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of -4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time $τ_g$. The inverse mass cascade from small to large scales leads to the halo random walk in mass space with $τ_g\propto m_h^{-λ}$, where $m_h$ is the halo mass and $λ$ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $λ$ for haloes below and above a critical mass scale $m_h^*$, i.e. a double-$λ$ halo mass function. A double-$γ$ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time $τ_g \propto Φ(r)^{-1} \propto r^{-γ}$, where $Φ$ is the gravitational potential and $r$ is the particle distance to halo center. Theory predicts $γ=2/3$ that leads to a cuspy density profile with an inner slope of -4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are special cases of proposed models. The small scale permanence can be identified due to the scale-independent rates of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $-4/3$ scaling law ($ρ_h \propto r^{-4/3}$) on small scales. Theory predicts halo number density scales with mass as $\propto m_h^{-1.9}$, while halo mass density scales as $\propto m_h^{4/9}$. Results were compared against the Illustris simulations.
