无标度宇宙学中的相空间密度分布
Phase-Space Density Profiles in Scale-Free Cosmologies
摘要：
利用一组高分辨率的无标度Einstein-de Sitter宇宙学模拟研究了暗物质晕相空间密度分布$Q(r) = ρ(r)/σ^3(r)$的对数斜率。模拟的初始条件由形式为$P(k) \propto k^n$的幂律功率谱确定。我们使用径向、切向和全速度色散以及速度各向异性参数$β(r)$来计算Q（r）剖面。我们将Q（r）表示为单个幂律$Q(r) \propto r^α$，并在每个模拟和Q的每个定义中导出中值斜率$α$。我们的主要发现是：1.各种Q（r）分布遵循幂律以达到良好的近似。2.斜率取决于DM晕的浓度参数c，其中对于$c \gtrsim 10$，斜率随着浓度的增加而变陡，而对于$c \lesssim 10$，趋势是陡峭的，甚至是扭转的。3.作为$r\to R_{\mathrm{vir}}$的$β$的渐近值随着c的值而增加。4.根据Zait等人（2007），随着维里半径处$β$的渐近值增加，$α_{\mathrm{rad}}$变得更负。5.这引入了$Q(r)$斜率对功率谱斜率的弱依赖性。
英文摘要：
We use a set of high-resolution simulations of scale-free Einstein-de Sitter cosmologies to investigate the logarithmic slope of the phase-space density profile $Q(r) = ρ(r)/σ^3(r)$ of dark matter (DM) haloes. The initial conditions for the simulations are determined by a power law power spectrum of the form $P(k) \propto k^n$. We compute the Q(r) profiles using the radial, tangential and full velocity dispersion, and the velocity anisotropy parameter, $β(r)$. We express Q(r) as a single power-law $Q(r) \propto r^α$ and derive a median slope $α$ in each simulation and for each definition of Q. Our main findings are: 1. The various Q(r) profiles follow a power law to a good approximation. 2. The slopes depend on the concentration parameter c of the DM haloes, where for $c \gtrsim 10$ the slopes steepen with rising concentration and for $c \lesssim 10$ the trend flattens and even turns around. 3. The asymptotic value of $β$ as $r\to R_{\mathrm{vir}}$ increases with the value of c. 4. In accordance with Zait et al. 2007 $α_{\mathrm{rad}}$ becomes more negative as the asymptotic value of $β$ at the virial radius increases. 5. This introduces a weak dependence of the $Q(r)$ slopes on the slope of the power spectrum.
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