arXiv 1502.020522015-02astro-ph.CO

非线性随机增长率与红移空间畸变

Nonlinear stochastic growth rates and redshift space distortions

Elise Jennings, David Jennings

备注：: 14 pages, 9 figures. Accepted for publication in MNRAS
DOI：: 10.1093/mnras/stv535

摘要：

线性增长率通常通过线性区域中速度发散和物质过密度之间的简单确定性关系来定义。我们介绍了一种形式主义，扩展到一个非线性，随机关系之间的$θ= \nabla \cdot v({\bf x},t)/aH$和$δ$。这提供了一种新的现象学方法，检查的条件平均值$< θ|δ>$，连同$θ$在这个平均值的波动。我们使用N体模拟测量这些随机分量，发现它们是非负的，并且随着从$k<0.2 h $ Mpc $^{-1}$的$\sim$ 10%到$z = 0$的$k\sim0.45h$ Mpc $^{-1}$的25%的尺度减小而增加。与$z=0$和$1$的暗物质相比，晕$M \le 5 \times 10^{12}M_\odot h^{-1}$的随机关系和非线性更明显。非线性增长效应表现为平均$< θ|δ>$偏离线性理论预测值$-f_{\tiny \rm LT}δ$的旋转，其中$f_{\tiny \rm LT}$为线性增长率。这种旋转随着波数$k$的增加而增加，并且我们证明了它可以很好地用二阶拉格朗日微扰理论（2LPT）描述$k < 0.1 h$ Mpc $^{-1}$。$θ$ - $δ$关系中的随机性并不简单地用2LPT来描述，我们从红移空间中的两点统计量讨论了它对$f_{\tiny \rm LT}$测量的影响.考虑到$δ$和$θ$之间的关系是随机和非线性的，这将对使用假定线性、确定性表达的模型提取的$f_{\tiny \rm LT}$的解释和精度产生影响。

英文摘要：

The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a nonlinear, stochastic relation between $θ= \nabla \cdot v({\bf x},t)/aH$ and $δ$. This provides a new phenomenological approach that examines the conditional mean $< θ|δ>$, together with the fluctuations of $θ$ around this mean. We measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from $\sim$10% at $k<0.2 h $Mpc$^{-1}$ to 25% at $k\sim0.45h$Mpc$^{-1}$ at $z = 0$. Both the stochastic relation and nonlinearity are more pronounced for halos, $M \le 5 \times 10^{12}M_\odot h^{-1}$, compared to the dark matter at $z=0$ and $1$. Nonlinear growth effects manifest themselves as a rotation of the mean $< θ|δ>$ away from the linear theory prediction $-f_{\tiny \rm LT}δ$, where $f_{\tiny \rm LT}$ is the linear growth rate. This rotation increases with wavenumber, $k$, and we show that it can be well-described by second order Lagrangian perturbation theory (2LPT) for $k < 0.1 h$Mpc$^{-1}$. The stochasticity in the $θ$ -- $δ$ relation is not so simply described by 2LPT, and we discuss its impact on measurements of $f_{\tiny \rm LT}$ from two point statistics in redshift space. Given that the relationship between $δ$ and $θ$ is stochastic and nonlinear, this will have implications for the interpretation and precision of $f_{\tiny \rm LT}$ extracted using models which assume a linear, deterministic expression.

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