Properties of the Cosmological Density Distribution Function
Properties of the Cosmological Density Distribution Function
复制标题
宇宙密度分布函数的性质
DOI：
10.1086/175542
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
L. Kofman
中科院分区：
文献类型：
--
作者：
F. Bernardeau;L. Kofman
研究了宇宙学连续密度场概率分布函数的性质。我们提出了进一步的发展，并比较动态激励的方法来获得PDF。其中之一是基于Zel'dovich近似（ZA）。我们将此方法推广到任意初始条件，不管它们是否是高斯的。另一种方法是基于高斯初始波动的微扰理论。我们在PDF中包含平滑效果。我们研究的PDF和时刻的形状之间的关系。结果发现，形式上有没有在ZA的时刻，但提出了一种方法来解决这个问题，积分的正则化的基础上。给出了ZA中矩的生成函数的封闭形式，包括平滑效应。我们建议的方法来建立PDF的整个系列的时刻，或出有限数量的时刻-埃奇沃思展开。最后一种方法为我们提供了一种通过测量峰值周围的PDF来评估偏度和峰度的替代方法。我们注意到小r.m.s $\sigma$的矩母函数与动力学模型中过密球涨落的非线性演化之间的一般联系。所有这些方法都已应用于一维的情况下，ZA是准确的，并得到简单的解析结果。3D的情况下，以同样的方式进行了分析，我们发现了一个相互协议的PDF由不同的方法在准线性政权。CDM数值模拟被用来验证所考虑的近似的准确性。我们解释成功的对数正态拟合的PDF从模拟在中等$\sigma$仅仅是运气，但不是作为一个普遍的形式的密度PDF一般。
The properties of the probability distribution function of the cosmological continuous density field are studied. We present further developments and compare dynamically motivated methods to derive the PDF. One of them is based on the Zel'dovich approximation (ZA). We extend this method for arbitrary initial conditions, regardless of whether they are Gaussian or not. The other approach is based on perturbation theory with Gaussian initial fluctuations. We include the smoothing effects in the PDFs. We examine the relationships between the shapes of the PDFs and the moments. It is found that formally there are no moments in the ZA, but a way to resolve this issue is proposed, based on the regularization of integrals. A closed form for the generating function of the moments in the ZA is also presented, including the smoothing effects. We suggest the methods to build PDFs out of the whole series of the moments, or out of a limited number of moments -- the Edgeworth expansion. The last approach gives us an alternative method to evaluate the skewness and kurtosis by measuring the PDF around its peak. We note a general connection between the generating function of moments for small r.m.s $\sigma$ and the non-linear evolution of the overdense spherical fluctuation in the dynamical models. All these approaches have been applied in 1D case where the ZA is exact, and simple analytical results are obtained. The 3D case is analyzed in the same manner and we found a mutual agreement in the PDFs derived by different methods in the the quasi-linear regime. Numerical CDM simulation was used to validate the accuracy of considered approximations. We explain the successful log-normal fit of the PDF from that simulation at moderate $\sigma$ as mere fortune, but not as a universal form of density PDF in general.