Recovering the non-linear density field from the galaxy distribution with a Poisson-lognormal filter
Recovering the non-linear density field from the galaxy distribution with a Poisson-lognormal filter
复制标题
使用泊松对数正态滤波器从星系分布中恢复非线性密度场
DOI：
10.1111/j.1365-2966.2009.16163.x
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发表时间：
2009
影响因子：
4.8
通讯作者：
R. Metcalf
中科院分区：
文献类型：
--
作者：
F. Kitaura;J. Jasche;R. Metcalf
我们提出了给定任意非线性星系偏差的对数正态滤波器的通用表达式。我们将此滤波器推导为最大后验解，假设具有给定平均场的物质场呈对数正态先验分布，并通过泊松过程对观测到的星系分布进行建模。我们使用非常高效的牛顿-克雷洛夫反演方案对该滤波器进行了三维实现。此外，我们还使用假设单位星系偏置关系的暗物质 N 体模拟对其进行了测试，并将结果与之前的密度场估计器（例如逆加权方案和维纳滤波）进行了比较。我们的结果表明，即使在 δ ~ 1000 以上，密度也与潜在的暗物质场有很好的一致性，这超出了对数正态预计有效的范围一个数量级。原因是，对于我们的过滤器，对数正态假设作为先验分布函数输入，但最大后验解也以数据为条件。我们发现对数正态滤波器在更高的相关系数和与底层物质场的更小的欧几里德距离方面优于以前的滤波方案。我们还展示了它如何能够将单位偏差关系的物质超密度场分布的正尾恢复到约 ≳2 Mpc h ―1 的尺度。
We present a general expression for a lognormal filter given an arbitrary non-linear galaxy bias. We derive this filter as the maximum a posteriori solution assuming a lognormal prior distribution for the matter field with a given mean field and modelling the observed galaxy distribution by a Poissonian process. We have performed a three-dimensional implementation of this filter with a very efficient Newton-Krylov inversion scheme. Furthermore, we have tested it with a dark matter N-body simulation assuming a unit galaxy bias relation and compared the results with previous density field estimators like the inverse weighting scheme and Wiener filtering. Our results show good agreement with the underlying dark matter field for overdensities even above δ ∼ 1000 which exceeds by one order of magnitude the regime in which the lognormal is expected to be valid. The reason is that for our filter the lognormal assumption enters as a prior distribution function, but the maximum a posteriori solution is also conditioned on the data. We find that the lognormal filter is superior to the previous filtering schemes in terms of higher correlation coefficients and smaller Euclidean distances to the underlying matter field. We also show how it is able to recover the positive tail of the matter overdensity field distribution for a unit bias relation down to scales of about ≳2 Mpc h ―1 .