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arXiv 1602.08503astro-ph.CO
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宇宙场对数正态模型的改进

Improving lognormal models for cosmological fields

Henrique S. Xavier, Filipe B. Abdalla, Benjamin Joachimi

摘要:

将大尺度结构观测量建模为对数正态随机场是宇宙学中的一种常见做法,这种方法在过去已经成功地分别应用于物质密度和弱透镜收敛场。我们认为,这种方法有根本的局限性,防止其用于联合建模这两个领域,因为对数正态分布的形状可以防止某些相关性是可以实现的。鉴于需要正在进行的和未来的大尺度结构调查快速联合模拟集群和弱透镜,我们提出了两种方法来克服这些限制。第一种方法使用两种算法之一来使场的功率谱略微失真,所述算法使绝对失真或分数失真最小化。第二种方法是通过沿视线积分对数正态密度来获得更精确的收敛边缘分布,为此我们提供了一个拟合函数。后一种方法还提供了一种直接从理论上确定收敛分布的偏度的方法,从而确定对数正态拟合的参数。我们提出的公共代码全天空对数正态天体场模拟工具包(FLASK),它可以使层析成像实现的任意数量的相关的对数正态或高斯随机场通过应用任何两个建议的解决方案的领域,并表明它可以创建联合模拟的聚类和透镜次百分之精度在相关的角尺度和红移范围。

英文摘要:

It is common practice in cosmology to model large-scale structure observables as lognormal random fields, and this approach has been successfully applied in the past to the matter density and weak lensing convergence fields separately. We argue that this approach has fundamental limitations which prevent its use for jointly modelling these two fields since the lognormal distribution's shape can prevent certain correlations to be attainable. Given the need of ongoing and future large-scale structure surveys for fast joint simulations of clustering and weak lensing, we propose two ways of overcoming these limitations. The first approach slightly distorts the power spectra of the fields using one of two algorithms that minimises either the absolute or the fractional distortions. The second one is by obtaining more accurate convergence marginal distributions, for which we provide a fitting function, by integrating the lognormal density along the line of sight. The latter approach also provides a way to determine directly from theory the skewness of the convergence distribution and, therefore, the parameters for a lognormal fit. We present the public code Full-sky Lognormal Astro-fields Simulation Kit (FLASK) which can make tomographic realisations on the sphere of an arbitrary number of correlated lognormal or Gaussian random fields by applying either of the two proposed solutions, and show that it can create joint simulations of clustering and lensing with sub-per-cent accuracy over relevant angular scales and redshift ranges.

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