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首页> 外文期刊>The Astrophysical journal >LOGNORMAL PROPERTY OF WEAK-LENSING FIELDS
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LOGNORMAL PROPERTY OF WEAK-LENSING FIELDS

机译：弱场的对数性质

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摘要

The statistical properties of weak-lensing fields are studied quantitatively using ray-tracing simulations. Motivated by an empirical lognormal model that excellently characterizes the probability distribution function of a three-dimensional mass distribution, we critically investigate the validity of the lognormal model in weak-lensing statistics. Assuming that the convergence field κ is approximately described by the lognormal distribution, we present analytic formulae of convergence for the one-point probability distribution function (PDF) and the Minkowski functionals. The validity of the lognormal models is checked in detail by comparing those predictions with ray-tracing simulations in various cold dark matter models. We find that the one-point lognormal PDF can accurately describe the non-Gaussian tails of convergence fields up to v ～ 10, where v is the level threshold given by v ≡ κ/<κ~2>~(1/2), although the systematic deviation from the lognormal prediction becomes manifest at higher source redshift and larger smoothing scales. The lognormal formulae for Minkowski functionals also fit the simulation results when the source redshift is low, z_s = 1. Accuracy of the lognormal fit remains good even at small angular scales 2′ approx< θ approx< 4′, where the perturbation formulae by the Edgeworth expansion break down. On the other hand, the lognormal model enables us to predict higher order moments, i.e., skewness S_(3,κ) and kurtosis S_(4,κ), and we thus discuss the consistency by comparing the predictions with the simulation results. Since these statistics are very sensitive to the high- and low-convergence tails, the lognormal prediction does not provide a successful quantitative fit. We therefore conclude that the empirical lognormal model of the convergence field is safely applicable as a useful cosmological tool, as long as we are concerned with the non-Gaussianity of v approx< 5 for low-z_s samples.
机译：使用光线跟踪模拟定量研究了弱透镜场的统计特性。受经验对数正态模型的启发，该模型很好地描述了三维质量分布的概率分布函数，我们批判性地研究了对数正态模型在弱透镜统计中的有效性。假设收敛域κ由对数正态分布近似描述，我们给出了单点概率分布函数（PDF）和Minkowski函数的收敛解析公式。通过将这些预测与各种冷暗物质模型中的光线追踪模拟进行比较，可以详细检查对数正态模型的有效性。我们发现，单点对数正态PDF可以准确地描述收敛域直到v〜10的非高斯尾部，其中v是由v≡κ/ <κ〜2>〜（1/2）给出的水平阈值，尽管对数正态预测的系统偏差在较高的源红移和较大的平滑比例下变得明显。当源红移低，z_s = 1时，Minkowski泛函的对数正态公式也拟合模拟结果。即使在较小的角度范围2'近似<θ近似<4'时，对数正态拟合的精度仍然良好。 Edgeworth扩张失败。另一方面，对数正态模型使我们能够预测高阶矩，即偏度S_（3，κ）和峰度S_（4，κ），因此我们通过将预测结果与仿真结果进行比较来讨论一致性。由于这些统计数据对高和低收敛尾部非常敏感，因此对数正态预测无法提供成功的定量拟合。因此，我们得出结论，只要我们关注低z_s样本的v约<5的非高斯性，收敛场的经验对数正态模型就可以安全地用作有用的宇宙学工具。

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