Lognormal Property of Weak-Lensing Fields
Lognormal Property of Weak-Lensing Fields
复制标题
弱透镜场的对数正态性质
DOI：
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发表时间：
2002
期刊：
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通讯作者：
T. Futamase
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作者：
A. Taruya;M. Takada;T. Hamana;I. Kayo;T. Futamase
利用光线追迹模拟方法定量研究了弱透镜场的统计特性。激励的经验对数正态模型，很好地表征了三维质量分布的概率分布函数，我们严格调查对数正态模型在弱透镜统计的有效性。假设收敛场κ近似为对数正态分布，给出了一点概率分布函数（PDF）和Minkowski泛函的收敛解析公式.对数正态模型的有效性进行了详细检查，通过比较这些预测与光线跟踪模拟在各种冷暗物质模型。我们发现，一点对数正态概率密度函数可以准确地描述直到ν ~ 10的收敛场的非高斯尾，其中ν是由ν κ κ/ν κ2 <$1/2给出的水平阈值，尽管在更高的源红移和更大的平滑尺度下，与对数正态预测的系统偏差变得明显。当源红移较低时（zs = 1），Minkowski泛函的对数正态公式也符合模拟结果。对数正态拟合的精度即使在小角标度2′ <$θ <$4 ′下也保持良好，其中Edgeworth展开的微扰公式失效。另一方面，对数正态模型使我们能够预测高阶矩，即，偏度S3，κ和峰度S4，κ，并通过与模拟结果的比较，讨论了预测结果的一致性。由于这些统计量对高收敛尾和低收敛尾非常敏感，对数正态预测不能提供成功的定量拟合。因此，我们得出结论，只要我们关注低zs样本的非高斯性，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。
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 ν ~ 10, where ν is the level threshold given by ν ≡ κ/⟨κ2⟩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, zs = 1. Accuracy of the lognormal fit remains good even at small angular scales 2′ ≲ θ ≲ 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 S3,κ and kurtosis S4,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 ν ≲ 5 for low-zs samples.