论文标题
使用球形谐波相调查宇宙微波背景温度图中的非高斯性
Investigating non-Gaussianity in Cosmic Microwave Background Temperature Maps using Spherical Harmonic Phases
论文作者
论文摘要
在本文中，我们扩展了基于CMB球形谐波相（SHP）的先前研究，以检查CMB温度场与高斯随机场（GRF）一致的假设的有效性。零假设是，相应的CMB SHP是独立的，并且在间隔[0，2 $π$] \ citep {1986apj ... 304 ... 15b，2013年Rossmanith}的间隔中均匀分布。我们设计了一种新的独立于模型的方法，其中我们基于样本弧长，使用有序和非参数rao的统计量来全面测试SHP的均匀性和独立性。我们对球形谐波模式限制的量表进行了分析，$ 128 $ 128，以将自己限制在信号主导的区域中。为了找到SHP的不均匀或依赖的集合，我们计算数据的统计量和10000 Monte Carlo模拟了SHP的统一随机集，并使用0.05和0.001 $α$级别的水平来区分统计学意义和非常重要的检测。我们首先使用模拟的高斯非高斯CMB温度图以及观察到的非高斯100和143 GHz Planck通道图建立了方法的性能。我们发现，我们的方法在检测所有非高斯模拟中产生的相关性方面有效，准确，并观察到前景污染了100和143 GHz Planck通道温度图。我们将我们的方法应用于普朗克卫星任务的最终发布的CMB温度各向异性映射司令，Smica，NILC和Sevem以及WMAP 9年度发布的ILC地图。我们报告说，对应于某些$ M $ modes的SHP是不均匀的，其中一些$ \ ell $模式SHP和相邻模式对SHP与清洁的CMB地图相关联。 SHP中不均匀性或相关性的检测表明，前景中存在非高斯信号最小化的CMB图。
In this article, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis is that the corresponding CMB SHP are independent and identically distributed in terms of a uniform distribution in the interval [0, 2$π$] \citep{1986ApJ...304...15B,2013rossmanith}. We devise a new model-independent method where we use ordered and non-parametric Rao's statistic, based on sample arc-lengths to comprehensively test uniformity and independence of SHP. We performed our analysis on the scales limited by spherical harmonic modes $\le$ 128, to restrict ourselves to signal-dominated regions. To find the non-uniform or dependent sets of SHP, we calculate the statistic for the data and 10000 Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001 $α$ levels to distinguish between statistically significant and highly significant detections. We first establish the performance of our method using simulated Gaussian, non-Gaussian CMB temperature maps, along with observed non-Gaussian 100 and 143 GHz Planck channel maps. We find that our method performs efficiently and accurately in detecting phase correlations generated in all of the non-Gaussian simulations and observed foreground contaminated 100 and 143 GHz Planck channel temperature maps. We apply our method on the Planck satellite mission's final released CMB temperature anisotropy maps- COMMANDER, SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report that SHP corresponding to some of the $m$-modes is non-uniform, some of the $\ell$ mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. The detection of non-uniformity or correlation in the SHP indicates the presence of non-Gaussian signals in the foreground minimized CMB maps.
