Detectability of the Gravitational Lensing Effect on the Two-Point Correlation Function of Hot Spots in Cosmic Microwave Background Maps
Detectability of the Gravitational Lensing Effect on the Two-Point Correlation Function of Hot Spots in Cosmic Microwave Background Maps
复制标题
宇宙微波背景图中热点两点相关函数的引力透镜效应的可检测性
DOI：
10.1086/318305
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
T. Futamase
中科院分区：
文献类型：
--
作者：
M. Takada;T. Futamase
我们定量研究了宇宙微波背景（CMB）图中局部最大值（热点）两点相关函数ξpk-pk（θ）的弱透镜效应。透镜效应取决于今天到红移zrec≈1100之间的预估质量波动。如果我们对原始温度波动场采用高斯假设，峰值统计量可以提供关于热点本征分布的附加信息：这些对具有一些特征分离角。弱透镜效应将观测到的CMB映射中的热点从本征分布重新分布，从而将非高斯特征印印到ξpk-pk（θ）上。特别是，由于固有的ξpk-pk（θ）在平坦宇宙的角尺度θ≈70′附近具有明显的凹陷特征，弱透镜在该尺度上产生了较大的平滑。因此，我们表明，透镜特征对于有效探测λ≈50 h-1 Mpc周围的大波长模式的质量波动具有优势。为了揭示微波各向异性探测器（MAP）和普朗克探测器（Planck Surveyor）的可探测性，我们进行了数值实验，包括光束平滑和探测器噪声的仪器效应。我们发现，我们的方法可以成功地提供有或没有宇宙常数的平坦宇宙中质量波动幅度和宇宙学参数的约束，前提是我们使用的地图具有普朗克预期的65%的天空覆盖率。
We present quantitative investigations of the weak-lensing effect on the two-point correlation functions of local maxima (hot spots), ξpk-pk(θ), in cosmic microwave background (CMB) maps. The lensing effect depends on the projected mass fluctuations between today and redshift zrec ≈ 1100. If we adopt the Gaussian assumption for the primordial temperature fluctuations field, the peak statistics can provide additional information about the intrinsic distribution of hot spots: that those pairs have some characteristic separation angles. The weak lensing then redistributes hot spots in the observed CMB maps from the intrinsic distribution and consequently imprints non-Gaussian signatures onto ξpk-pk(θ). In particular, since the intrinsic ξpk-pk(θ) has a pronounced depression feature around the angular scale of θ ≈ 70′ for a flat universe, the weak lensing induces a large smoothing at that scale. We show that the lensing signature therefore has an advantage for effectively probing mass fluctuations with large wavelength modes around λ ≈ 50 h-1 Mpc. To reveal the detectability, we performed numerical experiments with specifications of the Microwave Anisotropy Probe (MAP) and Planck Surveyor, including the instrumental effects of beam smoothing and detector noise. We find that our method can successfully provide constraints on the amplitude of the mass fluctuations and cosmological parameters in a flat universe with and without the cosmological constant, provided that we use maps with the 65% sky coverage expected from Planck.