Analysis method for 3D power spectrum of projected tensor fields with fast estimator and window convolution modeling: An application to intrinsic alignments
Analysis method for 3D power spectrum of projected tensor fields with fast estimator and window convolution modeling: An application to intrinsic alignments
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DOI：
10.1103/physrevd.105.123501
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发表时间：
2022-02
影响因子：
5
通讯作者：
Toshiki Kurita;M. Takada
中科院分区：
文献类型：
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作者：
Toshiki Kurita;M. Takada
大尺度结构的二阶张量场，例如从星系形状推断的张量场，打开了一个直接访问2标量、2矢量和2张量模式的窗口，其中标量场可以独立于由星系分布跟踪的标准密度场来测量。本文给出了三维张量场功率谱多极矩的一个估计式，它考虑了垂直于视线方向的平面上的投影。为此，我们发现，在局部平面平行(LPP)近似下，可以通过使用相关的勒让德多项式来获得功率谱多极子的方便的表示形式，该形式允许快速傅立叶变换估计。该公式还允许我们获得汉克尔变换，以连接傅立叶空间和位形空间中的两点统计，这是推导功率谱的理论模板所必需的，包括测量窗口的卷积。为了验证我们的估计器，我们使用了预测潮汐场的模拟数据，假设一个调查窗口模仿了BOSS式的调查足迹。我们表明，LPP估计器很好地恢复了从全局平面平行近似中推导出的多极矩。我们发现，与密度功率谱相比，测量窗对输入功率谱的投影张量功率谱的多极矩有更显著的影响。然而，我们计算包含测量窗口效应的理论模板的方法成功地再现了从模拟中测量的窗口卷积多极矩。本文提出的分析方法为在目前和未来的研究中使用大尺度结构的三维张量型示踪剂进行宇宙学分析铺平了道路。
Rank-2 tensor fields of large-scale structure, e.g. a tensor field inferred from shapes of galaxies, open up a window to directly access 2-scalar, 2-vector and 2-tensor modes, where the scalar fields can be measured independently from the standard density field that is traced by distribution of galaxies. Here we develop an estimator of the multipole moments of power spectra for the three-dimensional tensor field, taking into account the projection onto plane perpendicular to the line-of-sight direction. To do this, we find that a convenient representation of the power spectrum multipoles can be obtained by the use of the associated Legendre polynomials in the form which allows for the fast Fourier transform estimations under the local plane-parallel (LPP) approximation. The formulation also allows us to obtain the Hankel transforms to connect the two-point statistics in Fourier and configuration space, which are needed to derive theoretical templates of the power spectrum including convolution of a survey window. To validate our estimators, we use the simulation data of the projected tidal field assuming a survey window that mimics the BOSS-like survey footprint. We show that the LPP estimators fairly well recover the multipole moments that are inferred from the global plane-parallel approximation. We find that the survey window causes a more significant change in the multipole moments of projected tensor power spectrum at $k\lesssim 0.1\,h{\rm Mpc}^{-1}$ from the input power spectrum, than in the density power spectrum. Nevertheless, our method to compute the theory template including the survey window effects successfully reproduces the window-convolved multipole moments measured from the simulations. The analysis method presented here paves the way for a cosmological analysis using three-dimensional tensor-type tracers of large-scale structure for current and future surveys.