Likelihood reconstruction method of real-space density and velocity power spectra from a redshift galaxy survey
Likelihood reconstruction method of real-space density and velocity power spectra from a redshift galaxy survey
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DOI：
10.1111/j.1365-2966.2011.19203.x
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发表时间：
2011-03
影响因子：
4.8
通讯作者：
Jiayu Tang;I. Kayo;M. Takada
中科院分区：
文献类型：
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作者：
Jiayu Tang;I. Kayo;M. Takada
我们开发了一种基于最大似然的方法，从测量的红移空间中星系的群集特征中重建每个波数bin处的密度和速度功率谱的带功率，包括小尺度、非线性红移失真、上帝之指（FoG）效应中固有的不确定性的边缘化。假设密度和速度功率谱依赖于μ与μ2n （n= 0,1,2）的不同角度调制的红移空间功率谱，并且模型FoG效应是红移空间谱中的乘函数，可以进行重建。通过n体模拟和光晕表，我们将重建的功率谱与模拟直接测量的功率谱进行了比较，验证了我们的方法。对于μ0谱或等效的密度功率谱Pδδ(k)，我们的方法恢复的振幅精度为百分之几，达到k≃0.3 h Mpc−1。对于μ2的功率谱，即线性状态下的密度-速度功率谱Pδθ(k)，我们的方法可以在统计误差范围内恢复到k≤0.2 h Mpc−1且在红移z= 0和1处的输入功率谱。然而，对于受雾效应影响最小的光晕光谱，在波数0.05≤k≤0.3 h Mpc−1范围内，重建光谱的振幅大于模拟推断的光谱Pδθ(k)。我们认为，这种分歧可能归因于密度和速度摄动的交叉双谱引起的非线性效应。利用微扰理论，在模拟中假设爱因斯坦引力，导出了红移空间谱的非线性校正项，并发现在较大的k、较低的红移和较大的质量晕下，主阶校正项与μ2成正比，显著地增加了μ2-功率谱幅值。我们发现，在模拟中加入非线性校正项Pδθ(k)可以较好地再现高达k≃0.2 h Mpc−1的光晕的重构Pδθ(k)。
We develop a maximum likelihood based method of reconstructing the band powers of the density and velocity power spectra at each wavenumber bin from the measured clustering features of galaxies in redshift space, including marginalization over uncertainties inherent in the small-scale, non-linear redshift distortion, the Fingers-of-God (FoG) effect. The reconstruction can be done assuming that the density and velocity power spectra depend on the redshift-space power spectrum having different angular modulations of μ with μ2n (n= 0, 1, 2) and that the model FoG effect is given as a multiplicative function in the redshift-space spectrum. By using N-body simulations and the halo catalogues, we test our method by comparing the reconstructed power spectra with the spectra directly measured from the simulations. For the spectrum of μ0 or equivalently the density power spectrum Pδδ(k), our method recovers the amplitudes to an accuracy of a few per cent up to k≃ 0.3 h Mpc−1 for both dark matter and haloes. For the power spectrum of μ2, which is equivalent to the density–velocity power spectrum Pδθ(k) in the linear regime, our method can recover, within the statistical errors, the input power spectrum for dark matter up to k≃ 0.2 h Mpc−1 and at both redshifts z= 0 and 1, if the adequate FoG model being marginalized over is employed. However, for the halo spectrum that is least affected by the FoG effect, the reconstructed spectrum shows greater amplitudes than the spectrum Pδθ(k) inferred from the simulations over a range of wavenumbers 0.05 ≤k≤ 0.3 h Mpc−1. We argue that the disagreement may be ascribed to a non-linearity effect that arises from the cross-bispectra of density and velocity perturbations. Using the perturbation theory and assuming Einstein gravity as in simulations, we derive the non-linear correction term to the redshift-space spectrum, and find that the leading-order correction term is proportional to μ2 and increases the μ2-power spectrum amplitudes more significantly at larger k, at lower redshifts and for more massive haloes. We find that adding the non-linearity correction term to the simulation Pδθ(k) can fairly well reproduce the reconstructed Pδθ(k) for haloes up to k≃ 0.2 h Mpc−1.