标题： 大尺度红移空间畸变建模中的泊松噪声 显示英文标题

标题： The Poisson noise in modeling the redshift-space distortion at large scales

摘要： 我们研究了在大线性尺度上建模红移空间畸变（RSD）效应时的误差，使用的是千年模拟的数据。虽然标准理论模板（如Kaiser公式和TNS方法）能够精确地建模单个大尺度模式的RSD，但我们发现对于数密度低于$\sim10^{-3}({\rm Mpc}/h)^{-3}$的示踪物，预测的功率谱存在百分之几的偏差。这种误差源于真实空间功率谱在RSD建模过程中内在泊松噪声的放大。这种放大的噪声可以解析表达为$1 + \epsilon/[{\bar{n}P}({1+\epsilon})]$，其中$\epsilon=2\beta/3+\beta^2/5$，这里$P$表示真实空间示踪物功率谱，$\beta \equiv f/b$。具体而言，对于数密度约为$5\times10^{-4}({\rm Mpc}/h)^{-3}$的暗晕，这一现象导致额外的系统误差为2.5%。我们的结果表明，在利用从模拟或实际调查中测量的示踪物的真实空间功率谱直接建模RSD时应谨慎行事。这与一些情况相关，例如，当使用基于模拟数据训练的代理器预测真实空间示踪物功率谱时。 显示英文摘要

摘要： We investigate the errors in modeling the redshift-space distortion (RSD) effect at large linear scales, using data from the Millennium simulation. While standard theoretical templates, such as the Kaiser formula and the TNS method, could precisely model RSD for individual large-scale modes, we find that for tracers with number densities lower than $\sim10^{-3}({\rm Mpc}/h)^{-3}$, there is a few-percent level bias in the predicted power spectrum. This error arises due to the amplification of intrinsic Poisson noise during RSD modeling from real-space power spectrum. This amplified noise can be analytically expressed as $1 + \epsilon/[{\bar{n}P}({1+\epsilon})]$, with $\epsilon=2\beta/3+\beta^2/5$, where $P$ denotes the real-space tracer power spectrum and $\beta \equiv f/b$. Specifically, for halos with a number density of around $5\times10^{-4}({\rm Mpc}/h)^{-3}$, this phenomenon results in an additional systematic error of 2.5\%. Our result suggests that caution should be exercised when modeling the RSD directly using real-space power spectra of tracers measured from simulations or from the real surveys. This is relevant, e.g., in situations where the real-space tracer power spectrum is predicted by emulators trained using simulation data.