标题： 模型中大尺度红移空间畸变的泊松噪声 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）效应的误差，使用的是Millennium模拟的数据。 虽然标准的理论模板，如Kaiser公式和TNS方法，可以精确地对单个大尺度模式进行RSD建模，但我们发现，对于数量密度低于$\sim10^{-3}({\rm Mpc}/h)^{-3}$的示踪物，预测的功率谱存在几个百分点的偏差。 这种误差是由于在从实空间功率谱进行RSD建模时，固有泊松噪声被放大所致。 这种放大的噪声可以解析地表示为$1 + \epsilon/[{\bar{n}P}({1+\epsilon})]$，其中$\epsilon=2\beta/3+\beta^2/5$，其中$P$表示实空间示踪物功率谱，$\beta \equiv f/b$。 具体而言，对于数量密度约为$5\times10^{-4}({\rm Mpc}/h)^{-3}$的晕，这一现象会导致额外的系统误差为2.5%。 我们的结果表明，在直接使用来自模拟或实际调查的示踪物实空间功率谱来建模红移空间畸变（RSD）时需要谨慎。 这种谨慎在某些情况下尤为重要，例如使用训练于模拟数据的代理模型预测实空间示踪物功率谱的情况，以及使用星系样本进行重子声学振荡（BAO）重建的情况，我们估计，散粒噪声可能在位移场中引入约三分之一的随机误差，这可能会削弱BAO峰锐化的有效性。 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 is necessary when directly modeling redshift-space distortions (RSD) using real-space power spectra of tracers obtained from simulations or actual surveys. This caution is particularly pertinent in scenarios where emulators trained on simulation data forecast the real-space tracer power spectrum, as well as in baryon acoustic oscillation (BAO) reconstruction using galaxy samples, for which we estimate that shot noise could introduce random errors of about one-third in the displacement field, potentially diminishing the effectiveness of the BAO peak sharpening.