We study the power spectrum dipole of an N-body simulation which includes relativistic effects through ray-tracing and covers the low redshift Universe up to $z_{\rm max} = 0.465$ (RayGalGroup simulation). We model relativistic corrections as well as wide-angle, evolution, window and lightcone effects. Our model includes all relativistic corrections up to third-order including third-order bias expansion. We consider all terms which depend linearly on $\mathcal{H}/k$ (weak field approximation). We also study the impact of 1-loop corrections to the matter power spectrum for the gravitational redshift and transverse Doppler effect. We found wide-angle and window function effects to significantly contribute to the dipole signal. When accounting for all contributions, our dipole model can accurately capture the gravitational redshift and Doppler terms up to the smallest scales included in our comparison ($k=0.48\,h{\rm Mpc}^{-1}$), while our model for the transverse Doppler term is less accurate. We find the Doppler term to be the dominant signal for this low redshift sample. We use Fisher matrix forecasts to study the potential for the future Dark Energy Spectroscopic Instrument (DESI) to detect relativistic contributions to the power spectrum dipole. A conservative estimate suggests that the DESI-BGS sample should be able to have a detection of at least $4.4\sigma$, while more optimistic estimates find detections of up to $10\sigma$. Detecting these effects in the galaxy distribution allows new tests of gravity on the largest scales, providing an interesting additional science case for galaxy survey experiments.

中文翻译：

---

对光晕功率谱偶极子的相对论贡献建模

我们研究了 N 体模拟的功率谱偶极子，该模拟包括通过射线追踪的相对论效应，并涵盖了高达 $z_{\rm max} = 0.465 $（RayGalGroup 模拟）的低红移宇宙。我们对相对论校正以及广角、演化、窗口和光锥效应进行建模。我们的模型包括高达三阶的所有相对论修正，包括三阶偏差扩展。我们考虑所有线性依赖于 $\mathcal{H}/k$（弱场近似）的项。我们还研究了 1 环校正对引力红移和横向多普勒效应的物质功率谱的影响。我们发现广角和窗函数效应对偶极子信号有显着贡献。在考虑所有贡献时，我们的偶极子模型可以准确地捕获引力红移和多普勒项，最高可达我们比较中包含的最小尺度 ($k=0.48\,h{\rm Mpc}^{-1}$)，而我们的横向多普勒项模型不太准确。我们发现多普勒项是这个低红移样本的主要信号。我们使用 Fisher 矩阵预测来研究未来暗能量光谱仪 (DESI) 检测功率谱偶极子的相对论贡献的潜力。保守估计表明，DESI-BGS 样本应该能够检测到至少 $4.4\sigma$，而更乐观的估计发现检测到高达 $10\sigma$。在星系分布中检测到这些效应允许在最大尺度上进行新的重力测试，