arXiv 2512.040752025-12-03astro-ph.COastro-ph.GA

关于宇宙学中距离和速度估计

On distance and velocity estimation in cosmology

The Technion – Israel Institute of Technology（以色列理工学院）

Adi Nusser

备注：: 21 pages, 6 figures

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AI总结：

研究指出在宇宙学中，距离和速度估计存在系统偏差，改进的维纳滤波器无法有效消除速度马尔基乌斯偏差，建议将星系置于观测红移处以获得更优的重建效果。

摘要：

距离指标的分散性在从红移和距离重建多普勒速度场时引入了两个概念上不同的系统性偏差。第一个是距离马尔基乌斯偏差（dMB），它影响个体距离估计，原则上可以近似修正。第二个是速度马尔基乌斯偏差（vMB），当从分散的距离测量中构建连续速度场时出现：随机散射使星系处于嘈杂的空间位置，引入虚假的速度梯度，即使距离已修正dMB，这些梯度仍然存在。以特拉利-费雪关系为例，逆向和正向 formulations 都为具有相同真实距离的星系提供了无偏的多普勒速度，但 neither 消除 vMB 当星系被放置在推断的距离处。我们开发了一种改进的维纳滤波器，通过条件概率 P(r|d) 正确编码直接观测距离 d 和真实距离 r 之间的相关性，考虑了通过观测距离 d 采样的真实距离分布。然而，这种改进的滤波器导致了幅度估计的抑制。由于机器学习自动编码器在高斯场中收敛到维纳滤波器，因此它们不太可能显著改进速度场估计。因此，我们主张最优重建将星系置于其观测红移处而不是推断的距离；这种方法在距离误差超过 σ_v/H_0 时有效，这在典型调查中大多数星系的远距离调查中成立。

英文摘要：

Scatter in distance indicators introduces two conceptually distinct systematic biases when reconstructing peculiar velocity fields from redshifts and distances. The first is distance Malmquist bias (dMB) that affects individual distance estimates and can in principle be approximately corrected. The second is velocity Malmquist bias (vMB) that arises when constructing continuous velocity fields from scattered distance measurements: random scatter places galaxies at noisy spatial positions, introducing spurious velocity gradients that persist even when distances are corrected for dMB. Considering the Tully-Fisher relation as a concrete example, both inverse and forward formulations yield unbiased individual peculiar velocities for galaxies with the same true distance (the forward relation requires a selection-dependent correction), but neither eliminates vMB when galaxies are placed at their inferred distances. We develop a modified Wiener filter that properly encodes correlations between directly observed distance $d$ and true distance $r$ through the conditional probability $P(r|d)$, accounting for the distribution of true distances sampled by galaxies at observed distance $d$. Nonetheless, this modified filter yields suppressed amplitude estimates. Since machine learning autoencoders converge to the Wiener filter for Gaussian fields, they are unlikely to significantly improve velocity field estimation. We therefore argue that optimal reconstruction places galaxies at their observed redshifts rather than inferred distances; an approach effective when distance errors exceed $σ_v/H_0$, a condition satisfied for most galaxies in typical surveys beyond the nearby volume.

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