体积加权特征速度关联函数估计的改进方法
Improved Methods for Estimating Peculiar Velocity Correlation Functions Using Volume Weighting
摘要：
本文提出了一种改进的方法，利用加权最大似然估计直接从特殊的速度测量中计算平行和垂直速度关联函数。新方法的一个核心特征是使用与位置相关的加权方案，该方案可以减少附近星系的影响，在大多数调查中，这些星系相对于更遥远的星系通常被过度代表。我们证明，这种方式计算的关联函数是不容易受到偏见，由于我们在宇宙中的特定位置，因此更容易比较线性理论和调查之间。我们的研究结果表明，并行速度相关函数是一个很有前途的宇宙学探针，因为它提供了一个更好的近似高斯分布比其他速度关联函数，其偏差更容易通过加权最小化。虽然位置加权平行速度关联函数增加了统计不确定性，但它降低了宇宙方差，有望在未来更精确的速度测量中提供比其他相关方法更稳定和更严格的宇宙学参数约束。
英文摘要：
We present an improved method for calculating the parallel and perpendicular velocity correlation functions directly from peculiar velocity surveys using weighted maximum-likelihood estimators. A central feature of the new method is the use of position-dependent weighting scheme that reduces the influence of nearby galaxies, which are typically overrepresented relative to the more distant galaxies in most surveys. We demonstrate that the correlation functions calculated this way are less susceptible to biases due to our particular location in the Universe, and thus are more easily comparable to linear theory and between surveys. Our results suggest that the parallel velocity correlation function is a promising cosmological probe, given that it provides a better approximation of a Gaussian distribution than other velocity correlation functions and that its bias is more easily minimized by weighting. Though the position weighted parallel velocity correlation function increases the statistical uncertainty, it decreases the cosmic variance and is expected to provide more stable and tighter cosmological parameter constraints than other correlation methods in conjunction with more precise velocity surveys in the future.
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