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arXiv 1302.0857astro-ph.CO
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利用角互相关确定源的红移分布

On using angular cross-correlations to determine source redshift distributions

Matthew McQuinn, Martin White

摘要:

我们调查如何以及人口的河外天体的红移分布可以重建角互相关与样本的红移是已知的。我们推导出的最小方差二次估计,它具有简单的解析表示在非常适用的限制,是显着更敏感的比以前提出的估计程序。这种估计是直接适用于观测,它鲁棒地找到了似然最大值,它方便地选择角度尺度,在这些角度尺度上,波动很好地近似为独立的红移箱和线性理论。我们发现,线性偏置乘以一个红移仓中物体的数量,一般可以用互相关约束到分数误差(10^2 n/N)^1/2,其中N是每个dz的光谱总数,n是大部分未知总体所跨越的红移仓的数量。误差通常与天空面积和采样分数无关。此外,我们发现,每单位红移的角源密度,dN/dz,在原则上是可能的,虽然宇宙放大率需要占分数误差<~ 10%.We讨论的灵敏度dN/dz的变化作为测光和光谱深度的函数,以及如何优化的调查策略,以约束dN/dz。我们还量化如何以及光度红移箱的互相关可以用来自我校准光度红移样本。简单的公式,可以快速应用于衡量互相关不同的样本的效用。

英文摘要:

We investigate how well the redshift distribution of a population of extragalactic objects can be reconstructed using angular cross-correlations with a sample whose redshifts are known. We derive the minimum variance quadratic estimator, which has simple analytic representations in very applicable limits and is significantly more sensitive than earlier proposed estimation procedures. This estimator is straightforward to apply to observations, it robustly finds the likelihood maximum, and it conveniently selects angular scales at which fluctuations are well approximated as independent between redshift bins and at which linear theory applies. We find that the linear bias times number of objects in a redshift bin generally can be constrained with cross-correlations to fractional error (10^2 n/N)^1/2, where N is the total number of spectra per dz and n is the number of redshift bins spanned by the bulk of the unknown population. The error is often independent of the sky area and sampling fraction. Furthermore, we find that sub-percent measurements of the angular source density per unit redshift, dN/dz, are in principle possible, although cosmic magnification needs to be accounted for at fractional errors of <~ 10 per cent. We discuss how the sensitivity to dN/dz changes as a function of photometric and spectroscopic depth and how to optimize the survey strategy to constrain dN/dz. We also quantify how well cross-correlations of photometric redshift bins can be used to self-calibrate a photometric redshift sample. Simple formulae that can be quickly applied to gauge the utility of cross correlating different samples are given.

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