The optimal weighting function for cosmic magnification measurements through the foreground galaxy–background galaxy (quasar) cross-correlation

Authors

  • Xiaofeng Yang,

    Corresponding author
    1. Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, Nandan Road 80, Shanghai 200030, China
    2. Graduate University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
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  • Pengjie Zhang

    1. Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, Nandan Road 80, Shanghai 200030, China
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E-mail: xfyang@shao.ac.cn

ABSTRACT

Cosmic magnification has been detected through the cross-correlation between foreground and background populations (galaxies or quasars). It has been shown that weighting each background object by its α− 1 can significantly improve the cosmic magnification measurement. Here α is the logarithmic slope of the luminosity function of background populations. However, we find that this weighting function is optimal only for sparse background populations in which intrinsic clustering is negligible with respect to shot noise. We derive the optimal weighting function for a general case, including scale-independent and scale-dependent weights. The optimal weighting function improves the signal-to-noise ratio by ∼20 per cent for a BigBOSS-like survey and the improvement can reach a factor of ∼2 for surveys with much denser background populations.

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