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

Details The optimal weighting function for cosmic magnification measurement through foreground galaxy-background galaxy (quasar) cross correlation The optimal weighting function for cosmic magnification measurement through foreground galaxy-background galaxy (quasar) cross correlation

2011-04-13

arxiv.org/abs/1104.2487v2

MNRAS Letters. 415: L45-L48. 2011

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

5 pages, no figures, accepted for publication in MNRAS Letters after minor revision

Scientific paper

10.1111/j.1745-3933.2011.01075.x

Cosmic magnification has been detected through cross correlation between foreground and background populations (galaxies or quasars). It has been shown that weighing each background object by its $\alpha-1$ can significantly improve the cosmic magnification measurement \citep{Menard02,Scranton05}. Here, $\alpha$ 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 general case including scale independent and scale dependent weights. The optimal weighting function improves the S/N (signal to noise ratio) by $\sim 20%$ for a BigBOSS-like survey and the improvement can reach a factor of $\sim 2$ for surveys with much denser background populations.

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