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arXiv 1002.3615astro-ph.COastro-ph.IM
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宇宙剪切不应该以传统方式测量

Cosmic Shears Should Not Be Measured In Conventional Ways

Jun Zhang, Eiichiro Komatsu

摘要:

如何从星系图像中构造宇宙剪切估计是弱透镜研究中一个长期存在的问题。传统的方法平均每个星系的单个量来估计每个剪切分量。我们发现,任何这样的剪切估计必须减少到一个高度非线性的形式时,星系图像是由三个参数(纯椭圆),即使在没有的点扩散函数(PSF)。在PSF的存在下,我们认为这类剪切估计不太可能存在。或者,我们提出了一种测量宇宙剪切力的新方法:不是平均每个星系的单个值,而是平均两个数字,然后取比值来估计剪切力分量。特别是,这两个数字对应于在傅里叶空间中产生星系图像四极矩的分子和分母,正如Zhang(2008)所提出的那样。这产生剪切分量的统计无偏估计。因此,剪切场的n点空间相关性的测量也应该被修改:需要取两个关联函数的比率以得到期望的、无偏的剪切相关性。

英文摘要:

A long standing problem in weak lensing is about how to construct cosmic shear estimators from galaxy images. Conventional methods average over a single quantity per galaxy to estimate each shear component. We show that any such shear estimators must reduce to a highly nonlinear form when the galaxy image is described by three parameters (pure ellipse), even in the absence of the point spread function (PSF). In the presence of the PSF, we argue that this class of shear estimators do not likely exist. Alternatively, we propose a new way of measuring the cosmic shear: instead of averaging over a single value from each galaxy, we average over two numbers, and then take the ratio to estimate the shear component. In particular, the two numbers correspond to the numerator and denominators which generate the quadrupole moments of the galaxy image in Fourier space, as proposed in Zhang (2008). This yields a statistically unbiased estimate of the shear component. Consequently, measurements of the n-point spatial correlations of the shear fields should also be modified: one needs to take the ratio of two correlation functions to get the desired, unbiased shear correlation.

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