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arXiv 0709.1479astro-ph
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强透镜机制中的弱透镜椭圆度

Weak lensing ellipticities in a strong lensing regime

Richard Massey, David M. Goldberg

摘要:

从遥远星系的平均椭圆率测量微弱的引力透镜剪切信号已成为常规。然而,椭圆率和剪切之间的转换假定了透镜势的局部线性(即剪切的空间导数很小),而这个条件在天空中一些最有趣的区域并不满足。我们延长推导的透镜方程,包括高阶项,并评估水平的偏见,假设一阶弱透镜理论在一个相对较强的剪切制度。我们发现,即使在最坏的情况下,一个完全线性的分析是准确的1%以外的爱因斯坦半径的1.07倍的镜头,通过推导出一个解析函数,可用于估计任何一阶分析的适用性。这种效应太小,无法解释子弹状星团质量的弱透镜和强透镜估计之间的差异,并且在可预见的未来不应该影响星团调查。事实上,这意味着可以使用圆弧来测量比通常所理解的更靠近簇芯的剪切。然而,在未来的透镜调查所要求的精度水平,这种偏见应该被考虑在测量的内斜率的集群质量分布和小规模的质量功率谱。这两个都是决定重子物质和暗物质之间关系的核心。

英文摘要:

It is now routine to measure the weak gravitational lensing shear signal from the mean ellipticity of distant galaxies. However, conversion between ellipticity and shear assumes local linearity of the lensing potential (ie that the spatial derivatives of the shear are small), and this condition is not satisfied in some of the most interesting regions of the sky. We extend a derivation of lensing equations to include higher order terms, and assess the level of biases introduced by assuming that first-order weak lensing theory holds in a relatively strong shear regime. We find that, even in a worst-case scenario, a fully linear analysis is accurate to within 1% outside ~1.07 times the Einstein radius of a lens, by deriving an analytic function that can be used to estimate the applicability of any first-order analysis. The effect is too small to explain the discrepancy between weak- and strong-lensing estimates of the mass of the bullet cluster, and should not impact cluster surveys for the forseeable future. In fact, it means that arclets can be used to measure shears closer to a cluster core than has been generally appreciated. However, at the level of accuracy demanded by future lensing surveys, this bias ought to be considered in measurements of the inner slope of cluster mass distributions and the small-scale end of the mass power spectrum. Both of these are central in determining the relationship between baryonic and dark matter.

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