COSEBIs: Extracting the full E-/B-mode information from cosmic shear correlation functions
COSEBIs: Extracting the full E-/B-mode information from cosmic shear correlation functions
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DOI：
10.1051/0004-6361/201014235
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发表时间：
2010-02
影响因子：
6.5
通讯作者：
P. Schneider;T. Eifler;E. K. A. F. Astronomie;U. Bonn;Center for Cosmology;Particle Physics;O. University;C. I. O. Technology.;D. Astronomy
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文献类型：
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作者：
P. Schneider;T. Eifler;E. K. A. F. Astronomie;U. Bonn;Center for Cosmology;Particle Physics;O. University;C. I. O. Technology.;D. Astronomy
上下文。宇宙剪切被认为是研究宇宙中暗能量性质的最有力的方法之一。作为一种标准方法，宇宙切变场的两点相关函数ξ_±(ϑ)被用作切变场的统计量度。目标。为了将观测到的切变分为E模和B模，后者最有可能是由数据集中的剩余系统学和/或内在对准效应产生的，以前已经定义了几个统计量。在这里，我们的目标是在有限的角度间隔上对包含在ξ_±中的宇宙切变信息进行完全的E/B模分解。方法：研究方法。我们构造了两组这样的E/B模式度量，即E/B模式积分的完全正交集(COSEBI)，其特征在于ξ_±与COSEBI之间的权函数，它们分别是ϑ中的多项式或ϑ中的多项式。考虑到由COSEBI构造的宇宙参数空间中的似然，我们研究了它们的信息量。结果。我们证明了信息量随着ξ模数目的增加而增长，并且达到了一个渐近极限，它定义了E模分量的最大可用信息量。我们表明，测量ξ_±的角度范围越窄，达到这个极限的时间就越早(即，考虑的模式数越少)，而对于对数权函数，达到这个极限的时间要早得多。例如，对于区间1‘≤ϑ≤400’，参数对(Ω_m，σ_8)的渐近极限在线性情况下达到~25个模式，但在对数情况下已达到5个模式。COSEBI形成了一组自然离散的量，我们建议将其作为未来宇宙切变可能性分析的选择方法。
Context. Cosmic shear is considered one of the most powerful methods for studying the properties of dark energy in the Universe. As a standard method, the two-point correlation functions ξ_±(ϑ) of the cosmic shear field are used as statistical measures for the shear field. Aims. In order to separate the observed shear into E- and B-modes, the latter being most likely produced by remaining systematics in the data set and/or intrinsic alignment effects, several statistics have been defined before. Here we aim at a complete E-/B-mode decomposition of the cosmic shear information contained in the ξ_± on a finite angular interval. Methods. We construct two sets of such E-/B-mode measures, namely Complete Orthogonal Sets of E-/B-mode Integrals (COSEBIs), characterized by weight functions between the ξ_± and the COSEBIs which are polynomials in ϑ or polynomials in ϑ, respectively. Considering the likelihood in cosmological parameter space, constructed from the COSEBIs, we study their information content. Results. We show that the information grows with the number of COSEBI modes taken into account, and that an asymptotic limit is reached which defines the maximum available information in the E-mode component of the ξ_±. We show that this limit is reached the earlier (i.e., for a smaller number of modes considered) the narrower the angular range is over which ξ_± are measured, and it is reached much earlier for logarithmic weight functions. For example, for on the interval 1' ≤ ϑ ≤ 400', the asymptotic limit for the parameter pair (Ω_m, σ_8) is reached for ~25 modes in the linear case, but already for 5 modes in the logarithmic case. The COSEBIs form a natural discrete set of quantities, which we suggest as method of choice in future cosmic shear likelihood analyses.