用快速小波估计器对fNL进行威尔金森微波各向异性探测7年约束
Wilkinson Microwave Anisotropy Probe 7-yr constraints on fNL with a fast wavelet estimator
摘要：
提出了一种基于快速小波分解约束局部非线性耦合参数fNL的新方法。使用适应HEALPix像素化的多分辨率小波，我们开发了一种方法，该方法比以前基于各向同性小波的估计快10^2倍，比KSW双谱估计快10^3倍，分辨率为威尔金森微波各向异性探测器（WMAP）数据。该方法已应用于WMAP 7年V+W组合图，在95% CL下对fNL施加了-69该结果是在对估计为fNL = 7 +/- 6的剩余点源的贡献进行校正之后获得的。此外，高斯分析的数据进行了使用小波系数的三阶矩，发现与高斯的一致性。虽然对fNL施加的约束不那么严格，比发现与最佳估计，我们认为，一个非常快速的方法，在这项工作中提出的，可以是非常有用的，特别是考虑到大量的数据，将提供未来的实验，如普朗克卫星。此外，小波的局部化允许人们对天空的不同区域进行分析。作为应用，我们分别分析了由Hoftuft等人（2009）提出的偶极调制定义的两个半球。我们没有发现任何显着的不对称性，在这些半球的fNL的估计值。
英文摘要：
A new method to constrain the local non-linear coupling parameter fNL based on a fast wavelet decomposition is presented. Using a multiresolution wavelet adapted to the HEALPix pixelization, we have developed a method that is 10^2 times faster than previous estimators based on isotropic wavelets and 10^3 faster than the KSW bispectrum estimator, at the resolution of the Wilkinson Microwave Anisotropy Probe (WMAP) data. The method has been applied to the WMAP 7-yr V+W combined map, imposing constraints on fNL of -69 < fNL < 65 at the 95 per cent CL. This result has been obtained after correcting for the contribution of the residual point sources which has been estimated to be fNL = 7 +/- 6. In addition, a Gaussianity analysis of the data has been carried out using the third order moments of the wavelet coefficients, finding consistency with Gaussianity. Although the constrainsts imposed on fNL are less stringent than those found with optimal estimators, we believe that a very fast method, as the one proposed in this work, can be very useful, especially bearing in mind the large amount of data that will be provided by future experiments, such as the Planck satellite. Moreover, the localisation of wavelets allows one to carry out analyses on different regions of the sky. As an application, we have separately analysed the two hemispheres defined by the dipolar modulation proposed by Hoftuft et al. (2009). We do not find any significant asymmetry regarding the estimated value of fNL in those hemispheres.
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