弱引力透镜效应测量中的系统误差

Weak gravitational lensing is one of the most reliable detectors of dark matter and dark energy. The precision of weak lensing measurement is expected to be enhanced by at least a magnitude in the future. However, it will still suffer from some significant systematic errors to fulfill the requirement of precise cosmology. This project focuses on the systematic errors in weak lensing measurement, which includes two topics, 1) the impact of intrinsic alignment of galaxies on cosmic shear and flexion measurement; 2) the effects of dust extinction to the cosmic magnification reconstruction and the method of separating them. We adapt the halo model to calculate the power spectra of the galaxy intrinsic alignment and its gradient, especially on nonlinear scales. We will then analyze the contamination of the estimations of the power spectra of cosmic shear and flexion respectively. To confirm and show the effectiveness of this model, we will give a comparison between the model prediction and statistics from high resolution simulation samples, which can also give further constraints on the model. We construct an estimator of the cosmic magnification signal from the weighted summation of cross-correlations between different flux background galaxies and foreground galaxies. We require the minimal statistical error of the cosmic magnification signal and finally obtain a set of linear algebra equations. We can then separate the cosmic magnification and dust extinction by solving the above equations. The different flux dependence of cosmic magnification and dust extinction guarantee that the solution of such equations is solvable and unique. We will first use the Fisher Matrix to predict the error of cosmic magnification reconstructed from this method, in order to study whether the statistical error is within the bound of dust extinction, we then apply the method to realistic observational samples by cross-correlating the SDSS galaxies and high redshift QSOs. This project is to gain a deeper insight in the systematic error in weak lensing measurement through the above mentioned studies, and provide some theoretical and technical supports to the precise measurement of weak lensing measurement in the future.

本项目针对弱引力透镜测量中两种物理上的系统误差展开研究，分别是：1)星系内禀指向对宇宙剪切(shear，含高阶的flexion)测量的影响；2)尘埃消光对宇宙放大(magnification)效应的影响及二者的分离方法。我们利用暗晕模型来计算星系内禀指向及其梯度在非线性尺度上的功率谱，并分别分析其对shear和flexion相应功率谱估计所产生的污染；我们将利用高精度数值模拟来对模型的预言进行对比和限制。我们利用尘埃消光和宇宙放大效应不同的流量依赖关系，通过不同流量背景星系样本和同一个前景星系样本交叉相关的加权和，来构造一个弱引力透镜信号的估计量，以从中分离宇宙放大效应和尘埃消光效应。在要求重构出的弱引力透镜信号统计误差最小的情况下，我们从数学上对该系列权重值予以求解。我们首先将利用Fisher矩阵对该方法所重构出的宇宙放大效应进行误差估计，然后将该方法运用到SDSS观测样本的实际测量中。

弱引力透镜效应是一种原理上最干净的宇宙学探针，对宇宙学参数的限制、宇宙中物质(包括发光物质和通常方法很难探测到的暗物质)分布的研究具有非常重要的意义。一般而言，有两种方法提取弱引力透镜效应信号，即通过宇宙剪切效应或宇宙放大效应。本项目分别针对这两种弱引力透镜效应探测方法及其系统误差进行研究，主要内容包括通过高阶弱引力透镜效应flexion的功率谱来同时限制宇宙学参数和暗晕中物质分布，分析尘埃消光效应对宇宙放大效应的影响及两者的分离方法。研究结果证明flexion能有效区分并同时限制不同的宇宙学参数以及不同的暗晕中物质分布；发现尘埃消光和宇宙放大效应的功率在同等量级的情况下，我们仍能有效对二者进行分离。因为暗晕结构形成是依赖于宇宙学的，所以只有在给定一组基准宇宙学参数的前提下我们才能讨论暗晕结构形成及其中的物质分布，我们的方法则提供了一种能够同时兼顾宇宙学和结构形成研究以及二者联系的途径，从而加深我们对宇宙学框架下结构形成的认识，而这在不久的将来，当大尺度结构巡天拥有测量flexion的能力，这种设想就可能实现。我们还得到一种新颖而颇有前景的消除宇宙放大效应测量中系统误差的方法，从而对弱引力透镜效应信号进行提纯，利用目前的观测数据，这种方法就有望得到验证和应用。