三维星系功率谱测量的无偏污染去除
Unbiased contaminant removal for 3D galaxy power spectrum measurements
摘要：
我们评估和开发技术，以消除污染物时，计算三维星系功率谱。我们把这个过程分成三个独立的阶段：（i）去除污染信号，（ii）估计未污染的宇宙学功率谱，（iii）消除由此产生的估计。对于（i），我们证明了去除最佳拟合污染模式减法）和将协方差的污染分量设置为无穷大（模式解投影）在数学上是等价的。对于（ii），执行二次极大似然（QML）模式解投影后给出了一个最佳的无偏解，虽然它需要大的$N_{\rm mode}^2$矩阵（$N_{\rm mode}$是模式的总数）}，这是不可行的最近的三维星系调查的操作。如由\citet* [FKP]{Feldman}提出的测量（ii）的模式的分箱平均更快且更简单，但是是次优的并且产生有偏差的解决方案。我们提出了一种方法来消除偏置所产生的FKP测量，不需要任何大型矩阵计算。我们认为，次优的FKP估计相比，QML估计，污染物所造成的是不太严重的，通常被忽视，由于调查窗口。
英文摘要：
We assess and develop techniques to remove contaminants when calculating the 3D galaxy power spectrum. We separate the process into three separate stages: (i) removing the contaminant signal, (ii) estimating the uncontaminated cosmological power spectrum, (iii) debiasing the resulting estimates. For (i), we show that removing the best-fit contaminant mode subtraction), and setting the contaminated components of the covariance to be infinite (mode deprojection) are mathematically equivalent. For (ii), performing a Quadratic Maximum Likelihood (QML) estimate after mode deprojection gives an optimal unbiased solution, although it requires the manipulation of large $N_{\rm mode}^2$ matrices ($N_{\rm mode}$ being the total number of modes)}, which is unfeasible for recent 3D galaxy surveys. Measuring a binned average of the modes for (ii) as proposed by \citet*[FKP]{Feldman} is faster and simpler, but is sub-optimal and gives rise to a biased solution. We present a method to debias the resulting FKP measurements that does not require any large matrix calculations. We argue that the sub-optimality of the FKP estimator compared with the QML estimator, caused by contaminants is less severe than that commonly ignored due to the survey window.
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