Cross-Power Spectrum and Its Application on Window Functions in the WMAP data

TL;DR

This paper explores the use of cross-power spectrum estimators to accurately extract window functions from WMAP data, addressing error sources and demonstrating the method's effectiveness with extragalactic sources and planetary measurements.

Contribution

It introduces a detailed analysis of the residual errors in cross-power spectrum estimation and applies the method to derive window functions in WMAP data using point sources and Jupiter.

Findings

Residual errors from uncorrelated signals are quantified.

Window functions for WMAP frequency bands are successfully extracted.

The method improves accuracy in power spectrum estimation.

Abstract

Cross-power spectrum is a quadratic estimator between two maps that can provide unbiased estimate of the underlying power spectrum of the correlated signals, which is therefore used for extracting the power spectrum in the WMAP data. In this paper we discuss the limit of cross-power spectrum and derive the residual from uncorrelated signal, which is the source of error in power spectrum extraction. We employ the estimator to extract window functions by crossing pairs of extragalactic point sources. We desmonstrate its usefulness in WMAP Difference Assembly maps where the window functions are measured via Jupiter and then extract the window functions of the 5 WMAP frequency band maps.