Detection of point sources in maps of the cosmic microwave background radiation by means of optimal filters

Abstract

When we observe the sky with the most advanced instruments operating at microwave frequencies, the photons that we see were originated in very different regions in the universe. Most of them come from our own Galaxy (diffuse synchrotron, free-free and dust emission), others come from very distant galaxies and clusters of galaxies, and, finally, a fraction will have their origin in the relic radiation of the Big Bang, known as the Cosmic Microwave Background Radiation. This radiation is contaminated by the other components and the separation of the different emissions in a satisfactory way is still an open problem. In this thesis we will explore different techniques based on linear filters to detect and separate one of the contaminants, the contribution to the observed signal of distant radio and infrared galaxies. These galaxies are known as extragalactic point sources because, for the angular resolution of the typical experiments in microwave frequencies, they appear as point-like unresolved objects. First, we will study the performance of a family of matched filters when detecting point sources, where we allow the scale of the filter to be modified and where we introduce a Neyman-Pearson test to define the region of acceptance. Second, we will consider a new one-dimensional linear filter, the Biparametric Scale-Adaptive Filter (BSAF), that has two parameters that can be optimised to maximise the number of real detections for a fixed number of spurious detections, used in conjuction with a Neyman-Pearson test. Third, we will extend the BSAF to two dimensions, and compare it with the Mexican Hat Wavelet. Fourth, we will explore a new technique that combines lineal and quadratic fusion of images with linear filters, testing it with realistic simulations of one of the Planck satellite channels. Fifth, we will study in detail the performance of three filters, the Matched filter and two members of the Mexican Hat wavelet in realistic simulations of the nine channels of Planck. To conclude, we will use the second member of the Mexican Hat Family to do a non-blind study in the five frequencies of WMAP of a complete sample of 2491 sources observed at 5 GHz, producing a catalogue of 932 objects detected above 3s and a catalogue of 380 objects observed above 5s.