The shape of CMB temperature and polarization peaks on the sphere

TL;DR

This paper develops a harmonic space formalism to analyze the shape and polarization patterns of CMB temperature peaks on the sphere, accounting for eccentricity and providing tools for simulating constrained CMB maps.

Contribution

It introduces a covariant harmonic space approach to study CMB peaks, including eccentricity effects and a method for simulating constrained maps, advancing the analysis of large-scale CMB features.

Findings

Eccentricity causes a quadrupolar peak shape dependence.

Differences in peak statistics compared to flat-sky approximation.

A new mechanism for simulating constrained CMB maps with specific peaks.

Abstract

We present a theoretical study of CMB temperature peaks, including its effect over the polarization field, and allowing nonzero eccentricity. The formalism is developed in harmonic space and using the covariant derivative on the sphere, which guarantees that the expressions obtained are completely valid at large scales (i.e., no flat approximation). The expected patterns induced by the peak, either in temperature or polarization, are calculated, as well as their covariances. It is found that the eccentricity introduces a quadrupolar dependence in the peak shape, which is proportional to a complex bias parameter $b_\epsilon$, characterizing the peak asymmetry and orientation. In addition, the one-point statistics of the variables defining the peak on the sphere is reviewed, finding some differences with respect to the flat case for large peaks. Finally, we present a mechanism to simulate constrained CMB maps with a particular peak on the field, which is an interesting tool for analysing the statistical properties of the peaks present in the data.