Statistical Properties of Thermal Sunyaev-Zel'dovich Maps

TL;DR

This paper analyzes the statistical properties of thermal Sunyaev-Zel'dovich maps using models of dark matter clustering, providing a comprehensive framework to understand the distribution and hot spot statistics in CMB temperature fluctuations.

Contribution

It introduces a novel formalism for analyzing tSZ maps to all orders, incorporating biasing, projection effects, and different matter clustering models, validated against simulations.

Findings

Lognormal model better fits simulation data than hierarchical ansatz.

The formalism accurately predicts the PDF and hot spot statistics.

Analysis is adaptable to various observational configurations.

Abstract

At high angular frequencies, beyond the damping tail of the primary power spectrum, the dominant contribution to the power spectrum of cosmic microwave background (CMB) temperature fluctuations is the thermal Sunyaev-Zel'dovich (tSZ) effect. We investigate various important statistical properties of the Sunyaev-Zel'dovich maps, using well-motivated models for dark matter clustering to construct statistical descriptions of the tSZ effect to all orders enabling us to determine the entire probability distribution function (PDF). Any generic deterministic biasing scheme can be incorporated in our analysis and the effects of projection, biasing and the underlying density distribution can be analysed separately and transparently in this approach. We introduce the cumulant correlators as tools to analyse tSZ catalogs and relate them to corresponding statistical descriptors of the underlying density distribution. The statistics of hot spots in frequency-cleaned tSZ maps are also developed in a self-consistent way to an arbitrary order, to obtain results complementary to those found using the halo model. We also consider different beam sizes, to check the extent to which the PDF can be extracted from various observational configurations. The formalism is presented with two specific models for underlying matter clustering: (1) the hierarchical ansatz; and (2) the lognormal distribution. We find both models to be in very good agreement with the simulation results, though the lognormal model has an edge over the hierarchical model.