# An Accurate Analytic Model for the Thermal Sunyaev-Zel'dovich One-Point PDF

## TL;DR

This paper introduces a refined analytic halo model for the thermal Sunyaev-Zel'dovich one-point PDF, incorporating halo overlaps and clustering effects, validated against simulations, to enhance cosmological analyses with upcoming CMB data.

## Contribution

It presents a new, more accurate analytic model for the tSZ PDF that accounts for halo overlaps and clustering, improving upon previous simplified models.

## Key findings

- Model matches numerical simulations accurately.
- Necessary for analysis in upcoming CMB experiments.
- Potential applicability to other cosmological observables.

## Abstract

Non-Gaussian statistics of late-time cosmological fields contain information beyond that captured in the power spectrum. Here we focus on one such example: the one-point probability distribution function (PDF) of the thermal Sunyaev-Zel'dovich (tSZ) signal in maps of the cosmic microwave background (CMB). It has been argued that the one-point PDF is a near-optimal statistic for cosmological constraints from the tSZ signal, as most of the constraining power in tSZ $N$-point functions is contained in their amplitudes (rather than their shapes), which probe differently-weighted integrals over the halo mass function. In this paper, we develop a new analytic halo model for the tSZ PDF, discarding simplifying assumptions made in earlier versions of this approach. In particular, we account for effects due to overlaps of the tSZ profiles of different halos, as well as effects due to the clustering of halos. We verify the accuracy of our analytic model via comparison to numerical simulations. We demonstrate that this more accurate model is necessary for the analysis of the tSZ PDF in upcoming CMB experiments. The novel formalism developed here may be useful in modeling the one-point PDF of other cosmological observables, such as the weak lensing convergence field.