Angular Correlations of Cosmic Microwave Background Spectrum Distortions from Photon Diffusion

TL;DR

This paper derives an expression for the angular correlation function of diffusion-induced y-distortions in the cosmic microwave background and discusses its detectability with current experiments.

Contribution

It introduces a new analytical approach to compute the angular correlation of CMB spectrum distortions caused by photon diffusion during recombination.

Findings

Derived an expression for the y-distortion angular correlation function.

Predicted the cross-correlation between y-distortion and temperature fluctuations.

Suggested detectability with existing microwave background experiments.

Abstract

During cosmic recombination, charged particles bind into neutral atoms and the mean free path of photons rapidly increases, resulting in the familiar diffusion damping of primordial radiation temperature variations. An additional effect is a small photon spectrum distortion, because photons arriving from a particular sky direction were originally in thermal equilibrium at various spatial locations with different temperatures; the combination of these different blackbody temperature distributions results in a spectrum with a Compton $y$-distortion. Using the approximation that photons had zero mean free path prior to their second-to-last scattering, we derive an expression for the resulting $y$-distortion, and compute the angular correlation function of the diffusion $y$-distortion and its cross-correlation with the square of the photon temperature fluctuation. Detection of the cross-correlation is within reach of existing arcminute-resolution microwave background experiments such as the Atacama Cosmology Telescope and the South Pole Telescope.