Refined modelling of the radio SZ signal: kinematic terms, relativistic temperature corrections and anisotropies in the radio background

TL;DR

This paper develops a high-precision model for the radio SZ effect, including kinematic, relativistic, and anisotropic corrections, to better understand the cosmological radio background and its observational signatures.

Contribution

It provides analytical expressions for relativistic and kinematic corrections to the radio SZ signal, enabling more accurate modeling and potential constraints on the radio background properties.

Findings

Relativistic temperature corrections are a few percent.

Kinematic and anisotropic effects can be modeled analytically.

Stacking analyses can help constrain the radio background's redshift evolution.

Abstract

A significant cosmological radio background will inevitably lead to a radio Sunyaev-Zeldovich (SZ) effect. In the simplest limit, the combined signal from the scattered radio and cosmic microwave background exhibits a null at around $\nu \simeq 735$ MHz. Here, we show that kinematic and relativistic temperature corrections to this radio SZ signal are easily calculable. We treat both the cluster and observer motion, and the scattering of anisotropies in the radio background, highlighting how the spectrum of the radio SZ effect is affected in each case. Although relativistic temperature corrections only enter at the level of a few percent, our expressions allow high-precision modelling of these terms. By measuring the SZ signal around the radio null, one is in principle able to place constraints on the properties of a cosmological radio background. A combination with standard SZ measurements from large cluster samples could provide a promising avenue towards breaking degeneracies between different contributions. Stacking analyses can reduce the effect of kinematic corrections and dipolar anisotropies in the radio background, thereby providing a way to constrain the redshift dependence of the average radio background. Our qualitative discussion is meant to give an analytic understanding of the various effects and also motivate further studies with the aim to obtain quantitative forecasts of their observability. At this stage, a detection of the corrections seems rather futuristic, but the advent of large SZ and X-ray cluster samples could drastically improve our ability to disentangle various effects.