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

Understand

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.