# Mapping the relativistic electron gas temperature across the sky

## TL;DR

Future CMB experiments like PICO will enable detailed, sky-wide mapping of relativistic electron temperatures in galaxy clusters, providing new cosmological insights through advanced map-based analysis techniques.

## Contribution

This paper introduces a novel map-based method using SZ-temperature moment expansion and constrained-ILC to extract electron gas temperature maps from CMB data, expanding the observational capabilities beyond current stacking approaches.

## Key findings

- PICO can accurately map electron temperatures across the sky.
- Frequency coverage above 300 GHz is crucial for foreground separation.
- PICO can measure Coma cluster's electron temperature with 10σ significance.

## Abstract

With increasing sensitivity, angular resolution, and frequency coverage, future cosmic microwave background (CMB) experiments like PICO will allow us to access new information about galaxy clusters through the relativistic thermal Sunyaev-Zeldovich (SZ) effect. We will be able to map the temperature of relativistic electrons across the entire sky, going well beyond a simple detection of the relativistic SZ effect by cluster stacking methods that currently define the state-of-the-art. Here, we propose a new map-based approach utilizing SZ-temperature moment expansion and constrained-ILC methods to extract electron gas temperature maps from foreground-obscured CMB data. This delivers a new independent map-based observable, the electron temperature power spectrum $T_{\rm e}^{yy}(\ell)$, which can be used to constrain cosmology in addition to the Compton-$y$ power spectrum $C_\ell^{yy}(\ell)$ . We find that PICO has the required sensitivity, resolution, and frequency coverage to accurately map the electron gas temperature of galaxy clusters across the full sky, covering a broad range of angular scales. Frequency-coverage at $\nu\gtrsim 300\,{\rm GHz}$ plays an important role for extracting the relativistic SZ effect in the presence of foregrounds. For Coma, PICO will allow us to directly reconstruct the electron temperature profile using the relativistic SZ effect. Coma's average electron temperature will be measured to $10\sigma$ significance after foreground removal using PICO. Low-angular resolution CMB experiment like LiteBIRD could achieve $2\sigma$ to $3\sigma$ measurement of the electron temperature of this largest cluster. Our analysis highlights a new spectroscopic window into the thermodynamic properties of galaxy clusters and the diffuse electron gas at large angular scales.