# Thermal Sunyaev-Zel'dovich effect in the intergalactic medium with primordial magnetic fields

## TL;DR

This paper investigates how primordial magnetic fields influence the thermal Sunyaev-Zel'dovich effect in the intergalactic medium, revealing their significant impact on the CMB anisotropies at small angular scales.

## Contribution

It provides a detailed calculation of the IGM's evolution under primordial magnetic fields and predicts their imprint on the tSZ angular power spectrum at high multipoles.

## Key findings

- PMFs significantly increase the tSZ power spectrum at high multipoles.
- Ambipolar diffusion heating raises temperature and ionization in the IGM.
- Lorentz force enhances density contrast after recombination.

## Abstract

The presence of ubiquitous magnetic fields in the universe is suggested from observations of radiation and cosmic ray from galaxies or the intergalactic medium (IGM). One possible origin of cosmic magnetic fields is the magnetogenesis in the primordial universe. Such magnetic fields are called primordial magnetic fields (PMFs), and are considered to affect the evolution of matter density fluctuations and the thermal history of the IGM gas. Hence the information of PMFs is expected to be imprinted on the anisotropies of the cosmic microwave background (CMB) through the thermal Sunyaev-Zel'dovich (tSZ) effect in the IGM. In this study, given an initial power spectrum of PMFs as $P(k)\propto B_{\rm 1Mpc}^2 k^{n_{B}}$, we calculate dynamical and thermal evolutions of the IGM under the influence of PMFs, and compute the resultant angular power spectrum of the Compton $y$-parameter on the sky. As a result, we find that two physical processes driven by PMFs dominantly determine the power spectrum of the Compton $y$-parameter; (i) the heating due to the ambipolar diffusion effectively works to increase the temperature and the ionization fraction, and (ii) the Lorentz force drastically enhances the density contrast just after the recombination epoch. These facts result in making the tSZ angular power spectrum induced by the PMFs more remarkable at $\ell >10^4$ than that by galaxy clusters even with $B_{\rm 1Mpc}=0.1$ nG and $n_{B}=-1.0$ because the contribution from galaxy clusters decreases with increasing $\ell$. The measurement of the tSZ angular power spectrum on high $\ell$ modes can provide the stringent constraint on PMFs.