Measurement of angular cross-correlation between the cosmological dispersion measure and the thermal Sunyaev--Zeldovich effect

The dispersion measures (${\rm DMs}$) from fast radio bursts (FRBs) and the thermal Sunyaev--Zeldovich (tSZ) effect probe the free-electron density and thermal pressure, respectively, in the intergalactic medium (IGM) and the intervening galaxies and clusters. Their combination enables disentangling the gas density and temperature. In this work, we present the first detection of an angular cross-correlation between the ${\rm DMs}$ and the Compton $y$ parameter of the tSZ effect. The theoretical expectation is calculated using the halo model $\texttt{HMx}$, calibrated with hydrodynamic simulations. The observational cross-correlation is measured over angular separations of $1^\prime$--$1000^\prime$ using the ${\rm DMs}$ from $133$ localized FRBs and the $y$-maps from the Planck satellite and the Atacama Cosmology Telescope (ACT). We detect a positive correlation with amplitudes of $\mathcal{A}=2.01 \pm 0.50$ ($4.0 \sigma$) for Planck and $\mathcal{A}=1.23 \pm 0.82$ ($1.5 \sigma$) for ACT, where $\mathcal{A}=1$ corresponds to the theoretical prediction of the Planck 2018 $\Lambda$CDM cosmology. Assuming an isothermal gas, the measured amplitude implies an average electron temperature of $\approx 2 \times 10^7 \, {\rm K}$. The correlation is highly sensitive to the matter clustering parameter $\sigma_8$ and to baryon feedback, and its dependence on other cosmological and astrophysical parameters -- such as the ionized fraction and the Hubble constant -- differs from that of the ${\rm DM}$ alone. This suggests that future joint analyses of the ${\rm DMs}$ and the tSZ effect could help break degeneracies among these parameters.