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

TL;DR

This work reports the first detection of the angular cross-correlation between the cosmological dispersion measure ${\rm DM}_{\rm cos}$ from localized FRBs and the tSZ Compton $y$ parameter, measured over $1^{\prime}$–$1000^{\prime}$ with 133 FRBs and Planck/ACT maps. Using the HMx halo-model framework, the authors show the signal is primarily driven by hot gas in massive halos ($M \gtrsim 10^{14} \; h^{-1} M_{\odot}$) and is highly sensitive to $\sigma_8$, with smaller-scale signals constraining baryon feedback. They infer an average gas temperature around ${T}_{\rm e} \sim 2 \times 10^{7}$ K, highlighting the method’s potential to break degeneracies between gas density, temperature, and cosmology when combining ${\rm DM}$ and $y$-map data. The analysis accounts for host-galaxy contamination and foregrounds, finding robustness against Galactic masks and CIB contamination, and demonstrates that future joint FRB-${\rm DM}$ and tSZ analyses can tighten constraints on baryon physics and cosmological parameters. The results establish a promising path toward characterizing the distribution and state of baryons in the cosmic web using sparse FRB measurements.

Abstract

The dispersion measures (${\rm DMs}$) from fast radio bursts (FRBs) and the thermal Sunyaev--Zeldovich (tSZ) effect probe the free-electron density and 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 $\mathcal{A}=2.26 \pm 0.56$ ($4.0 σ$) for Planck and $\mathcal{A}=1.38 \pm 0.92$ ($1.5 σ$) for ACT, where $\mathcal{A}=1$ corresponds to the theoretical prediction of the Planck 2018 $Λ$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 $σ_8$, and its dependence on other cosmological and astrophysical parameters -- such as the ionized fraction, the Hubble constant, and baryon feedback -- 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.

Figures (14)

• Figure 1: Theoretical angular cross-correlation of $y$ and ${\rm DM}_{\rm cos}$ for $z_{\rm s}=1$ (top) and $0.3$ (bottom) obtained with HMx. The dotted orange and dashed blue curves represent the 1- and 2-halo terms, respectively, and the solid red curve is their sum. The dot-dashed green curve indicates the diffuse gas contribution in the 2-halo term. Here, we assume $f_{\rm e}=0.9$, and the overall amplitudes scale proportionally to $f_{\rm e}^2$.
• Figure 2: Similar to Fig. \ref{['fig_xi']}, but plotting the parameter dependencies of $w_{y{\rm DM}}^{\rm (theo)}(\theta;z_{\rm s})$. The top-left panel plots results at different source redshifts: $z_{\rm s}=1, 0.5, 0.3, 0.2$ and $0.1$ from top to bottom. The top-right panel displays results for different AGN heating temperatures at $z_{\rm s}=0.3$ and $1$: $\log_{10} (T_{\rm AGN}/{\rm K})=7.6, 7.8$, and $8.0$. The bottom-left panel presents results for different maximum halo virial masses at $z_{\rm s}=0.3$. The thick red curve corresponds to the default mass range $10^7 < M/(h^{-1} M_\odot) < 10^{17}$, and the other curves alter the maximum mass to $10^{16}, 10^{15}, 10^{14}$, and $10^{13} \, h^{-1} M_\odot$ from top to bottom. The red and black curves overlap. The bottom-right panel shows results for various $\sigma_8$ at $z_{\rm s}=0.3$. The thick red curve represents the default, and the other curves change the default value by $10 \%$, $5 \%$, $-5 \%$, and $-10 \%$ from top to bottom. In all panels, $f_{\rm e}=0.9$.
• Figure 3: Cross-power spectra of free-electron density and pressure (in units of ${\rm eV}/{\rm cm}^3$) at $z=0$ (top) and $0.5$ (bottom). The solid red curve represents our default HMx model (Subsection \ref{['sec:HMx']}). The other curves correspond to the constant gas-temperature model with $T_{\rm e}=10^7 {\rm K}$, using different $P_{n_{\rm e}}$ models: HMx (dashed purple curve), a fitting function from the TNG300 simulation (dot-dashed orange curve), and the linear matter power spectrum (dotted green curve). The amplitudes of these three curves scale as $\propto (f_{\rm e}/0.9)^2 (T_{\rm e}/10^7 {\rm K})$.
• Figure 4: Similar to Fig. \ref{['fig_xi']}, but plotting $w_{y{\rm DM}}^{\rm (theo)}(\theta;z_{\rm s})$ for the constant gas-temperature model with $T_{\rm e}=10^7 {\rm K}$. The curves are described in the captions of Fig. \ref{['fig_pk']}.
• Figure 5: A product of $y_{\rm host}$ and ${\rm DM}_{\rm host}$ obtained by HMx. The FRB is assumed to be located at the center of the host halo and the $y$ parameter is measured at an angular separation of $\theta$ from the center. The solid curves represent the results for host halo masses of $10^{15}$, $10^{14}$, $10^{13}$, and $10^{12} \, h^{-1} M_\odot$ from top to bottom. They are the sum of the 1-halo term (dotted curve) and the 2-halo term (dashed curve). The dot-dashed red curve is the cosmological cross-correlation $w_{y{\rm DM}}^{\rm (theo)}(\theta)$ in Subsection \ref{['sec:HMx']}. The amplitudes of all curves scale as $\propto (f_{\rm e}/0.9)^2$.